■ このスレッドは過去ログ倉庫に格納されています
■■発売日前のもせ情報 part2■■
- 1 : :02/08/31 20:43 ID:xM70xHt2
- 大好評に付き第2弾です。
ちなみに前スレは俺の全勝で終了しました。
- 2 :asdf:02/08/31 20:43 ID:a6RyHbcy
- このスレの削除依頼を出しました。
- 3 : :02/08/31 20:44 ID:xM70xHt2
- >>2
のアク禁を申請しました。
- 4 :asdf:02/08/31 20:46 ID:a6RyHbcy
- つーか、前スレはキティが埋め立ててたな
- 5 : :02/08/31 23:26 ID:xM70xHt2
- どうやら今回も俺の全勝で終了しそうだな(w
- 6 : :02/09/01 16:24 ID:kJNPJo3y
- part1とpart2両方俺の全勝で終了!
- 7 : :02/09/01 18:32 ID:hMgDve6D
- 悲惨なスレ記念かきこ
- 8 : :02/09/01 23:02 ID:y6kbNV9M
- http://dempa.2ch.net/prj/page/heisa/news5.html
- 9 : :02/09/01 23:28 ID:kJNPJo3y
- hMgDve6Dは悲惨な人生決定!
- 10 : :02/09/02 04:20 ID:nuNZ6e27
- kJNPJo3yは死亡決定!
- 11 : :02/09/02 08:34 ID:Lj3DJPdP
- nuNZ6e27は真性馬鹿だな(w人間だったらいつか死ぬのは当たり前だろ(wもっとまともな事言えないのかね。小学生以下だな(w
- 12 : :02/09/02 12:42 ID:GXxXGvm6
- みんなお前の真似して馬鹿なこと言ってるんだよ。
からかわれてるのに気付かないんだな、頭悪いな。
- 13 : :02/09/02 20:00 ID:Lj3DJPdP
- GXxXGvm6は自分が身体障害者ということに気づいていないキチガイ
- 14 : :02/09/02 21:39 ID:nuKCkoXC
- Lj3DJPdPは根暗のうんこ
- 15 : :02/09/02 21:47 ID:HNHb3EAF
- http://www.cotw.jena.co.uk/cotw/125-6ua3/green09a.jpg
↑>>1の顔
- 16 : :02/09/02 22:37 ID:Lj3DJPdP
- nuKCkoXCは「うんこ」とか小学生並みのことしか言えない知恵遅れ
HNHb3EAFはグロ画像貼るのを快感としているレイプ犯殺人鬼
- 17 : :02/09/03 04:35 ID:EVCfRYWB
-
- 18 : :02/09/03 19:57 ID:S+d4C8hU
-
- 19 : :02/09/03 23:09 ID:g0Qf3CxN
- またこの優良スレも1000まで行きそうだな(w
- 20 : :02/09/04 05:02 ID:3C8nkQTM
-
- 21 : :02/09/04 13:56 ID:Agk/05G4
- 結局夏厨は夏休みが終わると何も言い返せないのでした。
完
- 22 : :02/09/04 13:56 ID:Agk/05G4
- よって俺様の全勝で終了!
- 23 : :02/09/04 17:45 ID:MvLpZNAq
- ( ´,_ゝ`)プッ
- 24 :-:02/09/04 17:46 ID:5WWMEZBp
- よって皆様の全勝で終了!
- 25 :( ´,_ゝ`)プッ :02/09/04 17:47 ID:zc1keTnb
- Lj3DJPdPは根暗のくそったれヒッキー
- 26 : :02/09/05 02:41 ID:zzTVDLaD
- >>1
悲惨な人間…
- 27 : :02/09/05 03:02 ID:8WbHJEYk
- Agk/05G4は両親もカス
- 28 : :02/09/05 04:37 ID:nqvl7zr6
- MvLpZNAqは( ´,_ゝ`) プッを覚えたての厨
5WWMEZBpはもう少し日本語の勉強をしましょう(w
zc1keTnbは一生童貞のアニメヲタ
zzTVDLaDは悲惨なゴミ
8WbHJEYkは先祖から末代までゴミカス人でなしキチガイ家族
- 29 : :02/09/05 13:25 ID:Bpag5iJw
- nqvl7zr6は頭も性格も悪い嫌われ者
- 30 : :02/09/05 20:24 ID:QyuCtidk
-
- 31 : :02/09/05 21:33 ID:nqvl7zr6
- Bpag5iJwは全身マヒの植物人間
- 32 : :02/09/05 22:30 ID:ewoUNTyu
- >>1
(^Д^)ギャハ!
ははぁ・・・あなたもしかしたら施設から来た人ですね?
臭いですぐわかりますよ♪
この中学生のような書きこみは施設特有のものです(^^;ワラ
あなたもしかして「俺ってアングラ詳しいぜ」とか思ってませんか?
愛読書はもしかして「ハッカージャパンとゲームラボ」だったりして(^^;ワラ
あなたのようにインターネットを初めて数ヶ月の人には良くある事です♪
自分が裏の道に精通してるように錯覚してしまうようなことはね♪
小さいうちは悪人に憧れることはよくある事らしいですし♪
でもちょっと考えてみてください♪
それってものすごく恥ずかしいことなんですよ♪
あなたの書きこみをみてみんな笑ってます♪
「こいつガキだなー(^^;ワラ」って☆ミ
そう思われるのって悔しくないですか?
だったらそんなくだらないことは止めましょうよ♪
今だったら誰も本気で怒ってませんよ♪
まだ中学生なんだしいくらでもやり直しはできます♪
ほんのちょっと勇気を出すだけでいいんです♪
ほんのちょっとだけね(^^;ワラ
- 33 : :02/09/06 00:06 ID:nOiFFZau
- ewoUNTyuは煽りのコピペと得意げに使う2ch初心者
- 34 : :02/09/06 01:04 ID:pu3lePUb
- nOiFFZauは日本語が上手く話せない障害者
- 35 : :02/09/06 02:44 ID:nOiFFZau
- pu3lePUbは掲示板に書き込むことを話すと思っている知恵遅れ
- 36 : :02/09/06 20:31 ID:AN/CEG4k
-
- 37 : :02/09/06 23:07 ID:AMVAhmcP
- nOiFFZauは悲惨なスレしか立てられないクズ
- 38 : :02/09/06 23:11 ID:6gfDDAMU
- >>1は本物のキチガイっぽいな、頭も悪そうだし。
- 39 : :02/09/06 23:12 ID:DkjQGzDA
- AN/CEG4kは書き込み内容通り脳みそ空っぽのサル
AMVAhmcPは臆病でスレ立ても出来ないチキン野郎
お前ら人の真似ばっかで楽しいか?
創始者の俺様の全勝でこのスレは終了!
- 40 : :02/09/06 23:14 ID:QBvatXm8
- >人の真似ばっか
お前がな、障害者君
- 41 : :02/09/06 23:17 ID:1WDnz5t7
- 創始者?
( ´,_ゝ`)プッ
- 42 : :02/09/06 23:39 ID:RkG5kQAp
- このスレ悲惨すぎて笑えないな
- 43 : :02/09/07 01:45 ID:6A3Rs/vO
- AMVAhmcPは煽りしか楽しみのない引き篭もり。
6gfDDAMUは本物の奇形児っぽいな
DkjQGzDAは下手糞な騙り
QBvatXm8は「お前がな」という古典的なことしか言えない化石野郎
1WDnz5t7は「( ´,_ゝ`) プッ」を覚えたての2ch初心者
RkG5kQApはホームレス
- 44 :-:02/09/07 02:34 ID:y/NMBWXO
- 1の友達になってやるよ
ありがたく思えよゴミ
- 45 : :02/09/07 02:34 ID:urSw+v8D
- >>43
それ全部お前自身のことじゃん
- 46 : :02/09/07 02:41 ID:o8PtJptd
- こんなに馬鹿な>>1は珍しいな。
消防か?
- 47 : :02/09/07 07:26 ID:6A3Rs/vO
- y/NMBWXOは性病なので友達になりたくありません。
urSw+v8Dは単レスの単純馬鹿。ユモーアセンス0
o8PtJptdは視覚障害と聴覚障害の医学会を驚かせた奇形児。
- 48 : :02/09/07 16:29 ID:VCSfsY/q
- ワンパターンな煽りだな、もっとひねろよゴミ
毎日自分の馬鹿さ加減を晒して楽しいか?
- 49 : :02/09/07 21:39 ID:vj7JWWyP
-
- 50 : :02/09/08 01:03 ID:0utl7RX4
- VCSfsY/qももっとひねれよ(w
つうか死ね(wwww
- 51 : :02/09/08 05:06 ID:U5XnUgi1
-
- 52 : :02/09/08 20:12 ID:2ssGTnQd
-
- 53 : :02/09/09 04:42 ID:BWDzuSsS
-
- 54 : :02/09/09 06:27 ID:K5TbbuSS
- age荒らし必死だな(w
- 55 : :02/09/09 16:04 ID:GWkEIPiZ
- 一番必死なのは>>1
- 56 : :02/09/09 16:19 ID:okDU9O9U
- 本郷が自作自演してるスレはここですか?
- 57 : :02/09/09 20:09 ID:M0OxKkCW
-
- 58 : :02/09/09 20:41 ID:9hnYQibt
- >>1
お前は間違いなく社会不適合者だな。
カスは社会に出てこなくていいから引き籠もったまま死んでしまえ。
- 59 : :02/09/10 00:51 ID:qVLhN4rA
- GWkEIPiZは毎日残飯をあさる必死なホームレス
9hnYQibtは人間不適合者だな(w
- 60 : :02/09/10 04:55 ID:ojppz/zB
-
- 61 : :02/09/10 19:47 ID:qpPVq492
-
- 62 : :02/09/10 19:56 ID:ox607ksO
- ベックゲト
- 63 : :02/09/11 03:07 ID:b6m8dbjE
- もう全員ageる事しか抵抗のできない低脳腰抜けしかいないので。
俺の全勝で終了!
- 64 : :02/09/11 11:35 ID:oSVMkmAL
-
- 65 : :02/09/11 20:05 ID:hB3OrRd/
-
- 66 : :02/09/11 21:59 ID:oG7ml+iK
- >俺の全勝で終了!
ホームラン級の馬鹿ですな(プ
- 67 : :02/09/11 23:21 ID:b6m8dbjE
- oG7ml+iKはガチンコの大和龍門にあこがれる単純厨房
- 68 : :02/09/12 04:45 ID:T2RW1jvX
-
- 69 : :02/09/12 05:07 ID:8XUoB17P
- 空白スペースしか反論できないようなので俺の全勝で終了!!
- 70 : :02/09/12 13:56 ID:YrO5puJv
-
- 71 : :02/09/12 21:10 ID:ObZ3ATcG
-
- 72 : :02/09/13 04:18 ID:u8fyRkmQ
-
- 73 : :02/09/13 19:22 ID:oEjhi2xT
- 晒しage
- 74 : :02/09/13 23:23 ID:j6nutc+H
-
- 75 : :02/09/14 05:14 ID:oaXqHMae
-
- 76 : :02/09/14 06:30 ID:R+f0ILVB
- ところで、もせってなんですか?
まさかMP3のことじゃないですよね。
そんな大昔の言葉を使ってるとは、とても信じられないので
違うと信じてます。
- 77 : :02/09/14 07:10 ID:/FBpxPsX
- oEjhi2xTは晒しているつもりが実は保全になっていることに気づかない真性厨
R+f0ILVBは田舎者
- 78 : :02/09/14 12:43 ID:YFmN8Ws2
- 晒すために保守してるんだろ
- 79 : :02/09/14 13:40 ID:MeLHcKFf
- >>77-78
>>73や>>76に簡単に
釣られるお前らが一番見苦しい。
- 80 : :02/09/14 14:11 ID:PjkBxPjH
- >>73 = >>78 ですが何か?
- 81 : :02/09/14 18:13 ID:/FBpxPsX
- MeLHcKFfは釣られたくてレスする変態
- 82 : :02/09/14 18:14 ID:/FBpxPsX
- YFmN8Ws2は保守の意味をわかっていない必死で言い訳をする馬鹿
- 83 : :02/09/14 19:49 ID:I1kznctk
-
- 84 : :02/09/15 04:26 ID:AmP1gZkA
-
- 85 :(;´Д`):02/09/15 04:37 ID:O0uZM16h
- 100取った奴が真の糞
- 86 : :02/09/15 05:44 ID:AwuP+6s+
- 悲惨なスレ見つけた。
- 87 : :02/09/15 07:08 ID:6mkEpsik
- O0uZM16hは意味不明な事を言い出す馬鹿
AwuP+6s+は友達が1人もいない悲惨な人間
- 88 : :02/09/15 19:42 ID:CGd+foZd
-
- 89 : :02/09/16 06:37 ID:hXKai4dp
- はい、つーことで誰も言い返せないので
俺の全勝で終了!
- 90 : :02/09/16 07:13 ID:Ulm0xmQ6
- 悲惨なスレ…
- 91 : :02/09/16 07:17 ID:MHdhHCJB
-
- 92 : :02/09/16 08:48 ID:hXKai4dp
- Ulm0xmQ6は悲惨なウンコ
- 93 : :02/09/16 20:30 ID:Qz7ijA+T
-
- 94 : :02/09/16 22:26 ID:/e5BH18e
- >>1は今年の夏厨の中で一番頭悪いな。
- 95 : :02/09/17 03:21 ID:2j8+Y2tI
-
- 96 : :02/09/17 03:24 ID:xOPiKT3R
- そんなことないよ。僕の方が頭悪いから
1をいじめないで(泣)
- 97 : :02/09/17 04:04 ID:wLZhXgiV
-
- 98 : :02/09/17 05:46 ID:hxJkdmR+
- >>96 = >>1
自己弁護に必死だな(w
- 99 : :02/09/17 07:00 ID:CyoKOOzf
- /e5BH18eは2ch始まって以来の真性リアル厨だな。
xOPiKT3Rは下手糞な自作自演で1を装う単発ヒッキー。
hxJkdmR+はそれに騙される単純馬鹿
- 100 : :02/09/17 07:01 ID:CyoKOOzf
- 100ゲット。
よって俺の全勝で終了!!!!
- 101 : :02/09/17 21:04 ID:/5yeuTHf
-
- 102 : :02/09/17 21:08 ID:iGDfe2c9
- BoA「奇蹟/NO.1」(AVCD-30378)
DREAMS COME TRUE「IT'S ALL ABOUT LOVE」(DCTR-5001)
HB「Do my thing」(TFCC-89039)
Lyrico「キセキノハナ」(SRCL-5438)
michico「the superstar」(SICL-25)
MIO「Mother's Eternity」(SRCL-5437)
Neo「You've Got A Friend」(PCCA-70017)
PENICILLIN「花園キネマ」(IOCD-11025)
shela「Himawari」(AVCD-30362)
The Spy "C" Dildog「パープルビーヘヴン」(MUCD-5018)
WHiTE「ピンクのボトル」(SRCL-5411)
WORD SWINGAZ「Let it go!〜炎の五回裏−O-Town Players E.P.−」(PCCA-70015)
うたいびと はね「未タイトル」(FLCF-7029)
キセル「ギンヤンマ」(VICL-35431)
ゴスペラーズ「Promise」(KSCL-480)
ゴスペラーズ「Two-way Street」(KSCL-483)
ゴスペラーズ「U'll Be Mine」(KSCL-481)
ゴスペラーズ「Winter Cheers!」(KSCL-482)
ゴスペラーズ「カレンダー」(KSCL-484)
ゴスペラーズ「待ちきれない」(KSCL-485)
なおと「あの素晴らしい愛をもう一度」(SRCL-5441)
ミニ塾。feat.塾長「SMALL WORLD」(SRCL-5426)
岡村靖幸と石野卓球「come baby」(KSCL-476)
京田未歩「Dear Mr.毎日」(PCCA-1764)
小島麻由美「愛しのキッズ」(PCCA-1762)
松浦亜弥「The 美学」(EPCE-5176)
上原多香子「Air」(AVCD-16024)
オマイラMXがなかったとして、どれか『買い』ますか?
- 103 : :02/09/17 21:19 ID:zWHtOGLL
- >>102
スレ違い
- 104 : :02/09/17 21:28 ID:yPZuJ6Lr
- >>102
ゴスペラーズは今までDLしまくったんでMXが使えなくなったら1枚くらいは買う
- 105 : :02/09/18 04:43 ID:6hiByPGV
- >>104
スレ違い
- 106 : :02/09/18 07:54 ID:Uv5RxxiY
- zWHtOGLLは自分がすれ違いに気づかない知障
6hiByPGVは必死で荒らそうとする真性厨
- 107 : :02/09/18 09:48 ID:kqgwqczR
- Uv5RxxiYは母子相姦に毎日ふける時代錯誤な化石人間
- 108 : :02/09/18 18:29 ID:Uv5RxxiY
- kqgwqczRは母子相姦が時代錯誤と勘違いしている恥ずかしい脳内電波
- 109 : :02/09/18 22:11 ID:5J3W6Xar
-
- 110 : :02/09/19 02:03 ID:X0qqYk1h
- >>1以外の煽りは面白いな、>>1はカス
- 111 : :02/09/19 05:53 ID:LixqzuMq
- X0qqYk1hの煽りは今までの中で一番カスゴミ
- 112 : :02/09/19 21:33 ID:YN0lR2qu
-
- 113 : :02/09/20 04:23 ID:/p5wqTAY
-
- 114 : :02/09/20 06:14 ID:2FJ1s0n6
- Uv5RxxiYは本当に母子相姦やってる変質者
- 115 : :02/09/20 15:03 ID:OEMXc5V0
- CyoKOOzfは100ゲットして全勝した神
- 116 : :02/09/20 21:28 ID:6qkxhtUy
-
- 117 : :02/09/21 04:38 ID:t7G6Swqj
-
- 118 : :02/09/21 07:33 ID:LamGpuxo
- 2FJ1s0n6は母子相姦の意味をわかっていない低脳
- 119 : :02/09/21 09:25 ID:TAol1M94
- >>115
禿藁(w
- 120 : :02/09/21 10:07 ID:oYqhtCt8
- >>1以外は面白いな
- 121 : :02/09/21 17:51 ID:LamGpuxo
- oYqhtCt8は世界一つまらないハゲオヤジ
- 122 : :02/09/21 19:59 ID:VTRKvEc0
-
- 123 : :02/09/21 21:04 ID:YITqIW1s
- VTRKvEc0はIDに"VTR"が入っていて運のいい奴
- 124 : :02/09/22 05:55 ID:qvAVQJlG
-
- 125 : :02/09/22 19:33 ID:UyrfVGeV
-
- 126 : :02/09/23 04:44 ID:mHzbk7xa
-
- 127 : :02/09/23 09:04 ID:6TBQ7JZA
- 1の全勝で終了!
- 128 : :02/09/23 11:21 ID:bEWnZTob
- >>1は普通に頭が悪いだけで面白みがない
- 129 : :02/09/23 19:00 ID:6TBQ7JZA
- bEWnZTobは普通に童貞で知障者だから煽る価値無し
- 130 : :02/09/24 02:08 ID:aANKad4D
- 1の全勝で終了!
- 131 : :02/09/24 02:33 ID:mdgugHjT
- ryosure
- 132 : :02/09/24 02:41 ID:LVMZ1yHC
- いや・・・
もせは発売しないだろ?
- 133 : :02/09/24 02:49 ID:OsN83qW8
- クールなツッコミ…
しかし相変わらず歴代で悲惨なスレだなw
- 134 : :02/09/24 03:03 ID:5BDEKnwg
- 1は全勝で
■■■■■■■■■■■■■■■■■終了■■■■■■■■■■■■■■■■■■
- 135 : :02/09/24 08:40 ID:aANKad4D
- LVMZ1yHCは日本語を理解できない言語障害者
OsN83qW8は日本一悲惨な人生を送るホームレス
- 136 : :02/09/24 21:06 ID:Wvf4Cmjz
- 相変わらずつまらん煽りだな、もう少し考えろよゴミ
ひねった煽りに何も返してないとこをみると相当読解力のない障害者だな(プ
- 137 : :02/09/25 00:48 ID:524T44Ud
- Wvf4Cmjzは誰にレスするかも書けない2ch初心者( ´,_ゝ`) プッ
- 138 : :02/09/25 04:28 ID:XmIH1EeM
-
- 139 : :02/09/25 04:46 ID:AWiaEz3Y
- .┌┐
/ /
./ / i
| ( ゚Д゚) <そんなバナナ!
|(ノi |)
| i i
\_ヽ_,ゝ
U" U
- 140 : :02/09/25 21:27 ID:pxUOCgXX
-
- 141 : :02/09/26 00:43 ID:RuTs99MO
- 1の全勝で終了!
- 142 : :02/09/26 04:46 ID:DsKrToY5
-
- 143 : :02/09/26 21:03 ID:JJbGMMQn
-
- 144 : :02/09/26 21:37 ID:vn00n0Dg
- >>1は下手な揚げ足取りしかできない低学歴
- 145 : :02/09/26 23:57 ID:RuTs99MO
- vn00n0Dgはワンパターンな煽りしかできない単細胞
- 146 : :02/09/27 01:17 ID:WNPLnABU
- ワンパターンな煽りしかできないのは>>1だろ、幼稚園児並( ´,_ゝ`) プッ
- 147 :sage:02/09/27 01:22 ID:AuQIKxDH
- 常連スレなんだからマターリいこうや( ´ー`)y-~~
- 148 :hage:02/09/27 02:10 ID:nwJGaNvB
- age
- 149 : :02/09/27 08:57 ID:k6YoRSTY
- WNPLnABUは人の言われたことをそのまま返すことしかできない思考能力0の中卒
- 150 : :02/09/27 10:28 ID:yvevcn4e
- 関連スレ
清春(Sads&黒夢) VS 松岡(SOPHIA)【part2】
http://cocoa.2ch.net/test/read.cgi/musicj/1032319948/
松岡 VS 清春 VS Gackt VS hyde VS 河村隆
http://cocoa.2ch.net/test/read.cgi/musicj/1031660489/
- 151 : :02/09/27 17:00 ID:Z3cte2Pa
- >>1
>人の言われたことをそのまま返すことしかできない思考能力0の中卒
100%お前の事じゃないか、自分を煽ってんのか?(プ
- 152 : :02/09/27 18:06 ID:UwKr7qjk
- 電波2chでなぜかこのスレが良スレとして紹介されてる…
ttp://dempa.2ch.net/prj/page/ura2ch/news002090511667.htm
- 153 : :02/09/27 20:28 ID:k6YoRSTY
- Z3cte2Paは発狂した人格障害者
- 154 : :02/09/28 05:12 ID:hQlVEagC
-
- 155 : :02/09/28 21:09 ID:zfJ0JDZP
-
- 156 : :02/09/29 05:35 ID:VKhjfC0m
-
- 157 : :02/09/29 05:54 ID:Ohjb18w/
- レポート元 [Godsloop2] godsloop.dyndns.tv:7777
Sunday, September 29, 2002 05:44:30
ユーザ名 : BOSS
アクセスレベル : Human
オンライン時間 : 0:06:35
入室チャンネル :
状態 : Remote
共有ファイル数 : 5416
現在のダウンロード : 0
現在のアップロード: 3
接続種類 : T3+
クライアントバージョン : WinMX v2.6j Notice:
- 158 : :02/09/29 13:51 ID:Y8ArxHut
- ビビって誰も言い返せないので1の全勝で終了!
- 159 :age:02/09/29 18:07 ID:dZtowiC6
- age
- 160 : :02/09/30 05:47 ID:H/yk+wlD
- 1の全敗で終了!!!!!!1
- 161 : :02/09/30 19:11 ID:HCUqqDnw
- H/yk+wlDは根性なしの腰抜けインポ野郎。
- 162 : :02/10/01 00:10 ID:J8UvQU1b
- 1の全勝で終了!
- 163 : :02/10/01 00:11 ID:J8UvQU1b
- ↓毎日午前4時〜6時にageる引き篭もり童貞キチガイ馬鹿
- 164 : :02/10/01 04:07 ID:wU3yqZKK
-
- 165 : :02/10/01 10:13 ID:J8UvQU1b
- 予想通りキタ━━━━(゚∀゚)━━━━ !!!!!
ぎゃははは最高!
- 166 :( ゚Д゚)<うぐぅ ◆dKanonKQ :02/10/01 16:02 ID:TuheOqRM
- ID:J8UvQU1bは引き篭もり童貞キチガイ馬鹿
ID:wU3yqZKKは人の誘いもいやだぁっと断れないいいやつ。
- 167 : :02/10/01 18:10 ID:J8UvQU1b
- TuheOqRMは毎日2chしか楽しみのないDQN
- 168 : :02/10/01 19:26 ID:X2bmeJ6D
-
- 169 :1:02/10/02 01:55 ID:OcdiW5qd
-
- 170 :( ゚Д゚)<うぐぅ ◆dKanonKQ :02/10/02 05:10 ID:kf9IiYV7
- ID:OcdiW5qdはネタがないくせに保守する糞
- 171 : :02/10/02 05:12 ID:4/IEIHFL
- kf9IiYV7は169を1と勘違いする恥ずかしい香具師
- 172 : :02/10/02 05:15 ID:4/IEIHFL
- 「うぐぅ」←この響きがオタク丸出し(w
秋葉原で狩られるなよ(w
- 173 :1:02/10/02 05:50 ID:bkPXeDqA
-
- 174 :1(本物):02/10/02 15:29 ID:4/IEIHFL
-
- 175 :1(本物):02/10/02 20:08 ID:qIqEnP5d
-
- 176 : :02/10/03 02:30 ID:2TaXqhMb
- ↓毎日午前4時〜6時にageる引き篭もり童貞キチガイ馬鹿
- 177 :( ゚Д゚)<うぐぅ ◆dKanonKQ :02/10/03 02:37 ID:M7EgxnS9
- ↑は☆ず☆れ〜☆残念でしたぁ〜☆ば〜かば〜か☆
- 178 :1:02/10/03 05:26 ID:YEn7RGAT
-
- 179 : :02/10/03 09:46 ID:WmVyBEPC
- LIVの「SOUL」って検索してもHITしないね。3.3WPN
- 180 : :02/10/03 11:31 ID:2TaXqhMb
- M7EgxnS9は自分に↑を付けてば〜かば〜か☆と言う知的障害者
- 181 :( ゚Д゚)<うぐぅ ◆YgdKanonKQ :02/10/03 18:39 ID:wwHWDXxx
- ↑ちげぇよ、糞がぁ〜お前盲目すぎだゾ〜ID:2TaXqhMbに言い返してやったんだぃ
- 182 : :02/10/03 20:05 ID:KtHr/qIk
- >>181
糞ワラタw
- 183 : :02/10/04 00:17 ID:Xz944BiZ
- 177 :( ゚Д゚)<うぐぅ ◆dKanonKQ :02/10/03 02:37 ID:M7EgxnS9
↑は☆ず☆れ〜☆残念でしたぁ〜☆ば〜かば〜か☆
181 :( ゚Д゚)<うぐぅ ◆YgdKanonKQ :02/10/03 18:39 ID:wwHWDXxx
↑ちげぇよ、糞がぁ〜お前盲目すぎだゾ〜ID:2TaXqhMbに言い返してやったんだぃ
- 184 :1:02/10/04 04:44 ID:eIpbZ9mK
-
- 185 :1:02/10/04 20:19 ID:cxI+ZD2v
-
- 186 : :02/10/04 20:21 ID:Dc/Sva1J
-
- 187 : :02/10/04 20:23 ID:Dc/Sva1J
- zzzzzzzzz
- 188 :1:02/10/05 06:03 ID:V3vJMg+A
-
- 189 : :02/10/05 18:09 ID:ETunqVPQ
- モセは2.6の子鯖と3.3どっちが数多い?
- 190 : :02/10/06 05:54 ID:1kEiPxGL
- >>189
スレ違い
- 191 : :02/10/06 06:56 ID:oFPkGCyM
- 3.3でWPNへ逝きつつ2.6申請して子鯖へ逝けばいいだろ
- 192 : :02/10/06 20:07 ID:ta59VNPb
-
- 193 :_:02/10/07 03:49 ID:zlzoirJk
- 前スレの>>1がまた糞スレ立てて悲惨な目にあってます↓
※洋楽動画専門情報局※
http://tmp.2ch.net/test/read.cgi/download/1033574413/l50
- 194 : :02/10/07 03:51 ID:JSVa9wG5
- 新作情報
http://tmp.2ch.net/test/read.cgi/download/1033754497/
- 195 : :02/10/07 05:53 ID:l++5CmN4
-
- 196 : :02/10/07 12:21 ID:lfv1Qn3d
- zlzoirJkは妄想で現実逃避している夢遊病患者
- 197 : :02/10/07 14:17 ID:lfv1Qn3d
- http://www.need4xxx.net/asian/hamedori/data/099/dir/
- 198 :1:02/10/07 22:27 ID:RB3J4wGC
-
- 199 : :02/10/07 22:27 ID:fHpy7xG2
- 199
- 200 : :02/10/07 22:28 ID:fHpy7xG2
- 未だ!
2 0 0 下 っ ト !
- 201 :( ゚Д゚)<うぐぅ ◆YgdKanonKQ :02/10/07 22:32 ID:NQTjJyAd
- くっ!!!俺様が200とろうとカキコボタンおそうと思ったらおす直前に回線切れやがったあぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁ
ID:fHpy7xG2はほんと、カコワルイネ!
- 202 : :02/10/07 22:33 ID:fHpy7xG2
- >>201
あなたがいちばんこっこ悪いですが何か?
- 203 :( ゚Д゚)<うぐぅ ◆YgdKanonKQ :02/10/07 22:35 ID:NQTjJyAd
- こっここ〜ここここ〜こいはこいはこい
- 204 : :02/10/08 00:29 ID:li/ERLW5
- NQTjJyAdダサッ( ´,_ゝ`)
- 205 :1:02/10/08 05:29 ID:TNcOaC2A
-
- 206 :1:02/10/08 20:05 ID:0nJ27vtV
-
- 207 :1:02/10/09 04:34 ID:MWeypArE
-
- 208 :1:02/10/09 21:34 ID:QPPel4aB
-
- 209 : :02/10/09 23:36 ID:HNPOhVic
- 200 : :02/10/07 22:28 ID:fHpy7xG2
未だ!
2 0 0 下 っ ト !
201 :( ゚Д゚)<うぐぅ ◆YgdKanonKQ :02/10/07 22:32 ID:NQTjJyAd
くっ!!!俺様が200とろうとカキコボタンおそうと思ったらおす直前に回線切れやがったあぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁぁ
- 210 : :02/10/10 04:33 ID:cgzPTgDU
-
- 211 :1:02/10/10 20:13 ID:iz2xZlKv
-
- 212 :1:02/10/11 04:50 ID:y2xR9N5b
-
- 213 :1:02/10/11 20:58 ID:4Naw5TDO
-
- 214 :1:02/10/12 05:05 ID:d2SrF1tR
-
- 215 :1:02/10/12 19:51 ID:HBXQpbJL
-
- 216 :1:02/10/13 05:19 ID:BJFaw+86
-
- 217 :1:02/10/13 19:31 ID:PqW7xtXI
-
- 218 : :02/10/14 05:01 ID:SvgLFPIm
- ↓今日は来ないのかな
- 219 :1:02/10/14 19:51 ID:quT2Wcac
-
- 220 :( ゚Д゚)<うぐぅ ◆YgdKanonKQ :02/10/14 23:27 ID:mYfxfBR7
- ↑来た
↓次はいつかな
- 221 : :02/10/15 04:14 ID:WBEllCv0
- ↓そろそろ来るぞ
- 222 : :02/10/15 05:51 ID:WBEllCv0
- ↓19時〜21に来るぞ
- 223 :1:02/10/15 21:30 ID:WBEllCv0
- もうバカしかいないので俺様の全勝で終了!
- 224 :1:02/10/16 05:16 ID:B6NfFWkU
-
- 225 :( ゚Д゚)<うぐぅ ◆YgdKanonKQ :02/10/16 05:20 ID:34NynnRk
- ↑出た!
- 226 : :02/10/16 17:32 ID:I5I8GrNL
- ↓今日も19時〜21に来るぞ
- 227 :ナナシサソ:02/10/17 00:19 ID:Bppn5ep/
- 浜崎のCMで
「BOSS,君がそばにいてて、BOSS、〜〜〜〜〜〜〜」
あれって曲名あるの?
- 228 : :02/10/17 03:41 ID:nn9RwTES
- ↓今日も4時〜6時に来るぞ
- 229 :-:02/10/17 07:32 ID:5lKnxRfr
- オリコンより今週の気になる新譜を・・・(個人的ですが)
10/16 My Own Destruction - ELLEGARDEN
エモコア&メロディックパンク。情緒的エモ好き必聴の一枚。
10/16 黒盤 - マスラヲコミッショナー
インディーズで話題沸騰中・・・・かもしれない爽やかパンクス・マスラヲコミッショナーの1stアルバム。
名曲「追風」を含む全11曲。
10/16 TERMINAL BOREDOM ver.2 - REGISTRATORS
ラフでポップなパンクロック。
格好良すぎるREGISTRATORSの新アルバム。
10/17 一期一会 Sweets for my SPITZ
コアなロックリスナーも愛聴という日本の宝スピッツのカバーアルバム。
椎名林檎やLOST IN TIME、ポリシックス、中村一義などが参加。
- 230 :1:02/10/17 23:34 ID:sxI/+SPz
- >>227 >>229
スレ違い
- 231 : :02/10/18 00:44 ID:DQuqQAuw
- もうバカしかいないので1の全勝で終了!
- 232 :1:02/10/18 05:30 ID:a79vV64a
-
- 233 :↑:02/10/18 15:35 ID:DQuqQAuw
- 馬鹿がキタ━━━━(゚∀゚)━━━━ !!!!!
↓
- 234 : :02/10/19 00:36 ID:/Wbq9AS2
- ピンポンほすぃ
- 235 :1:02/10/19 05:40 ID:ASVSLLzK
-
- 236 :ナナシサソ:02/10/19 05:58 ID:NmliIG1k
-
- 237 :ナナシサソ:02/10/19 06:53 ID:ofK+WK/s
- 諸君!DLが好きだ 諸君!!DLが好きだ 諸君!DLが大好きだ。
lriaが好きだ 偽装解凍ツールが好きだ WinMXが好きだ
もせが好きだ ロムが好きだ エロ画像が好きだ ムービーが好きだ
割れずが好きだ
学校で 会社で 自宅で 地球で 幸福都市で ほめすてで WPNPで
ネット上で行われる ありとあらゆるDL行動が大好きだ
諸君 私はDLを 地獄のようなDLを望んでいる
諸君 私に付き従うワレザー諸君 君達はいったい何を望んでいる?
更なるDLを望むか? 情け容赦のない糞のようなDLを望むか?
回線速度と時間の限りを尽くし 飯を食うのもわすれ 永遠に続く
テレホのようなDLを望むか?
DL!! DL!! DL!!
- 238 : :02/10/19 15:28 ID:69gH8plS
- >>234
>ピンポンほすぃ
( ´,_ゝ`) プッ馬鹿じゃねーの?
- 239 :1:02/10/19 20:30 ID:S7U4ED/p
-
- 240 : :02/10/19 22:10 ID:69gH8plS
- 自分で1とか言って毎日午後9時前後と午前4時前後にageてる奴って
頭悪いよね引き篭もりなんじゃないの?病院行けって感じ(w
- 241 :1:02/10/20 05:50 ID:U4yYQvuO
-
- 242 :↑:02/10/20 06:22 ID:dwdByhbY
- 低脳キタ━━━━(゚∀゚)━━━━ !!!!!
- 243 :1:02/10/20 21:14 ID:0/Qi7r4o
-
- 244 :↑:02/10/20 21:15 ID:dwdByhbY
- 低脳キタ━━━━(゚∀゚)━━━━ !!!!!
- 245 : :02/10/20 21:16 ID:dwdByhbY
- ↓次は4時ごろかな(w
- 246 :1:02/10/21 04:56 ID:N6B/EyHE
-
- 247 :…:02/10/21 05:27 ID:24DW7VLd
- 106 :番組の途中ですが名無しです :02/10/21 01:05 ID:pg2/gNLj
http://www2.strangeworld.org/uedakana/sahra6138.jpg
コレマジ?
- 248 : :02/10/21 08:04 ID:UVp1Wj+H
- 低脳予想通りキタ━━━━(゚∀゚)━━━━ !!!!!
↓今度は9時ごろかな?(w
- 249 :-:02/10/21 18:36 ID:hHVB3BBz
- ▄██ ▀▄ █▄ ▀█▄
▄▄▄████▀ █ ▄ ▄███▄ █▄ ▀▄
█▀ █ ▄▄ █▄██ █▀ ▀█ ▄ █ ▄████▄▄
█▄▄████▀ █▀█▀ █ ██▄██▀▀ ▀██
█▀▀ ▀▄ ▄██ █ ▀▀ █ █▀
█ █▄ █ ██ ▄████ ▀█ ▀██▀
█▄▄█▀ █▄██ █ █ █ ██▄ █▄
███▀ ██▀ █ ▀███▀ ▀▄ ██
- 250 : :02/10/22 00:16 ID:1r51zkv7
- ↓今度は4時ごろかな?(w
- 251 : :02/10/22 06:02 ID:UgiflVvW
- ↓今度は21時ごろかな?(w
- 252 : :02/10/22 21:06 ID:ATxSND3f
- ↓今度は4時ごろかな?(w
- 253 :ナナシサソ:02/10/22 23:16 ID:f2eHcD76
- 落ち目倉木手に入れマスタ!!(・∀・)
皆さんQよろw
- 254 : :02/10/23 04:57 ID:15udnl1B
- >>253
スレ違い
- 255 : :02/10/23 05:52 ID:bjsj/Lxz
- もうバカしかいないので1の全勝で終了!
- 256 : :02/10/23 19:15 ID:iPnZRlRZ
- >>237
よろしいならばDLだ。
われわれは満身の力を込めて今順番待ちした糞共有だ
だがこのくらい闇の底で並びつづけてきた我々に
多少のもせでは物足りない
DOMを!
一心不乱のDOMを!!
われらはわずかな少数派。子鯖の隅に追いやられる存在かもしれない
だが私は君らが一騎当千のDOMだと信じている
ならば君らと私で総量100TのDOMになろうではないか
DOMを忘却の彼方へと追いやり
眠りこけている連中を叩き起こそう
髪の毛をつかんで引きずり降ろし
眼を開けさせ思い出させよう
連中に恐怖の味を思い出させてやる
連中に寝起きの見知らぬ青い文字を思い出させてやる
天と地のはざまには奴らの哲学では思いもよらない事がある事を思い出させてやる
総兵力100TのDOM信者の戦闘団で
良共有のファイルの価値を壊し尽くしてやる
「行くぞ諸君!」
- 257 : :02/10/23 20:52 ID:bjsj/Lxz
- PnZRlRZはキチガイ
- 258 :1:02/10/24 04:19 ID:e9rQDS94
-
- 259 :1:02/10/24 21:17 ID:gdhBZgHx
-
- 260 : :02/10/24 22:18 ID:dqiVTwhQ
- >PnZRlRZはキチガイ
>>1はこんな返ししかできないのか?障害者?( ´,_ゝ`)プッ
- 261 : :02/10/24 22:23 ID:bYx/7UIL
- >>1は1行レスしかできない知恵遅れ
- 262 : :02/10/25 01:33 ID:o7rWCBFF
- dqiVTwhQはアルツハイマー病
bYx/7UILは一生童貞
- 263 :1:02/10/25 04:29 ID:MoaFkrz0
-
- 264 :↑:02/10/25 16:13 ID:589SK39r
- 4時9時キチガイキタ━━━━(゚∀゚)━━━━ !!!!!
- 265 :1:02/10/26 05:13 ID:YtAyIrL5
-
- 266 :↑:02/10/26 06:27 ID:9ZNikLjU
- 4時9時キチガイキタ━━━━(゚∀゚)━━━━ !!!!!
- 267 :ナナシサソ:02/10/26 06:29 ID:9ZNikLjU
- 毎日夜9時に起きて朝の5時に寝てるのかな(w
完全な引き篭もりだね。
てゆうか知的障害者かな?( ´,_ゝ`) プッ
- 268 :1:02/10/26 22:33 ID:DAvKLqCy
-
- 269 :ナナシサソ:02/10/27 00:39 ID:95Wx0wzC
- >>1は本物の知的障害者っぽいな。
文章を考えることができないらしい。
死んでもいい人間。
- 270 :ナナシサソ:02/10/27 00:41 ID:PrEHrFC7
- >4時9時キチガイキタ━━━━(゚∀゚)━━━━ !!!!!
こんなレス堂々とできるなんて障害者以外ありえないだろ。
- 271 : :02/10/27 01:09 ID:ZsPk29AN
- ↓ >>1(キチガイ)の悲惨な1行レス
- 272 : :02/10/27 06:25 ID:f0kIgu8m
- ↑
- 273 : :02/10/27 15:26 ID:GWH7KQ/v
- ID:PrEHrFC7=4時9時キチガイ
- 274 : :02/10/27 15:27 ID:GWH7KQ/v
- 95Wx0wzCは死んでも地獄に迷惑がかかる価値0の生物
- 275 :1:02/10/27 21:44 ID:ETbsT2zC
-
- 276 : :02/10/27 21:55 ID:GWH7KQ/v
- 1の偽者4時9時キチガイキタ━━━━━━(゚(゚∀(゚∀゚(゚∀゚)゚∀゚)∀゚)゚)━━━━━━!!!!!!
毎日夜9時に起きて朝の5時に寝てるのかな(w
完全な引き篭もりだね。
てゆうか知的障害者かな?( ´,_ゝ`) プッ
- 277 : :02/10/28 04:36 ID:zCPZYA4O
-
- 278 :↑:02/10/28 05:49 ID:B4szCDrN
- 4時9時キチガイキタ━━━━━━(゚(゚∀(゚∀゚(゚∀゚)゚∀゚)∀゚)゚)━━━━━━!!!!!!
毎日夜9時に起きて朝の5時に寝てるのかな(w
完全な引き篭もりだね。
てゆうか知的障害者かな?( ´,_ゝ`) プッ
- 279 :ナナシサソ:02/10/28 16:14 ID:wFzqvLRs
- 1です。改心しました。
いま病院に行って来ました。
入院が正式決定しました。
医師に「今日にも入院したほうがいい」と勧められましたが、
準備などがあるので来週の火曜日から入院します。
治療方法があるかどうかさえわからない状態ですが、
まずいろいろと検査を受けてみます。
今日も体中の筋肉がだるくて体の置き場のない状態が続いています。
特に激しい運動をしているわけでもなく、
栄養も何とかそれなりにとれてはいるのに、
体だけが不調で日常生活がきちんと送ることができません。
これも皆さんに迷惑をかけた当然の報いだと痛感いたしております。
誠に申し訳ございませんでした。皆さんにこれ以上ご迷惑をかけないためにももう二度とここには来ません。さようなら。
- 280 : :02/10/28 16:28 ID:B4szCDrN
- >>279
ネタにしてはツマランな
- 281 : :02/10/28 23:16 ID:PfdIbF2X
-
- 282 : :02/10/29 00:44 ID:F1SXa/LK
- ↓4時〜5時キチガイ
- 283 : :02/10/29 05:22 ID:IX8bLjMW
- ↓
- 284 :↑:02/10/29 06:55 ID:F1SXa/LK
- 4時〜5時キチガイ予想通りキタ━━━━(゚∀゚)━━━━ !!!!!
↓次は9時かな?(w
- 285 : :02/10/29 21:30 ID:Zm15ImLN
- ↓次は9時かな?(w
- 286 :↑:02/10/29 23:13 ID:V77iE9TT
- 9時キチガイ予想通りキタ━━━━(゚∀゚)━━━━ !!!!!
引くに引けなくなった5時9時キチガイに激藁
- 287 :ナナシサソ:02/10/30 01:44 ID:QxsZu7n9
- 情報はこっちにあります
http://tmp.2ch.net/test/read.cgi/download/1035714872/
- 288 : :02/10/30 04:34 ID:cZY9efrr
- ↓6時11時キチガイ
- 289 : :02/10/30 21:28 ID:c5RGoC3x
- ↓6時11時キチガイ
- 290 : :02/10/31 04:04 ID:3OfvBXOR
- ↓6時11時キチガイ
- 291 : :02/10/31 21:54 ID:6lMehnlU
- ↓6時11時キチガイ
- 292 : :02/11/01 03:20 ID:iOfmnPRt
- ↓6時11時キチガイ
- 293 : ↓ ↑:02/11/01 05:04 ID:AmTEtDSR
- ↓ ↑
↓ ↑
↓ ↑
→→→↑
誰もこねーよ(´`c_,'` ) プッ
5時9時キチガイ必死だな( ´,_ゝ`) プッ
1人でやってろよ中卒暇人童貞引き篭もりが(w
- 294 : :02/11/01 09:08 ID:Je5iug04
- 293 : ↓ ↑ :02/11/01 05:04 ID:AmTEtDSR
↑5時9時キチガイ
- 295 : :02/11/01 10:55 ID:AmTEtDSR
- Je5iug04は知恵遅れ決定!
- 296 :ナナシサソ:02/11/01 10:55 ID:AmTEtDSR
- 288 : :02/10/30 04:34 ID:cZY9efrr
↓6時11時キチガイ
289 : :02/10/30 21:28 ID:c5RGoC3x
↓6時11時キチガイ
290 : :02/10/31 04:04 ID:3OfvBXOR
↓6時11時キチガイ
291 : :02/10/31 21:54 ID:6lMehnlU
↓6時11時キチガイ
292 : :02/11/01 03:20 ID:iOfmnPRt
↓6時11時キチガイ
↑どう見ても頭おかしい(www
- 297 : :02/11/01 22:57 ID:3zPyLvky
- AmTEtDSRは知能障害
- 298 : :02/11/02 04:17 ID:yFNzbjUj
- 3zPyLvkyはパクリしか能のない猿真似野郎
- 299 : :02/11/02 20:32 ID:AACqLE23
- yFNzbjUjはワンパターンの低脳
- 300 : :02/11/03 01:46 ID:cc3DiI5A
- ここまで極端に頭の悪い>>1って珍しいね、なんか可愛そう・・・
- 301 : :02/11/03 06:23 ID:XmSLNk4X
- >>300
チンパンジーのあいちゃんだからな
- 302 : :02/11/03 09:34 ID:LT6hGIRt
- cc3DiI5AはIQ17
XmSLNk4Xはゴキブリのゴキちゃん
- 303 :1:02/11/03 10:20 ID:4w5Ocrtj
-
- 304 : :02/11/03 19:40 ID:JgqMDNsj
-
- 305 : :02/11/04 05:39 ID:2pt/oBuQ
-
- 306 : :02/11/04 19:44 ID:QNtjAvEB
-
- 307 : :02/11/05 05:18 ID:zjlHjs/b
-
- 308 : :02/11/05 20:36 ID:BHgphzUr
-
- 309 : :02/11/06 04:39 ID:xJwzboKx
-
- 310 :( ゚Д゚)<うぐぅ ◆YgdKanonKQ :02/11/06 05:18 ID:W8UL+NV4
- おうおう、丁寧に4時、20時前後にご苦労さんなぁ。
こちとら、お前さんの無駄な努力に涙がちょちょぎれてくんべぇ。
まぁ、がんばってくんなはれや。
- 311 : :02/11/06 07:21 ID:VqvgTyI/
- きっと、これしか楽しみがない香具師なんだろうね(w
- 312 : :02/11/06 15:34 ID:piNwnlU2
- >>1
死ねよ障害者
- 313 : :02/11/06 23:44 ID:2z0ceaTX
-
- 314 : :02/11/07 00:01 ID:dOEiys/P
- >>312
死ねよ障害者
- 315 : :02/11/07 06:34 ID:G73NuwCE
-
- 316 :↑:02/11/07 07:51 ID:dOEiys/P
- お前友達いないんだろうね。いい加減社会復帰したら?(wwww
- 317 : :02/11/07 22:30 ID:1cRItW02
-
- 318 :↑:02/11/07 23:23 ID:dOEiys/P
- お前毎日毎日暇人だね。
きっと友達いないんだろうね。いい加減社会復帰したら?(wwww
- 319 : :02/11/08 06:44 ID:sVMBiBlH
-
- 320 :↑:02/11/08 06:55 ID:rSBWF9Hl
- ぎゃはは
怖くて言い返せないから無言でageるしかないんだね(w
ダサいよ。(´`c_,'` ) プッ
- 321 :ナナシサソ:02/11/08 08:27 ID:LUnKDZ4Y
- 障害者と遊んであげるスレはここですか?
- 322 :ナナシサソ:02/11/08 08:33 ID:4tsefHW1
- >>321
ここは>>1が自動保守機能と会話するスレ
- 323 : :02/11/08 08:58 ID:e0Bkkcbv
- >XmSLNk4Xはゴキブリのゴキちゃん
こんな寒くて頭悪そうなレスはじめて見たな
- 324 : :02/11/08 10:13 ID:VHQPdsCK
- e0Bkkcbvは煽るしか楽しみのない一生童貞の引き篭もり無職キチガイ知障宗教信者
- 325 :ナナシサソ:02/11/08 12:39 ID:h7XCXyov
- >>324
自動保守と遊んでろよ障害者(プ
- 326 :ナナシサソ:02/11/08 12:50 ID:JB7+7z7k
- >e0Bkkcbvは煽るしか楽しみのない一生童貞の引き篭もり無職キチガイ知障宗教信者
↑>>1が知ってる全単語
- 327 : :02/11/08 21:57 ID:VHQPdsCK
- JB7+7z7k
は在日
- 328 : :02/11/08 21:59 ID:VHQPdsCK
- h7XCXyovは平日の昼間からやる事のないホームレス
- 329 : :02/11/08 22:32 ID:QHT8TjNj
- >>322
手動
- 330 : :02/11/09 05:39 ID:Jh8FxdtL
- >>1の全敗で終了!
- 331 : :02/11/09 07:59 ID:YgsT8IOO
- Jh8FxdtLは世の中勝ち負けで判断する低脳
- 332 : :02/11/09 12:26 ID:8Hk3zYBc
- 1 名前: 投稿日:02/08/31 20:43 ID:xM70xHt2
大好評に付き第2弾です。
ちなみに前スレは俺の全勝で終了しました。
- 333 : :02/11/09 13:29 ID:qDuvEYbo
- 332 : :02/11/09 12:26 ID:8Hk3zYBc
1 名前: 投稿日:02/08/31 20:43 ID:xM70xHt2
大好評に付き第2弾です。
ちなみに前スレは俺の全勝で終了しました。
- 334 :ナナシサソ:02/11/09 14:04 ID:T+zUMVLD
- 333 名前: [sage]:02/11/09 13:29 ID:qDuvEYbo
332 : :02/11/09 12:26 ID:8Hk3zYBc
1 名前: 投稿日:02/08/31 20:43 ID:xM70xHt2
大好評に付き第2弾です。
ちなみに前スレは俺の全勝で終了しました。
- 335 :ナナシサソ:02/11/09 14:26 ID:qDuvEYbo
- T+zUMVLDはコピペ猿
- 336 : :02/11/09 21:19 ID:wKHfQSyF
- qDuvEYboは猿山のボス
- 337 :ナナシサソ:02/11/09 21:27 ID:KXpn0cwQ
- wKHfQSyFは俺の彼女(猿)
- 338 :ナナシサソ:02/11/09 21:41 ID:olbicHhy
- 突然すいません! MXオンリーのバンド作りました!ぜひ聞いてください聞いてみて糞ならすぐ捨ててください 気に入った方は共有にいれてくださるとうれしいです バンド名はコイモですMP3 2曲あります たくさんのDLおまちしております 失礼しましたー逝きマース
- 339 :ナナシサソ:02/11/09 23:22 ID:qDuvEYbo
- wKHfQSyFは象の糞
- 340 : :02/11/10 05:53 ID:s7gXZ39m
- qDuvEYboの全敗で終了
- 341 : :02/11/10 09:30 ID:yGGrkqsa
- s7gXZ39mは精神異常でドクターストップにより全敗
- 342 : :02/11/10 21:38 ID:9tCA3Gl5
- >>1の全焼で終了
- 343 : :02/11/11 03:46 ID:csaDytiz
- >>1の全勝で9tCA3Gl5の全灰で終了
- 344 : :02/11/11 15:12 ID:Ze4Ul2s5
- >>1はパラリンピックで全勝
- 345 :ナナシサソ:02/11/11 15:21 ID:/B6/QYub
- 100 : :02/09/17 07:01 ID:CyoKOOzf
100ゲット。
よって俺の全勝で終了!!!!
- 346 : :02/11/11 16:48 ID:X7y7YnyI
- 「パラリンピックで全勝」
だってよ。(´`c_,'` ) プッ馬鹿じゃねーの?
何それ?ギャグ?ツマンネー。死ねよ。ユーモア0だなw。
- 347 : :02/11/12 05:35 ID:Ijfq41TD
- X7y7YnyIもちっとも面白くないから負けで終了
- 348 :ナナシサソ:02/11/12 10:43 ID:IUMQ/Ci+
- Ijfq41TDは毎日夜9時に起きて朝5時に寝る引き篭もり
- 349 : :02/11/12 14:29 ID:L09PpyDD
- IUMQ/Ci+は毎日このスレをチェックしてる>>1ということで終了!
- 350 : :02/11/13 05:43 ID:R6vDVplO
- >>1は全敗
- 351 : :02/11/13 08:45 ID:8/7pnY+u
- L09PpyDDは毎日2回チェックしてる引き篭もり
R6vDVplOは全敗以下のゴミ
- 352 : :02/11/13 18:15 ID:OYzZqh8H
- >>1
つまんねー煽りだな。そんなのじゃ健常者はお前みたいに必死にならないぞ。
このスレはお前が可愛そうなだけだな( ´,_ゝ`)プッ
障害者は死ねば?
- 353 :ナナシサソ:02/11/13 18:29 ID:km7IUBIu
- >L09PpyDDは毎日2回チェックしてる引き篭もり
>R6vDVplOは全敗以下のゴミ
ワンパターンでボキャブラリーが貧困。頭の悪さ丸出し。
こいつはリアル消防じゃないのか?
- 354 :ナナシサソ:02/11/13 18:33 ID:8cMBlr52
- >>1は本当に知恵遅れとかじゃないのか?
- 355 :ナナシサソ:02/11/13 18:39 ID:Vw1PCxUL
- 新作もせ+PV*TV+LIVE情報【part@】
http://tmp.2ch.net/test/read.cgi/download/1035714872/
こっちはまともな人間が立てたので盛り上がってます
- 356 :ナナシサソ:02/11/13 20:00 ID:490S+TmG
- ゴキブリのゴキちゃん
↑>>1にはこれが面白いのか?いかにも障害者だな
- 357 : :02/11/14 04:16 ID:UH+lu/K4
- >>1の負けで終了
- 358 :ナナシサソ:02/11/14 16:02 ID:m6ifzTn2
- 粘厨キチガイに追われて>>1がかわいそう
- 359 : :02/11/14 17:55 ID:asYAHIVb
- m6ifzTn2は引き篭もりのクズ
- 360 :ナナシサソ:02/11/14 18:38 ID:HDBEr649
- ゴキブリのゴキちゃんって…発想が幼稚園児みたい
- 361 : :02/11/15 03:02 ID:SOgQStOm
-
- 362 :ナナシサソ:02/11/15 03:08 ID:ksdkpNmp
- m6ifzTn2はいちいちモデムの電源を切って別人を装ってる大根役者
- 363 :ナナシサソ:02/11/15 12:51 ID:19/6FfH5
- >>1はとっくの昔にいない罠
- 364 : :02/11/16 04:50 ID:+YHjgWaD
- そろそろ>>1の負けが確定!
- 365 :ナナシサソ:02/11/16 05:51 ID:BRB2bxCY
- >>355
ピエト炉がまともな人間・・・ (藁
- 366 : :02/11/16 13:11 ID:b+tzoGBV
- >>1も馬鹿だが>>1にかまってもらおうと必死な奴はもっと馬鹿
- 367 :ナナシサソ:02/11/16 16:15 ID:vMUklkRB
- b+tzoGBVはゴキブリのゴキちゃん
- 368 : :02/11/16 17:30 ID:szxF7xf+
- >>1は自作自演も下手だな。頭悪ぅ
- 369 : :02/11/17 06:03 ID:AXBAB6H9
- >>1は全敗
- 370 :ナナシサソ:02/11/17 10:28 ID:cJaRi5lC
- 悲惨なかまって君がいるスレ・・・
- 371 :ナナシサソ:02/11/17 18:43 ID:q+NCE9wZ
- >>1の頭の悪さは病的だな
- 372 :ナナシサソ:02/11/17 22:37 ID:cJaRi5lC
- >>1よ、早く言い返せよ、俺毎日、暇なんだからさあ
- 373 : :02/11/18 05:22 ID:dGvwucFq
- 悲惨な>>1がいるスレ
- 374 :ナナシサソ:02/11/18 12:29 ID:FOyL6q0/
- >>1 出てこーい、暇だー >>1死ね >>1の負け ほら言い返してみろよ
- 375 : :02/11/19 04:31 ID:YI8PtbnO
- >>1の全敗が確定!
- 376 : :02/11/20 05:03 ID:k5hNvEHg
- >>1の全敗で終了!
- 377 :ナナシサソ:02/11/20 19:28 ID:+bMBixHq
- 1は氏んだか
- 378 :ナナシサソ:02/11/20 22:28 ID:aUzOU2EB
- >>1 の負けなんだから出て来いよ。 毎日毎日暇だからさー俺と遊んでくれよ
- 379 : :02/11/21 03:45 ID:aDqEifLA
- >>1は負け犬
- 380 :ナナシサソ:02/11/21 15:16 ID:WunsQdX7
- >>1 のバーカバーカ!悔しかったら反論してみろ!!
- 381 : :02/11/22 00:58 ID:nTIKd2nf
- >>1はゴキブリのゴキちゃん
- 382 :ナナシサソ:02/11/22 01:38 ID:mN4WUzMx
- >>1 いい加減に反論しろ!!!殺すぞ!
- 383 :ナナシサソ:02/11/22 01:39 ID:mN4WUzMx
- >>1はまだかー おーい 早くしろ
- 384 :ナナシサソ:02/11/22 13:46 ID:mN4WUzMx
- 今日も1日暇だなー。>>1はまだ来ないの?
- 385 :ナナシサソ:02/11/22 13:47 ID:mN4WUzMx
- >>1死ね
ほれ悔しいだろ?このままじゃお前の負けで終了になっちゃうぞ。
- 386 :ナナシサソ:02/11/22 16:36 ID:mN4WUzMx
- >>1 よーお前がいないとつまんないよ
- 387 :ナナシサソ:02/11/22 16:37 ID:mN4WUzMx
- >>1 何とか言えよ たのむから
- 388 :ナナシサソ:02/11/22 16:38 ID:mN4WUzMx
- このスレの>>1だけが楽しみで生きてるのに
- 389 :ナナシサソ:02/11/22 16:39 ID:mN4WUzMx
- >>1はチョベリバ
- 390 : :02/11/23 05:04 ID:/gmdrFao
- そろそろ>>1の葬式が始まる
- 391 :ナナシサソ:02/11/23 08:17 ID:dp9z+Pdt
- >>1 氏ね知恵遅れ
- 392 :ナナシサソ:02/11/23 15:27 ID:XoakmFiA
- >>1 の母ちゃんでべそ
- 393 :ナナシサソ:02/11/23 15:31 ID:XoakmFiA
- >>1早く出てこーい終了するぞ
- 394 :ナナシサソ:02/11/23 21:54 ID:XoakmFiA
- >>1 マジでもう出てこないの?かなり暇なんだけど。
- 395 : :02/11/24 06:04 ID:LUEgv/oS
- >>1の死亡確定!
- 396 :ナナシサソ:02/11/24 19:52 ID:p4UywlwH
- >>1はまだかよ!今日俺だけ飲み会誘われなくて暇なんだYO!
- 397 : :02/11/25 04:47 ID:w1wjL+dj
- >>1は負け犬で終了!!!
- 398 :ナナシサソ:02/11/25 06:09 ID:6CZ0XUtN
- 【ピエト炉鯖】
pietro.dip.jp : 8888
041
備考
100file 10GB
- 399 : :02/11/25 22:52 ID:WwH9VAAw
- >>1の亡霊まだ〜?
- 400 :1:02/11/26 00:16 ID:3XCq3bcF
- 400ゲット
- 401 : :02/11/26 04:11 ID:2XkoSaFJ
- >>1の全敗、俺の全勝で終了!
- 402 :ナナシサソ:02/11/26 04:34 ID:ZtGq3SZD
- >>1 知恵遅れは死ね
- 403 :ナナシサソ:02/11/26 20:16 ID:XIZohOjy
- ゴキブリのゴキちゃんまだ〜?
- 404 :ナナシサソ:02/11/27 04:00 ID:9Xb1P/5D
- >>1は怖くなって出て来れなくなったんだろ
- 405 : :02/11/27 08:50 ID:xQg3V+9E
- >>1は精神病院に入院しますた
- 406 :ナナシサソ:02/11/27 13:01 ID:6K05XjNc
- >>1 が来ないと平日の昼間が暇になるな。早く帰ってこーい
- 407 :ナナシサソ:02/11/27 15:34 ID:6K05XjNc
- あー暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ暇だ
>>1出て来い>>1出て来い>>1出て来い>>1出て来い>>1出て来い>>1出て来い>>1出て来い
>>1氏ね>>1氏ね>>1氏ね>>1氏ね>>1氏ね>>1氏ね>>1氏ね>>1氏ね>>1氏ね>>1氏ね>>1氏ね>>1氏ね
>>1の負け>>1の負け>>1の負け>>1の負け>>1の負け>>1の負け>>1の負け>>1の負け
速く戻って来いやぁぁぁぁあぁぁぁぁぁぁぁぁあああああああああ!!!!!!あsfqsふ
- 408 :ナナシサソ:02/11/27 19:40 ID:6K05XjNc
- 夜も暇だ・・・
- 409 : :02/11/28 04:06 ID:3ahKPQ8F
- >>1の全敗で終了しますた!!!
- 410 :ナナシサソ:02/11/28 21:07 ID:KBKTU6M0
- 大好評に付き第2弾です。
ちなみにこのスレは>>1の全敗で終了しました。
- 411 : :02/11/29 04:12 ID:t6h/cmZj
- >>1は負け犬
- 412 :ナナシサソ:02/11/29 19:25 ID:SmwSsLh+
- >>1まだ〜?
- 413 :ナナシサソ:02/11/30 04:33 ID:X5cTFCOT
- >>1の負けで糸冬了
- 414 : :02/11/30 18:14 ID:C2nuqJrq
- >>1は1勝もできなかった
- 415 : :02/12/01 04:10 ID:6dJflItd
- おいおい、マジで>>1は氏んだのか?
- 416 : :02/12/02 00:21 ID:clffXYDB
- ( ´,_ゝ`) プッ
- 417 :ナナシサソ:02/12/02 05:42 ID:9gaFwIkl
- 悲惨なスレ…
- 418 :ナナシサソ:02/12/02 15:02 ID:clffXYDB
- ホント悲惨なスレだな、そんなに>>1にかまってもらいたいのか(w
- 419 :ナナシサソ:02/12/02 21:51 ID:clffXYDB
- かなり爆笑させてもらったよ。このスレ
- 420 : :02/12/03 00:08 ID:DJG/RsmX
- 悲惨なかまって君がいるスレ・・・
- 421 :ナナシサソ:02/12/03 02:49 ID:vhnrS72n
- >ゴキブリのゴキちゃん
( ´,_ゝ`) プッ
- 422 :ナナシサソ:02/12/03 04:13 ID:DJG/RsmX
- >おいおい、マジで>>1は氏んだのか?
( ´,_ゝ`) プッ
- 423 :ナナシサソ:02/12/03 06:57 ID:QYRxXqx/
- >>1は真似しかできない知恵遅れ
- 424 :ナナシサソ:02/12/03 15:20 ID:DJG/RsmX
- で?>>1はどこいった?
- 425 :ナナシサソ:02/12/03 21:14 ID:DJG/RsmX
- ( ´,_ゝ`) プッ
晒しage
- 426 :ナナシサソ:02/12/03 21:14 ID:DJG/RsmX
- ( ´,_ゝ`) プッ
- 427 :ナナシサソ:02/12/03 21:14 ID:DJG/RsmX
- ( ´,_ゝ`) プッ
- 428 :ナナシサソ:02/12/03 21:15 ID:DJG/RsmX
- プププ
- 429 :ナナシサソ:02/12/03 21:15 ID:DJG/RsmX
- (  ̄,_√):::プッ
- 430 :ナナシサソ:02/12/03 21:15 ID:DJG/RsmX
- (´゚c_,゚` ) プッ
- 431 :ナナシサソ:02/12/03 21:15 ID:DJG/RsmX
- (´`c_,'` ) プッ
- 432 :ナナシサソ:02/12/03 21:16 ID:DJG/RsmX
- プッ━━━━(゚∀゚)━━━━ !!!!!
- 433 :ナナシサソ:02/12/03 21:16 ID:DJG/RsmX
- (゚Д゚)プッ
- 434 :ナナシサソ:02/12/03 21:17 ID:FioTSTIy
- (|||゚Д゚)!!ブリッ
- 435 :ナナシサソ:02/12/03 21:22 ID:DJG/RsmX
- ┌──────────────────────―─┐
│ |
│ |
│ ∧_∧ |
| ( ;´∀`) |
| 人 Y / |
| ( ヽ し |
| (_)_) |
| |
│ Now Bokkiing. ... |
│ |
│ |
│ しばらくちんちん勃ててお待ちください。 |
│ |
└───────────────────────―┘
- 436 :ナナシサソ:02/12/03 21:22 ID:DJG/RsmX
- ┌──────────────────────―─┐
│ |
│ |
│ ∧_∧ |
| ( ;´∀`) |
| /, つ |
| (_(_, ) |
| しし' |
| |
│ Now Kusoing. ... |
│ |
│ |
│ しばらくうんちが出るまでお待ちください。 |
│ |
└───────────────────────―┘
- 437 :ナナシサソ:02/12/03 21:24 ID:04dxt3XM
- ID:DJG/RsmX = >>1
- 438 :ナナシサソ:02/12/03 21:25 ID:DJG/RsmX
- ,,-''lllllllllllllllllllllllllllllllllllllll 、
/||||||||||||||||||||||||||||||||||||||ii;、
/ ̄ ̄\||||||||||||||||||||||||||||||||||||ii;゙ヽ,
/ ヽ!!|||||||||||||||| ||||||||||!!,/
/ / ゙!!!|||||||||||| |||||||!!
\____/ ゙゙ヽ、ll,,‐''''""
______
/ `ヽ
/ `、 \ ___|_|」
/ ̄ ̄\ | ヽ / |__ |
'" ̄ヽ ヽ!! |,," ヘ < | |
ヽ ゙!!!、 ,,-' iヽ── / 丿 /
|||l ゙゙ヽ、ll,,‐''''"" | ヽ||||||||| ヽ/
|||l ___,,,,,, ゙l ,,,,, \||||||||| _
||!' /ヽ、 ;::''“”“~`゙>┴<;''“”~` /\ |'" ̄| | |
\ / |ミミヽ──‐'"ノ≡- ゙'──''彡| |、 | | | |
 ̄| |ミミミ/"~( ,-、 ,:‐、 ) '彡|| |、/ / | |
ヽ、l| |ミミミ| |、─\\\\ |彡l| |/ /_ | |
\/|l |ミミミ| \_/ ̄\\\\''|l/  ̄/ | |
\ ノ l|ミミミ| \二二\\\\ フ | |
 ̄\ l|ミミミ|  ̄ ̄ ̄\\\\ \ | |
| \ ヽ\ミヽ  ̄ ̄"' \\\\ / |_|
/ \ヽ、ヾ''''ヽ、_____//\\\\ /
/ ヽ ゙ヽ─、──────'/| \\\\ ̄/
. / ゙\ \ / / \__\\\\
───'''" ̄ ̄ ゙゙̄ヽ、__,,/,-'''" \\\\
- 439 :ナナシサソ:02/12/03 21:26 ID:DJG/RsmX
- >>437=↓
r「l l h
| 、. !j
ゝ .f _
| | ,r'⌒ ⌒ヽ、
,」 L_ f ,,r' ̄ ̄ヾ. ヽ.
ヾー‐' | ゞ‐=H:=‐fー)r、)
| じ、 ゙iー'・・ー' i.トソ
\ \. l、 r==i ,; |'
\ ノリ^ー->==__,..-‐ヘ___
\ ノ ハヽ |_/oヽ__/ /\
\ / / / |.
y' /o O ,l
,r(( ( ,r─、 ,,、zニ二ィ
/rO ヾ==、/=ニ~∨∠´ O ヽ
/__,,,ィイ叮叮(O) |「叮叮-iト┬ェ─┘
!シ┴┴ヾ==ノ`┴┴--、ノ-ヽ-、
<´ _,,,,,,_ ,r┬─-、  ̄`'''",>
`ー/;;;,, \ ( { ;;;;;:;;;ヽー''´
//,',';; ノ--、>!, ',',;;::',',゙i
/,',',';;" //_ | ̄| \ ',',',;;,'i
i 、 / `ー┴┴'´ヽ ',;::'、|
| 〈 ヽ'' {
ト, i | 、 i
|',',;; } ! ',',;;i
|,','、 / ヽ',',','|
!;;', / !,',;,;'|
゙i',';;;;i |:::;;;i
!'' { }'' !
/ i, 〉 ヽ、
彡、,,,-‐┘ └ュュュュ
- 440 :ナナシサソ:02/12/03 21:27 ID:DJG/RsmX
- ああっ、もうダメッ!
ぁあ…ウンチ出るっ、ウンチ出ますうっ!!
ビッ、ブリュッ、ブリュブリュブリュゥゥゥーーーーーッッッ!!!
いやああああっっっ!!見ないで、お願いぃぃぃっっっ!!!
ブジュッ!ジャアアアアーーーーーーッッッ…ブシャッ!
ブババババババアアアアアアッッッッ!!!!
んはああーーーーっっっ!!!ウッ、ウンッ、ウンコォォォッッ!!!
ムリムリイッッ!!ブチュブチュッッ、ミチミチミチィィッッ!!!
おおっ!ウンコッ!!ウッ、ウンッ、ウンコッッ!!!ウンコ見てぇっ ああっ、もうダメッ!!はうあああーーーーっっっ!!!
ブリイッ!ブボッ!ブリブリブリィィィィッッッッ!!!!
いやぁぁっ!あたし、こんなにいっぱいウンチ出してるゥゥッ!
ぶびびびびびびびぃぃぃぃぃぃぃっっっっ!!!!ボトボトボトォォッッ!!!
ぁあ…ウンチ出るっ、ウンチ出ますうっ!!
ビッ、ブリュッ、ブリュブリュブリュゥゥゥーーーーーッッッ!!!
いやああああっっっ!!見ないで、お願いぃぃぃっっっ!!!
ブジュッ!ジャアアアアーーーーーーッッッ…ブシャッ!
ブババババババアアアアアアッッッッ!!!!
んはああーーーーっっっ!!!ウッ、ウンッ、ウンコォォォッッ!!!
- 441 :ナナシサソ:02/12/03 21:28 ID:DJG/RsmX
- \ 毛 /
腿 \_ | _/
彡彡彡
ミミミミ クリトリス
ミミミミ / ̄ ̄ ̄ ̄
ノ σ ヽ 尿道
/ / ゚ヽ ̄ ̄ ̄ ̄
大陰唇 / //\\ \
 ̄ ̄ ̄ ̄ ( ( 膣 ) ── 小陰唇
\ \\// /
` \/ '
\ *──肛門
\_____/\_____/
- 442 :ナナシサソ:02/12/03 21:28 ID:DJG/RsmX
- 己 嗚 己 嗚 己 嗚 求 男 強 日 己 嗚 歩 男 色 日
の 呼 の 呼 の 呼 め の く 本 の 呼 み の 無 本
夢 男 道 男 夢 男 て 夢 男 道 男 て 道 し 男
を 塾 を 塾 を 塾 を 激 児 を 塾 明 を 児
魁 魁 魁 明 ひ し の 魁 日 ひ 恋 の
よ 男 よ 男 よ 男 日 た く 魂 よ 男 を た 無 生
意 意 意 を す は 意 魁 す し き
気 気 気 魁 ら 温 気 る ら 様
る に か に 情 は
く け
有
り
,.-'" ̄ ̄ヽ、 . ,.-'" ̄ ̄ヽ、 ,.-'" ̄ ̄ヽ、 ,.-'" ̄ ̄ヽ、 ,.-'" ̄
/ヽ____ゝヽ /ヽ____ゝヽ /ヽ____ゝヽ ./ヽ____ゝヽ /ヽ__
| } ニ ニ | | | } ニ ニ | | | } ニ ニ | | | } ニ ニ | | .| } ニ
ヽ_| /」 |_ノ .ヽ_| /」 |_ノ .ヽ_| /」 |_ノ ヽ._| /」 |_ノ ヽ_| /
 ̄ヽ、 -==.,.'" ̄ ̄ヽ、 -==,..'" ̄ ̄ヽ、 -==,..'" ̄ ̄ヽ、 -==,.'" ̄ ̄ヽ、 -=
__ゝヽ /ヽ____ゝヽ ./ヽ____ゝヽ ./ヽ____ゝヽ ./ヽ____ゝヽ ./
. ニ | | | } ニ ニ | | | } ニ ニ | | | } ニ ニ | | | } ニ ニ | | .|
'」 |_ノ ヽ_| /」 |_ノ .ヽ_| /」 |_ノ .ヽ_| /」 |_ノ .ヽ_| /」 |_ノ. ヽ
=‐ / .ヽ、-==‐ / ヽ、-==‐ / ヽ、-==‐ / .ヽ、-==‐ /
‐‐'〉、 _}ー‐‐‐'〉、. _}ー‐‐‐'〉、. _}ー‐‐‐'〉、 _}ー‐‐‐'〉、
- 443 :ナナシサソ:02/12/03 21:30 ID:DJG/RsmX
- 」´ ̄`lー) \
T¨L |_/⌒/ ← >>1
`レ ̄`ヽ〈
| i__1
_ゝ_/ ノ
L__jイ´_ )
| イ
| ノ--、 ,,;;;;;;;;;;;;、〜
ゝ、___ノ二7 {;;;;;;;;;;;;;;}〜
|ーi | l_/ . '::;;;;;;;;;::' 〜
__〉 { ,r''''"~ ""''ヽ
'ー‐┘ i' 'i ← >>2-999
| 'i,
! i'> }
,.`! ; _ノ
__,,,... 'i, `'i'''―--―''''i'ニ-'""ノ -- ...,,,__
_,, -‐ ´ ヽ.i' "' '''"'; _/´ ` ‐- ,,_
, ‐ ´ `ゝ_,.i、__ _,;..-'" ,,..i'"':, ` ‐ 、
|\`、: i'、
. \\`_',..-i
\|_,..-┘
- 444 :ナナシサソ:02/12/03 21:31 ID:DJG/RsmX
- 2ちゃんねるの文字絵はアスキーアートAAではありません。
2ちゃんねるの文字絵はAAでもないのにAAと
嘘の情報を垂れ流すことは犯罪行為です。
■ 文字絵(テキストアートtext art)の内のアメリカのアートがアスキーアートAA asciiartである。
■ 文字絵(テキストアートtext art)の内の日本のアートがJISアートJapanOriginalityartである。
■ テキストアート(文字絵)のジャンルの中の内のひとつがアスキーアートAAである。
■ テキストアート(文字絵)のジャンルの中の内のひとつがascii picturesである。
■ テキストアート(文字絵)のジャンルの中の内のひとつがJISアートである。
■ テキストアート(文字絵)のジャンルの中の内のひとつが顔文字(フェイスマーク)
■ テキストアートtext artとはすべて(世界の文字絵)の文字絵の総称 → 世界共通名。
なぜならば文字(text)絵(art)はすべて(必要条件)→text(文字記号)で作られている由縁。
文字絵(text art)とは それぞれ各々の国の文字(text)環境で作った文字絵(art)のこと。
だから それぞれの国の文字環境でしか作れないし それぞれの国の文字環境でしか
正しく見えないのである。
■ 文字(text ←必要条件)で作った絵(art)のことすべてをテキストアート(text art)と言う。
■ なぜならば文字絵(text art)は それぞれ各々の国の文字記号(text)で出来ている由縁である。
■ テキスト(text)とは→ 文書(文字記号の集合体)のことで制御コードを含まない文字記号列。
■ つまり文字絵(世界の文字絵)は それぞれ各々の国の文字環境でしか見えない作れないのです。
■ つまりアスキーアートは我々日本の漢字カナ混じり環境では正しく見えない作れないのである。
■ アスキーアートはwindowsの英語版(アスキー文字)でしか描けないし英語版でしか見えないのです。我々日本人のパソコンは日本語版でありアスキーアート(AA)を作ることも見ることも出来ません。
- 445 :ナナシサソ:02/12/03 21:32 ID:DJG/RsmX
- lllllll;l|||lll;;;;;|ミ;|;;(》厂 '''''''エー⌒^゙^^リl|uz,,,,,、,i´_アrミ!‐゙¨ミ;》ミ「冖'!「|l;|l;《;ll
lllll;;;;lll;;;l|;;l;;;l|厂′ , .二y,. .:(v‐ ┐.⌒¨了爻iy,¬rli;hriizy,,,,ア《lミllll
ll;llll;》;;;|;;l;;⌒|゙‐¬llリlア巛》リミリ(;., イ¨゙゙゙^^^ミ厂 .,yv《'_.¨,、 ,ブミ;|ト|;|i|;;
l|l》lll;;;;;;||リ .} ^' .‐ .、 .′゙″ ノ/、 . .,个 ,,l);l)|《》》ミ《lllレ(>,〔ミ;iミ;l
llllllll;||》|^|゙.、.}, ¨‐′ .{|彡.´. ,..,,. ,,;. ^゙'^‐´〔;i;ll;
lllllll;ll;|ll}′ .゙()、 、^ ´ '〕′ .´厂 .′<ミ《;ll
llll;lll》レ彡 ` .、 .、、 .、. . - ゙|!ー .ヾ..(ミ|ll
llll;ll;;;ト;リ゙: ... .,、..- .ノ>vy,.. . :》「:{lll
lll;;ll|l;》ミ_、 .ノ厂 .´.┐ .゙¨^冖^.ヾ'冖 .丁|ll
lllllllll》(《レ 「‐、 _ 、 :v '゙- .hzllllll
lllllllllll||l|(`, ヽ'゙゙'ア>ur‐' ‐_uァ ._:(|;lll;l;
llll;l|;;;;l;;|! ゙ .⌒ .'┘ ′ ,r巛;lllll;ll
lllllllll;lllll|h-, .:ソ(|;;lllllll;ll|
llllllllllllllllll》;ァ,,., .′ ¬llWiW;;!フ厂)l^''7)(liyyァ ' .r.,.();;;llllllllllllll
lllllllllllllllllll;h(「「″ \、、‐.´゙¨゙ ´ :{r厂゙.′ /ー:{;;;;llll;lllllllll
こんな自分で良ければ使いたければ使え、という気分があったんです。
写真はわざとデブって見えるものを送りましたが、それは本当の事を言うと、
「使ってほしく無い」という気持ちもあったのです。
- 446 :ナナシサソ:02/12/03 21:35 ID:DJG/RsmX
- 探し人は誰ですか 見つけにくい人ですか?
日本の中も北朝鮮も 探したけれど見つからないのに
まだまだ探す気ですか それより米をよこしませんか?
米と金を 米と金を 援助したいと思いませんか?
ウフッフー ウフッフー ウフッフー さーあー!
抗う事は許されず 金出すことを迫られて
這いつくばって 這いつくばって いったい何をしようと言うのか
やっと探し当てた時 死んでることもよくある話で
忘れましょう! 米と金を 援助したいと思いませんか?
ウフッフー ウフッフー ウフッフー さーあー!
探し人は誰ですか 見つけにくいひとですか?
米と金を 米と金を 援助したいと思いませんか?
ウフッフー ウフッフー ウフッフー さーあー!
ヽ、____ \\ ~\_____ノ|
- 447 :ナナシサソ:02/12/03 21:37 ID:DJG/RsmX
- 謝れとは言いませんがこちらもちょっと大人げないのですが
ムカついたので友達の川崎魔夜に頼んで 君の輪姦写真を
撮ってもらうことにしました。あ、もう遅いですよ。
もうすでに友達輪姦始めちゃってますから・・・(^^;
ちなみにこれは自慢じゃないんですがその友達は日本でも
5の指に入るくらい凄腕の腰の持ち主です 。
この前彼の家に遊びに行ったらものの5分で不感症のぞま本を
逝かせていました。
彼にとってそれくらい赤子の腕をひねるくらい簡単なんですよね(爆)
これで君もいっかんの終わりってやつですね(^^;
まあせいぜい後悔してくださいね。
それからもう二度と荒らしはしないこと(その友達は荒らしが大嫌いらしいです。
荒らしを見つけたら即輪姦に入るみたいです(^^;)
それでは、う〜ん二日後くらいかな?また例の所に来てくださいね。
あなたの性感帯その他もろもろのせておきますんで(笑)
あ、警察とかに言ったって無駄ですよ。
あなたは荒らし(犯罪)なんだから通報したところで捕まるのは
アナタです。私の友達は他人の肛門を自在に操ることができるんです。
と、いうことでbye♪(^0^)/~~
- 448 :ナナシサソ:02/12/03 21:41 ID:DJG/RsmX
- 勇者 「おいおまいら!! モンスターが現われますた。馬車前に集合しる」
ライアン 「詳細キボンヌ」
勇者 「メタルキングですが何か?」
ライアン 「メタルキングキタ━━━━━━(゚∀゚)━━━━━━ !!!!」
アリーナ 「キタ━━━━━━(゚∀゚)━━━━━━ !!!!」
マーニャ 「ケコーン!」
ライアン 「(;´Д`)ハァハァ」
ブライ 「ハァハァすんなヴォケ」
マーニャ 「オマエモナー」
勇者 「会心の一撃うpキボンヌ」
クリフト 「ザラキage」
ミネア 「聖水うp」
マーニャ 「↑誤爆?」
ブライ 「( ´,_ゝ`)プッ」
クリフト 「ザラキage」
アリーナ 「ザラキ厨uzeeeeeee!!」
魔物 「もうこねえよ! ヽ(`Д´)ノウワァァン!!」
勇者 「--------終了-------- 。・゚・(ノД`)・゚・。」
ミネア 「ヽ(゚ー゚*)ゲンキダシテ」
ピサロ 「イタイ導かれし者たちがいるパーティはここですか?」
アリーナ 「氏ね」
トルネコ 「そんなことより勇者よ、ちょっと聞いてくれよ。戦闘とは関係ないんだけどさ。
昨日ふとんが吹っ飛んだんです。」
- 449 :ナナシサソ:02/12/03 21:42 ID:DJG/RsmX
- Two hunters are out in the woods when one of them collapses.
He doesn't seem to be breathing and his eyes are glazed.
The other guy whips out his phone and calls the emergency services.
He gasps: "My friend is dead! What can I do?" The operator says:
"Calm down, I can help. First, let's make sure he's dead." There is
a silence, then a shot is heard. Back on the phone, the guy says:
"OK, now what?"
- 450 :ナナシサソ:02/12/03 21:42 ID:DJG/RsmX
- Two hunters are out in the woods when one of them collapses.
He doesn't seem to be breathing and his eyes are glazed.
The other guy whips out his phone and calls the emergency services.
He gasps: "My friend is dead! What can I do?" The operator says:
"Calm down, I can help. First, let's make sure he's dead." There is
a silence, then a shot is heard. Back on the phone, the guy says:
"OK, now what?"Two hunters are out in the woods when one of them collapses.
He doesn't seem to be breathing and his eyes are glazed.
The other guy whips out his phone and calls the emergency services.
He gasps: "My friend is dead! What can I do?" The operator says:
"Calm down, I can help. First, let's make sure he's dead." There is
a silence, then a shot is heard. Back on the phone, the guy says:
"OK, now what?"
- 451 :ナナシサソ:02/12/03 21:44 ID:DJG/RsmX
- ┌─────────────────────────┐
│☆★☆★☆★☆―おいらの尻の心の愛 ―★☆★☆★☆★│
│★ ┏━┓┏┳┓ ┏┳━━━┳━┓┏┓ ☆│
│☆ ┣━┫┃┃┣┳━━┛┣━┳┓┣━┛┃┃ ★│
│★ ┗━┛┣╋┛┗┳┓┏┛ ┃┣┛ ┃┃ ☆│
│☆ ┏━━┛┣┓┣┛┃┃┏━┛┃┏━━┛┃ ★│
│★ ┗━━━┛┗┛ ┗┛┗━━┛┗━━━┛ ☆│
│☆ ┏━━━┓┏┓┏┓ ┏━━━┓ .★│
│★ ┗━━┓┣┛┗┫┃ ┃┏━┓┃ .☆│
│☆ ┏━━┛┣┓┃┃┗━┫┃ ┃┃ .★│
│★ ┃┏┓┏┛┃┃┃┏━┫┗━┛┃ .☆│
│☆ ┗┛┗┛ ┗┻┻┛ ┗━━━┛ .★│
│★ ┏┳┓┏┳┓ ┏┳━━┳┳┓ ☆│
│☆ ┃┃┣┛ ┗┳━┛┃ ━ ┃┃┃ ★│
│★ ┃┃┣┓┃┏┻┓┏┫┏┓┃┃┃ ☆│
│★ ┗┫┃┗┫┃ ┃┃┗┛┃┃┃┗┓ ★│
│☆ ┗┛ ┗┛ ┗┛ ┗┻┻━┛ ☆│
│★ ▼▼▼▼ ★│
│☆ 本日 PM 3:00 開演 場所 空地 ・__・ ☆│
│★ 来ないやつは糞喰わす 〇 ..★│
│☆ 3 .☆│
│★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★☆★│
└─────────────────────────┘
- 452 :ナナシサソ:02/12/03 21:46 ID:DJG/RsmX
- +=*撮撮盗代代∀∀∀∀∀∀∀∀田代*∀∀∀****∀∀∀∀代田盗撮撮撮∀=
+==盗撮田田代代∀∀∀∀∀∀∀∀代*******∀∀∀∀∀∀盗盗撮撮盗==
+=*盗撮田代代代∀∀∀∀∀***∀**∀***∀代∀∀∀∀代田撮撮撮盗=:
++*田撮盗盗代∀∀∀∀∀∀******∀∀代田田代代代∀∀∀∀盗撮撮撮**
++*田撮盗盗∀∀∀∀∀代∀∀∀∀∀∀∀∀∀盗田田代代田撮撮撮盗田撮撮盗∀∀
+=*田撮盗盗代代撮撮撮撮撮撮代代代∀代代田撮撮撮撮盗撮撮撮撮盗撮撮撮田盗田
+:=*撮撮盗代田代田撮撮盗田田∀∀∀田盗撮∀∀田撮田代代代代田代盗田田撮田
++**田撮撮代田田田田代撮撮撮撮撮盗盗田代田田撮撮撮盗代代盗田撮撮田撮∀∀
++=*田撮撮田盗田∀∀∀∀田∀代撮盗盗撮∀代代代代∀∀代∀代代田盗田田∀∀
++=*∀撮盗盗田代撮撮撮撮撮撮代盗田∀撮田∀∀∀∀∀代∀∀田代代盗田代∀∀
++=*田田盗田代代田撮代∀代∀∀田∀∀田盗∀∀∀∀∀∀代盗田∀田田代代∀∀
++**代田盗田田代田代∀代∀∀田盗∀*∀田撮撮盗田代代盗∀∀代代盗代代∀∀
++**田撮盗代盗∀∀∀∀代∀∀撮∀∀*∀∀田田∀∀∀∀∀∀代代田代代∀∀∀
++**∀代撮撮撮撮代田代代代∀撮代∀*∀∀∀∀∀∀代∀∀∀∀∀代田田代代∀
++==∀∀田盗撮撮撮田∀∀∀∀∀∀∀∀∀∀∀∀**∀∀∀∀∀代代田∀***
++===代田田撮田代∀∀∀∀∀∀∀∀代田撮田代**∀代∀∀∀∀代田*==+
++*=*∀代田撮田代∀∀∀∀∀代撮撮盗撮撮撮代∀∀∀∀∀∀∀∀代田+==+
++=+==田代撮田代∀∀∀代∀∀田田代撮代代代代∀∀∀∀∀∀代代田+=++
++=*=**∀代撮代∀∀∀∀∀∀撮田田盗盗盗盗撮撮∀∀∀代∀代撮田==+:
- 453 :ナナシサソ:02/12/03 21:46 ID:DJG/RsmX
- +=*撮撮盗代代∀∀∀∀∀∀∀∀田代*∀∀∀****∀∀∀∀代田盗撮撮撮∀=
+==盗撮田田代代∀∀∀∀∀∀∀∀代*******∀∀∀∀∀∀盗盗撮撮盗==
+=*盗撮田代代代∀∀∀∀∀***∀**∀***∀代∀∀∀∀代田撮撮撮盗=:
++*田撮盗盗代∀∀∀∀∀∀******∀∀代田田代代代∀∀∀∀盗撮撮撮**
++*田撮盗盗∀∀∀∀∀代∀∀∀∀∀∀∀∀∀盗田田代代田撮撮撮盗田撮撮盗∀∀
+=*田撮盗盗代代撮撮撮撮撮撮代代代∀代代田撮撮撮撮盗撮撮撮撮盗撮撮撮田盗田
+:=*撮撮盗代田代田撮撮盗田田∀∀∀田盗撮∀∀田撮田代代代代田代盗田田撮田
++**田撮撮代田田田田代撮撮撮撮撮盗盗田代田田撮撮撮盗代代盗田撮撮田撮∀∀
++=*田撮撮田盗田∀∀∀∀田∀代撮盗盗撮∀代代代代∀∀代∀代代田盗田田∀∀
++=*∀撮盗盗田代撮撮撮撮撮撮代盗田∀撮田∀∀∀∀∀代∀∀田代代盗田代∀∀
++=*田田盗田代代田撮代∀代∀∀田∀∀田盗∀∀∀∀∀∀代盗田∀田田代代∀∀
++**代田盗田田代田代∀代∀∀田盗∀*∀田撮撮盗田代代盗∀∀代代盗代代∀∀
++**田撮盗代盗∀∀∀∀代∀∀撮∀∀*∀∀田田∀∀∀∀∀∀代代田代代∀∀∀
++**∀代撮撮撮撮代田代代代∀撮代∀*∀∀∀∀∀∀代∀∀∀∀∀代田田代代∀
++==∀∀田盗撮撮撮田∀∀∀∀∀∀∀∀∀∀∀∀**∀∀∀∀∀代代田∀***
++===代田田撮田代∀∀∀∀∀∀∀∀代田撮田代**∀代∀∀∀∀代田*==+
++*=*∀代田撮田代∀∀∀∀∀代撮撮盗撮撮撮代∀∀∀∀∀∀∀∀代田+==+
++=+==田代撮田代∀∀∀代∀∀田田代撮代代代代∀∀∀∀∀∀代代田+=++
++=*=**∀代撮代∀∀∀∀∀∀撮田田盗盗盗盗撮撮∀∀∀代∀代撮田==+:
- 454 :ナナシサソ:02/12/03 21:47 ID:DJG/RsmX
- ああっ、もうダメッ!
ぁあ…ウンチ出るっ、ウンチ出ますうっ!!
ビッ、ブリュッ、ブリュブリュブリュゥゥゥーーーーーッッッ!!!
いやああああっっっ!!見ないで、お願いぃぃぃっっっ!!!
ブジュッ!ジャアアアアーーーーーーッッッ…ブシャッ!
ブババババババアアアアアアッッッッ!!!!
んはああーーーーっっっ!!!ウッ、ウンッ、ウンコォォォッッ!!!
ムリムリイッッ!!ブチュブチュッッ、ミチミチミチィィッッ!!!
おおっ!ウンコッ!!ウッ、ウンッ、ウンコッッ!!!ウンコ見てぇっ ああっ、もうダメッ!!はうあああーーーーっっっ!!!
ブリイッ!ブボッ!ブリブリブリィィィィッッッッ!!!!
いやぁぁっ!あたし、こんなにいっぱいウンチ出してるゥゥッ!
ぶびびびびびびびぃぃぃぃぃぃぃっっっっ!!!!ボトボトボトォォッッ!!!
ぁあ…ウンチ出るっ、ウンチ出ますうっ!!
ビッ、ブリュッ、ブリュブリュブリュゥゥゥーーーーーッッッ!!!
いやああああっっっ!!見ないで、お願いぃぃぃっっっ!!!
ブジュッ!ジャアアアアーーーーーーッッッ…ブシャッ!
ブババババババアアアアアアッッッッ!!!!
んはああーーーーっっっ!!!ウッ、ウンッ、ウンコォォォッッ!!!
ムリムリイッッ!!ブチュブチュッッ、ミチミチミチィィッッ!!!
おおっ!ウンコッ!!ウッ、ウンッ、ウンコッッ!!!ウンコ見てぇっ ああっ、もうダメッ!!はうあああーーーーっっっ!!!
ブリイッ!ブボッ!ブリブリブリィィィィッッッッ!!!!
いやぁぁっ!あたし、こんなにいっぱいウンチ出してるゥゥッ!
ぶびびびびびびびぃぃぃぃぃぃぃっっっっ!!!!ボトボトボトォォッッ!!!
ぁあ…ウンチ出るっ、ウンチ出ますうっ!!
ビッ、ブリュッ、ブリュブリュブリュゥゥゥーーーーーッッッ!!!
いやああああっっっ!!見ないで、お願いぃぃぃっっっ!!!
ブジュッ!ジャアアアアーーーーーーッッッ…ブシャッ!
ブババババババアアアアアアッッッッ!!!!
んはああーーーーっっっ!!!ウッ、ウンッ、ウンコォォォッッ
- 455 :ナナシサソ:02/12/03 21:48 ID:DJG/RsmX
- ,A、
/∧\
______//.^.\\______
i_;,____///─\\_____;,_i
/;;/;;;;;;;;;;;;;;;;;//-‐~ ̄ ̄~‐-\;;;;;;;;;;;;;;;;;ヽ;;ヽ
┌‐´‐´‐ ~//_ -‐~/ ̄二二 ̄\~‐-_ヽヽ~‐`‐`‐┐
┌‐ ~ ̄ ヽ~~~~~~~~~──~ ,〜(((((((〜、 ~──~~~~~~~~~/  ̄~ ‐┐
`ー~~~~~~~ヽ´´´´´´´´´´´. ( __((((((__ )````````````/~~~~~~~-´
l:::::::::::::::::::l´~~_~~l.|/^^ヽ)/ ^~ヽ|l~~~~~~~~ll::::::::::::::::::l
l::::::::::::::::::l ー‐ l(|-(//)-(//)-|) ─‐ ll::::::::::::::::::l
l l::::::l l  ̄ ̄ l::| ム、 |:l  ̄ ̄ l.l l:::::l l
,l二.l::::::l二l-‐~ ̄ ̄:::\ |||||| /:: ̄ ̄~‐-l.l二l:::::l二l、
∧ ∧ l;;;;/lトトトトトトトトトトトl__,`l.~~~.l´ヽ- _トトトトトトトトトトl\;;;;l ∧ ∧
( ゚Д゚) /三l/三三三 - ̄::::>:: ヽV/:::/::::::::::ヽ 三三三 \l三ヽ (゚Д゚ )
/ | ──────l\\:ヽ:::;l´/::::/:::::::::::::,:::::ヽ────── | ヽ
___/ / /::::\\l::::V::/_,:_-‐ ´/:::::l \ ヽ__)/
二二◎ / /:::::::::::ヽ-‐:::~ ̄l l ミヽ:::l \ ◎二二l
l l / /:::::::::::::::::::::::::::::::::l<-_ ミヽ::l \ l l
- 456 :ナナシサソ:02/12/03 21:49 ID:DJG/RsmX
- 2ちゃんねるの文字絵はアスキーアートAAではありません。
2ちゃんねるの文字絵はAAでもないのにAAと
嘘の情報を垂れ流すことは犯罪行為です。
■ 文字絵(テキストアートtext art)の内のアメリカのアートがアスキーアートAA asciiartである。
■ 文字絵(テキストアートtext art)の内の日本のアートがJISアートJapanOriginalityartである。
■ テキストアート(文字絵)のジャンルの中の内のひとつがアスキーアートAAである。
■ テキストアート(文字絵)のジャンルの中の内のひとつがascii picturesである。
■ テキストアート(文字絵)のジャンルの中の内のひとつがJISアートである。
■ テキストアート(文字絵)のジャンルの中の内のひとつが顔文字(フェイスマーク)
■ テキストアートtext artとはすべて(世界の文字絵)の文字絵の総称 → 世界共通名。
なぜならば文字(text)絵(art)はすべて(必要条件)→text(文字記号)で作られている由縁。
文字絵(text art)とは それぞれ各々の国の文字(text)環境で作った文字絵(art)のこと。
だから それぞれの国の文字環境でしか作れないし それぞれの国の文字環境でしか
正しく見えないのである。
■ 文字(text ←必要条件)で作った絵(art)のことすべてをテキストアート(text art)と言う。
■ なぜならば文字絵(text art)は それぞれ各々の国の文字記号(text)で出来ている由縁である。
■ テキスト(text)とは→ 文書(文字記号の集合体)のことで制御コードを含まない文字記号列。
■ つまり文字絵(世界の文字絵)は それぞれ各々の国の文字環境でしか見えない作れないのです。
■ つまりアスキーアートは我々日本の漢字カナ混じり環境では正しく見えない作れないのである。
■ アスキーアートはwindowsの英語版(アスキー文字)でしか描けないし英語版でしか見えないのです。我々日本人のパソコンは日本語版でありアスキーアート(AA)を作ることも見ることも出来ません。
- 457 :ナナシサソ:02/12/03 21:50 ID:DJG/RsmX
- □△△△△△△△
,, △△△△△△△△△△△△
/△□¶¶¶¶¶¶¶¶ヾ /¶¶¶¶¶¶¶¶¶△ヽ
/¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶ヽ;:¶¶¶/"""ヾ¶¶¶¶ヽ
/¶¶¶¶¶¶¶¶¶¶¶;:;;:≡≡≡l¶¶/;≡≡' \¶¶¶¶
/¶¶¶¶¶¶¶¶¶¶¶/≡≡≡≡ ■ ヽ¶¶¶¶
¶¶¶¶¶¶¶¶¶¶¶¶¶≡≡≡≡≡≡ ■ ヽ¶¶¶¶¶
/000◯◯○0000≡≡≡≡ミミ■ ≡ 00○○
/00¶¶¶¶¶ ¶¶ ¶ヽ≡≡≡≡≡≡ ▼ ┏━━:¶¶¶0
¶¶¶¶¶¶¶¶¶ ¶¶ ¶/≡≡,,━━━━ミ /≡__ ヽ¶¶¶
¶¶¶¶¶¶¶¶¶ ¶¶ ¶¶≡≡"≡≡≡::: \≡ 《(・)〉'-¶¶¶
¶¶¶¶¶¶¶¶¶ ¶¶ ¶.≡≡ - '"〈 (・)》 ≡|| ≡ ¶¶¶
¶¶¶¶¶¶¶¶ ¶¶ ¶¶|≡≡≡"" ̄ ≡ミ | ミ ¶¶¶
¶¶¶¶¶¶¶ ¶¶ ¶¶ヽ.≡≡≡ミ ( ,-、 〉,:‐、 ¶¶¶
¶¶¶¶¶¶ ¶¶ ¶¶ヾ..ミミミミミミ ¶¶¶
¶¶¶¶¶¶¶ ¶¶ ¶¶ ミミミミミミミ __,-'ニニニヽ . ¶¶¶ きさまら
.. ¶¶¶¶¶¶ ¶¶ ¶¶¶、ヽ≡≡≡≡ミミヾ━━ン" ¶¶¶ 生きて
¶¶¶¶¶¶ ¶¶ ¶¶¶ヽ\≡≡≡≡ミ┗┳ ┛ /¶¶¶¶ 帰れると思うなよ
¶¶¶¶¶¶ ¶¶ ¶¶¶¶ミミ`ー-::、≡≡ミ ■ ,,..¶¶¶¶
- 458 :ナナシサソ:02/12/03 21:51 ID:DJG/RsmX
- | | /,'‐':::/::..;/;;/;:r:::l::: \:;;::|:::: .:|⌒)___) / 砲艦外交を@
r===-、 ̄ /:// :/::../ /| i ヾ ..i|: .::|ー'ヾ \ / 警察庁を斬るA
|r―、| | /:イ:::::i:::/:..::;イ:::./ |. |::..::.|、..::::::| ..:::::::|i 、 \ / 東京藝術大學のB
|;;;;;;;;;|| | |/ |rー|:/i::/,-|- | |;' l ─|、|::::::||:::::::::::::| | トゝ / 小和田は駒井哲郎C
二二ー' |/-|i | | ヽ ,r‐、\:|'|::::i:::::::|ー`y⌒ヽ| / 人権は敵だ熊本県庁D
ヾ::;;:::ノ /::|::::ヽ ,=、 0i |' |:::::|::::::i-、:| / 少担空母機動部隊西大E
 ̄ //::/:::i::| 、 ー' |:::/:::::/ ) l' / 女が、肉体に一糸(いっし)F
|'|::;|::イ:::、'''' ー‐ '''' /;;ノi::;:/イ:| / 纏(まと)わぬと生まれたままG
|/i' |r'' i\ ー' _, イ/::/::/|::;/:| < 姿になっていると、女の裸体H
|ヽ、__ ` ー _'l |;/:;ノ |ノヾ| \ 対して、「下品だ」と吐き捨てI
|  ̄ l / ̄ ̄ ! / \__ \ 輩に、美を語る資格はないJ
| __ | / ヽ _ \ \ 新幹線半島史観北海道K
,|/ __`) |/ ノ  ̄ | \ 当時は難民受け入れL
__________ / //`l_| / / ,r' ̄ 〕___ \ 反対を主張することM
_______/||  ̄ _/7 / / | / r‐ ' ___) \ をできる雰囲気はN
三三|彡|\ ') |O) | (O) | __/ ´ j ̄ト、 \
三三|彡| Tー' ゝ ヾ ,, ヽ〔 __, -' ー'ノ
- 459 :ナナシサソ:02/12/03 21:52 ID:DJG/RsmX
- >>25-63>>64-65>>66-72までの原版は、ズレないようにしたつもりだから、
あとは、台詞(セリフ)を>>25-63>>64-65>>66-72の文字にそって、年賀状用
の台詞(セリフ)入れ直せば、ピッタリと合うはずだよ。
年賀状に合う台詞(セリフ)を入れて、使ってね♪
年賀状に合う台詞(セリフ)を入れて、使ってね♪
>>25-63>>64-65>>66-72までの原版は、ズレないようにしたつもりだから、
あとは、台詞(セリフ)を>>25-63>>64-65>>66-72の文字にそって、年賀状用
の台詞(セリフ)入れ直せば、ピッタリと合うはずだよ。
年賀状に合う台詞(セリフ)を入れて、使ってね♪
年賀状に合う台詞(セリフ)を入れて、使ってね♪
- 460 :ナナシサソ:02/12/03 21:54 ID:DJG/RsmX
- たった今、アパートの天井に向かって「キキのマンコ!キキのマンコ!」と怒鳴ってみました。
反応がありません。
しょうがないので全裸になり、自分の尻を両手でバンバン叩きながら白目をむき
「びっくりするほどユートピア!びっくりするほどユートピア!」
とハイトーンで連呼しながらベットを昇り降りしてみました。
これだけやってもまだ反応がありません。
これを10分程続けると妙な脱力感に襲われ、解脱気分に浸れます。
ヤキソバUFOのカップを舐めつつ「オスでよかった!!オスでよかった!!!」と絶叫。
クローゼットの扉の開け閉めを繰り返ししながら「バーバー、バーバー」と
鳩時計のように首を振りながら言い続けた事がよくある。
この行動に特に意味は無いのだが、自分は実はルンペンではないのかと度々考えることがある.
- 461 :ナナシサソ:02/12/03 21:58 ID:DJG/RsmX
- ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
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[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
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[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
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[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
- 462 :ナナシサソ:02/12/03 22:00 ID:DJG/RsmX
- ハモケム。ァメケサナムエ。テミキテヌァネヨ。ノメクヤ。メテ 猴郢、ヌメチハ
モ、ムュ。メティムエ。ヤィ。テテチハヌムハエヤ。メテタメツ羯ハ霽ケテメェ。メ
テハケヘァケ篦コメツテムーコメナ オメチテミ犲ユツコハモケム。ケメツ。テムー
チケオテユ セ.ネ. 2530 ケヘ。ィメ。ィムエ羯。ナメァ眷鯢 ツムァチヘ
コヘモケメィ耆鯡モケム。セムイケメ。メテネヨ。ノメマ 爐オ。メテネヨ。ノメ
オ靨ァ・キユ鞨サ郢ヒケ霽ツテメェ。メテハ霽ケ。ナメァサッヤコムオヤ
ヒケ鰓キユ鞳ケハ霽ケタルチヤタメ、 莇
鯏霽チ。ヤィ。テテチハヌムハエヤ。メテ爼雹。ムケ
コムエケユ・ハモケム。セムイケメ。メテネヨ。ノメマ 爐オ。メテネヨ。ノメ 7
莇鮟ッヤコムオヤ耆鰲。ヤエチヤオヤ耆チ・羯。テミコヌケ。メティムエ
。ヤィ。テテチハヌムハエヤ。メテ 耆鬘ムコ「鰓テメェ。メテ羯ハムァ
。ムエ 箒ツィムエ。ヤィ。テテチヒメテメツ莇鮖モ爰ヤケキユ鞴エ鯡ル陦
テミコヌケ。メテコテヤヒメティムエ。メテキユ霖ユテミ犲ユツコテヘァテムコ 爍
ヤエ、ヌメチェヘコクテテチキユ靉クヤコメツ莇・ナ鯢ケハ隗シナエ鰓ケ、靨、テヘァェ
ユセ。靉耆鰲。ヤエ「ヌムュ眷ミセナムァ羯。メテサッヤコムオヤヒケ鰓キユ
鞳ケハ霽ケテメェ。メテヘツ靨ァツヤ隗
- 463 :ナナシサソ:02/12/03 22:00 ID:DJG/RsmX
- コムエケユ・ハモケム。セムイケメ。メテネヨ。ノメマ 爐オ。メテネヨ。ノメ 7
莇鮟ッヤコムオヤ耆鰲。ヤエチヤオヤ耆チ・羯。テミコヌケ。メティムエ
。ヤィ。テテチハヌムハエヤ。メテ 耆鬘ムコ「鰓テメェ。メテ羯ハムァ
。ムエ 箒ツィムエ。ヤィ。テテチヒメテメツ莇鮖モ爰ヤケキユ鞴エ鯡ル陦
テミコヌケ。メテコテヤヒメティムエ。メテキユ霖ユテミ犲ユツコテヘァテムコ 爍
ヤエ、ヌメチェヘコクテテチキユ靉クヤコメツ莇・ナ鯢ケハ隗シナエ鰓ケ、靨、テヘァェ
ユセ。靉耆鰲。ヤエ「ヌムュ眷ミセナムァ羯。メテサッヤコムオヤヒケ鰓キユ
鞳ケハ霽ケテメェ。メテヘツ靨ァツヤ隗コムエケユ・ハモケム。セムイケメ。メテネヨ。ノメマ 爐オ。メテネヨ。ノメ 7
莇鮟ッヤコムオヤ耆鰲。ヤエチヤオヤ耆チ・羯。テミコヌケ。メティムエ
。ヤィ。テテチハヌムハエヤ。メテ 耆鬘ムコ「鰓テメェ。メテ羯ハムァ
。ムエ 箒ツィムエ。ヤィ。テテチヒメテメツ莇鮖モ爰ヤケキユ鞴エ鯡ル陦
テミコヌケ。メテコテヤヒメティムエ。メテキユ霖ユテミ犲ユツコテヘァテムコ 爍
ヤエ、ヌメチェヘコクテテチキユ靉クヤコメツ莇・ナ鯢ケハ隗シナエ鰓ケ、靨、テヘァェ
ユセ。靉耆鰲。ヤエ「ヌムュ眷ミセナムァ羯。メテサッヤコムオヤヒケ鰓キユ
鞳ケハ霽ケテメェ。メテヘツ靨ァツヤ隗
- 464 :ナナシサソ:02/12/03 22:04 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
- 465 :ナナシサソ:02/12/03 22:04 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
dgさg
- 466 :ナナシサソ:02/12/03 22:05 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
eat
- 467 :ナナシサソ:02/12/03 22:05 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeee
- 468 :ナナシサソ:02/12/03 22:06 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aaetqqqqqqqqq
- 469 :ナナシサソ:02/12/03 22:06 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
- 470 :ナナシサソ:02/12/03 22:08 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeee333333333333333333333333333333333333333
- 471 :ナナシサソ:02/12/03 22:08 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeee51322222222222222222222222222222222
- 472 :ナナシサソ:02/12/03 22:08 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeeghaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
- 473 :ナナシサソ:02/12/03 22:09 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
- 474 :ナナシサソ:02/12/03 22:09 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhagaga
- 475 :ナナシサソ:02/12/03 22:10 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhageeeeeee
- 476 :ナナシサソ:02/12/03 22:10 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh22222222
- 477 :ナナシサソ:02/12/03 22:10 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhaeetatetat
- 478 :ナナシサソ:02/12/03 22:12 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhag
- 479 :ナナシサソ:02/12/03 22:12 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhaggae
- 480 :ナナシサソ:02/12/03 22:13 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay
- 481 :ナナシサソ:02/12/03 22:13 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452
- 482 :ナナシサソ:02/12/03 22:13 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452aet356
- 483 :ナナシサソ:02/12/03 22:14 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452tate3
- 484 :ナナシサソ:02/12/03 22:14 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452ageagag4
- 485 :ナナシサソ:02/12/03 22:15 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg5
- 486 :ナナシサソ:02/12/03 22:15 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg56
- 487 :ナナシサソ:02/12/03 22:15 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567
- 488 :ナナシサソ:02/12/03 22:16 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqg
- 489 :ナナシサソ:02/12/03 22:16 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
- 490 :ナナシサソ:02/12/03 22:18 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafwe
- 491 :ナナシサソ:02/12/03 22:18 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaegggggggggggggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaa
- 492 :ナナシサソ:02/12/03 22:19 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 493 :ナナシサソ:02/12/03 22:19 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshawr
- 494 :ナナシサソ:02/12/03 22:20 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 495 :ナナシサソ:02/12/03 22:20 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 496 :ナナシサソ:02/12/03 22:24 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw2
- 497 :ナナシサソ:02/12/03 22:24 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \ge{(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw4
- 498 :ナナシサソ:02/12/03 22:25 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 499 :ナナシサソ:02/12/03 22:26 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 500 :ナナシサソ:02/12/03 22:26 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 501 :ナナシサソ:02/12/03 22:28 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrsh
- 502 :ナナシサソ:02/12/03 22:28 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhr
- 503 :ナナシサソ:02/12/03 22:29 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshs
- 504 :ナナシサソ:02/12/03 22:29 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrw
- 505 :ナナシサソ:02/12/03 22:30 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhr
- 506 :ナナシサソ:02/12/03 22:30 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwh
- 507 :ナナシサソ:02/12/03 22:31 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 508 :ナナシサソ:02/12/03 22:32 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsha
- 509 :ナナシサソ:02/12/03 22:32 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\fr}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 510 :ナナシサソ:02/12/03 22:32 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhw
- 511 :ナナシサソ:02/12/03 22:33 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrs
- 512 :ナナシサソ:02/12/03 22:33 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 513 :ナナシサソ:02/12/03 22:34 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw2
- 514 :ナナシサソ:02/12/03 22:34 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^p{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw3
- 515 :ナナシサソ:02/12/03 22:34 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\f{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw4
- 516 :ナナシサソ:02/12/03 22:35 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}rac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw5
- 517 :ナナシサソ:02/12/03 22:36 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw6
- 518 :ナナシサソ:02/12/03 22:36 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensur{(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw7
- 519 :ナナシサソ:02/12/03 22:36 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\fra{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}}\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw8
- 520 :ナナシサソ:02/12/03 22:37 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^rac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw9
- 521 :ナナシサソ:02/12/03 22:38 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwh
- 522 :ナナシサソ:02/12/03 22:38 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaah
- 523 :ナナシサソ:02/12/03 22:39 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsha
- 524 :ナナシサソ:02/12/03 22:39 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 525 :ナナシサソ:02/12/03 22:40 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaegggggggggggggggggggggggggggggggggggggggggg
- 526 :ナナシサソ:02/12/03 22:40 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsha
- 527 :ナナシサソ:02/12/03 22:40 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 528 :ナナシサソ:02/12/03 22:41 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrs
- 529 :ナナシサソ:02/12/03 22:41 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwh
- 530 :ナナシサソ:02/12/03 22:41 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}eq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 531 :ナナシサソ:02/12/03 22:43 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhh
- 532 :ナナシサソ:02/12/03 22:44 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhr
- 533 :ナナシサソ:02/12/03 22:44 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhr
- 534 :ナナシサソ:02/12/03 22:45 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhr
- 535 :ナナシサソ:02/12/03 22:45 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaa
- 536 :ナナシサソ:02/12/03 22:46 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhr
- 537 :ナナシサソ:02/12/03 22:48 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshs
- 538 :ナナシサソ:02/12/03 22:48 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaer
- 539 :ナナシサソ:02/12/03 22:49 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwh
- 540 :ナナシサソ:02/12/03 22:50 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\fr{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 541 :ナナシサソ:02/12/03 22:50 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhr
- 542 :ナナシサソ:02/12/03 22:51 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerh
- 543 :ナナシサソ:02/12/03 22:51 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrs
- 544 :ナナシサソ:02/12/03 22:52 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1es ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 545 :ナナシサソ:02/12/03 22:56 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 546 :ナナシサソ:02/12/03 22:57 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 547 :ナナシサソ:02/12/03 22:58 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 548 :ナナシサソ:02/12/03 22:59 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshs
- 549 :ナナシサソ:02/12/03 22:59 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhw
- 550 :ナナシサソ:02/12/03 23:01 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwah
- 551 :ナナシサソ:02/12/03 23:01 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrsh
- 552 :ナナシサソ:02/12/03 23:01 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwh
- 553 :ナナシサソ:02/12/03 23:02 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrsh
- 554 :ナナシサソ:02/12/03 23:02 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrh
- 555 :ナナシサソ:02/12/03 23:03 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrsh
- 556 :ナナシサソ:02/12/03 23:03 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrw
- 557 :ナナシサソ:02/12/03 23:04 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrh
- 558 :ナナシサソ:02/12/03 23:05 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 559 :ナナシサソ:02/12/03 23:07 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsha
- 560 :ナナシサソ:02/12/03 23:07 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrsh
- 561 :ナナシサソ:02/12/03 23:08 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsha
- 562 :ナナシサソ:02/12/03 23:08 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhh
- 563 :ナナシサソ:02/12/03 23:09 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ es ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 564 :ナナシサソ:02/12/03 23:09 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhr
- 565 :ナナシサソ:02/12/03 23:11 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 566 :ナナシサソ:02/12/03 23:11 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\fra})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 567 :ナナシサソ:02/12/03 23:12 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahr
- 568 :ナナシサソ:02/12/03 23:14 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 569 :ナナシサソ:02/12/03 23:15 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 570 :ナナシサソ:02/12/03 23:15 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshs
- 571 :ナナシサソ:02/12/03 23:16 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrw
- 572 :ナナシサソ:02/12/03 23:17 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^c{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 573 :ナナシサソ:02/12/03 23:20 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrsh
- 574 :ナナシサソ:02/12/03 23:21 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}ures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 575 :ナナシサソ:02/12/03 23:22 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 576 :ナナシサソ:02/12/03 23:22 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 577 :ナナシサソ:02/12/03 23:23 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhr
- 578 :ナナシサソ:02/12/03 23:23 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 579 :ナナシサソ:02/12/03 23:25 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \ge}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 580 :ナナシサソ:02/12/03 23:25 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 581 :ナナシサソ:02/12/03 23:27 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \ge)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 582 :ナナシサソ:02/12/03 23:27 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 583 :ナナシサソ:02/12/03 23:27 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2 \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 584 :ナナシサソ:02/12/03 23:28 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 585 :ナナシサソ:02/12/03 23:28 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaegggggggggggggggggggggggggggggggggggggggaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 586 :ナナシサソ:02/12/03 23:29 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 587 :ナナシサソ:02/12/03 23:33 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 588 :ナナシサソ:02/12/03 23:33 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsha
- 589 :ナナシサソ:02/12/03 23:34 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 590 :ナナシサソ:02/12/03 23:36 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 591 :ナナシサソ:02/12/03 23:36 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\f{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 592 :ナナシサソ:02/12/03 23:36 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}{(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 593 :ナナシサソ:02/12/03 23:39 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 594 :ナナシサソ:02/12/03 23:40 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 595 :ナナシサソ:02/12/03 23:40 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})rac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} ^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 596 :ナナシサソ:02/12/03 23:41 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 597 :ナナシサソ:02/12/03 23:42 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 598 :ナナシサソ:02/12/03 23:42 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 599 :ナナシサソ:02/12/03 23:43 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 600 :ナナシサソ:02/12/03 23:43 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\f$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 601 :ナナシサソ:02/12/03 23:45 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 602 :ナナシサソ:02/12/03 23:45 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fr{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 603 :ナナシサソ:02/12/03 23:45 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 604 :ナナシサソ:02/12/03 23:45 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 605 :ナナシサソ:02/12/03 23:46 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ esures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 606 :ナナシサソ:02/12/03 23:46 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \ge 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} c{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 607 :ナナシサソ:02/12/03 23:47 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frc{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 608 :ナナシサソ:02/12/03 23:47 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 609 :ナナシサソ:02/12/03 23:47 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 610 :ナナシサソ:02/12/03 23:49 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 611 :ナナシサソ:02/12/03 23:49 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 612 :ナナシサソ:02/12/03 23:50 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$es ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 613 :ナナシサソ:02/12/03 23:50 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ enss ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 614 :ナナシサソ:02/12/03 23:50 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 615 :ナナシサソ:02/12/03 23:52 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 616 :ナナシサソ:02/12/03 23:53 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 617 :ナナシサソ:02/12/03 23:53 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 618 :ナナシサソ:02/12/03 23:54 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrsh
- 619 :ナナシサソ:02/12/03 23:55 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 620 :ナナシサソ:02/12/03 23:55 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 621 :ナナシサソ:02/12/03 23:57 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 622 :ナナシサソ:02/12/03 23:58 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 623 :ナナシサソ:02/12/03 23:58 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensus ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 624 :ナナシサソ:02/12/03 23:59 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshs
- 625 :ナナシサソ:02/12/03 23:59 ID:DJG/RsmX
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrh
- 626 :ナナシサソ:02/12/04 00:00 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 627 :ナナシサソ:02/12/04 00:00 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 628 :ナナシサソ:02/12/04 00:01 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}es ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 629 :ナナシサソ:02/12/04 00:05 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 630 :ナナシサソ:02/12/04 00:05 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 631 :ナナシサソ:02/12/04 00:05 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsha
- 632 :ナナシサソ:02/12/04 00:08 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 633 :ナナシサソ:02/12/04 00:08 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 634 :ナナシサソ:02/12/04 00:09 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 635 :ナナシサソ:02/12/04 00:10 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhwhrwhrhhrshshaw1
- 636 :ナナシサソ:02/12/04 00:11 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 637 :ナナシサソ:02/12/04 00:11 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 638 :ナナシサソ:02/12/04 00:11 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 639 :ナナシサソ:02/12/04 00:13 ID:pfLzQlnP
- 謎
- 640 :ナナシサソ:02/12/04 00:13 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 641 :ナナシサソ:02/12/04 00:13 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 642 :ナナシサソ:02/12/04 00:15 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r eq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 643 :ナナシサソ:02/12/04 00:15 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 644 :ナナシサソ:02/12/04 00:15 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 645 :ナナシサソ:02/12/04 00:18 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 646 :ナナシサソ:02/12/04 00:19 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 647 :ナナシサソ:02/12/04 00:19 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^fra{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 648 :ナナシサソ:02/12/04 00:22 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 649 :ナナシサソ:02/12/04 00:22 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 650 :ナナシサソ:02/12/04 00:23 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 651 :ナナシサソ:02/12/04 00:32 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 652 :ナナシサソ:02/12/04 00:32 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 653 :ナナシサソ:02/12/04 00:32 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 654 :ナナシサソ:02/12/04 00:35 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 655 :ナナシサソ:02/12/04 00:35 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 656 :ナナシサソ:02/12/04 00:35 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsh
- 657 :ナナシサソ:02/12/04 00:37 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 658 :ナナシサソ:02/12/04 00:37 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 659 :ナナシサソ:02/12/04 00:37 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geqr}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 660 :ナナシサソ:02/12/04 00:39 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 661 :ナナシサソ:02/12/04 00:39 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshsha
- 662 :ナナシサソ:02/12/04 00:39 ID:dgTWQMkP
- 晒しage
- 663 :ナナシサソ:02/12/04 00:40 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 664 :ナナシサソ:02/12/04 00:42 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 665 :ナナシサソ:02/12/04 00:42 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw
- 666 :ナナシサソ:02/12/04 00:45 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 667 :ナナシサソ:02/12/04 00:49 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
- 668 :ナナシサソ:02/12/04 00:51 ID:pfLzQlnP
- ${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p
\geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}}
B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{
2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}}}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$
ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $
(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$
for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac
{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^
{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\fr
ac{1}{q}}$ ensures ${(A^{\frac{r}{2}} A^pA^{\frac{r}{2}})}^fra\geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})}^frac{1}{q}}$ for $p \geq 0, q \geq 1, r \
geq 0$ with $(1+r)q${(A \geq B \geq 0)}^{\frac{1}{q}}$ ensures ${(A^{\c{r}{2}} A^pA^{\frac{r}{2}})}^frac{1}{q}} \geq {(A^{\frac{r}{2}} B^pA^{\frac{r}{2}})
aeeeeeeeeeeeeeeeeeehaqhreahreahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhayeayeay32452etaegaeggaeg567tgageeqgqgaerrrrrrrrrrrrr
afafweaegeaegeagaeggggggggggggggggggggggggggggggggggggggggggggggggeaaaaaaaaaahaerhrhrwahrwhrwhwhrwhrhhrshshaw1
502 KB
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read.cgi ver 05.04.02 2018/11/22 Walang Kapalit ★
FOX ★ DSO(Dynamic Shared Object)