Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
関数方程式のあやしい世界
Search
Yoriyuki Yamagata
April 13, 2019
Science
0
740
関数方程式のあやしい世界
関数方程式の闇
Yoriyuki Yamagata
April 13, 2019
Tweet
Share
More Decks by Yoriyuki Yamagata
See All by Yoriyuki Yamagata
科学の虚構主義的解釈と祖先以前性の問題
yoriyuki
1
240
5分で分る直観主義数学
yoriyuki
0
570
算道 − 古代・中世日本の数学 -
yoriyuki
1
720
指数関数は存在しないという話
yoriyuki
0
380
Other Decks in Science
See All in Science
点群ライブラリPDALをGoogleColabにて実行する方法の紹介
kentaitakura
1
390
Cross-Media Technologies, Information Science and Human-Information Interaction
signer
PRO
3
31k
データベース11: 正規化(1/2) - 望ましくない関係スキーマ
trycycle
PRO
0
940
ランサムウェア対策にも考慮したVMware、Hyper-V、Azure、AWS間のリアルタイムレプリケーション「Zerto」を徹底解説
climbteam
0
110
白金鉱業Meetup Vol.16_数理最適化案件のはじめかた・すすめかた
brainpadpr
4
2k
CV_3_Keypoints
hachama
0
200
安心・効率的な医療現場の実現へ ~オンプレAI & ノーコードワークフローで進める業務改革~
siyoo
0
320
Machine Learning for Materials (Challenge)
aronwalsh
0
330
Hakonwa-Quaternion
hiranabe
1
130
データベース09: 実体関連モデル上の一貫性制約
trycycle
PRO
0
990
Masseyのレーティングを用いたフォーミュラレースドライバーの実績評価手法の開発 / Development of a Performance Evaluation Method for Formula Race Drivers Using Massey Ratings
konakalab
0
190
Quelles valorisations des logiciels vers le monde socio-économique dans un contexte de Science Ouverte ?
bluehats
1
490
Featured
See All Featured
Building Better People: How to give real-time feedback that sticks.
wjessup
368
19k
個人開発の失敗を避けるイケてる考え方 / tips for indie hackers
panda_program
112
20k
Automating Front-end Workflow
addyosmani
1370
200k
The Illustrated Children's Guide to Kubernetes
chrisshort
48
50k
Optimizing for Happiness
mojombo
379
70k
Art, The Web, and Tiny UX
lynnandtonic
303
21k
Chrome DevTools: State of the Union 2024 - Debugging React & Beyond
addyosmani
7
840
CSS Pre-Processors: Stylus, Less & Sass
bermonpainter
358
30k
Java REST API Framework Comparison - PWX 2021
mraible
33
8.8k
KATA
mclloyd
32
14k
Building a Scalable Design System with Sketch
lauravandoore
462
33k
ReactJS: Keep Simple. Everything can be a component!
pedronauck
667
120k
Transcript
͜ͷΑ͏ͳfΛͯ͢ٻΊΑ f(x) = x͕Ұͭͷղ͕ͩ… ؔํఔࣜ f(x + y) = f(x)
+ f(y) f(1) = 1
ղ ଞʹղʁ f(x) + f(y) = f(x + y +
2f(xy)) f: ℝ≥0 → ℝ≥0 f(x) = 0 and f(x) = x
ఆཧ f͕࿈ଓͳΒɺղ f(x) = 0 ·ͨ f(x) = x
ิ̍ f͕୯ࣹͳΒf(x)=√x f(x) + f(y) + f(1) = f(x +
y + 1 + 2f(y) + 2f(xy + x + 2xf(y)) f(x) + f(y) + f(1) = f(x + y + 1 + 2f(xy) + 2f(x) + 2f(y)) ূ໌ɿ f͕୯ࣹΑΓ f(xy + x + 2xf(y)) = f(xy) + f(x) = f(xy + x + 2f(x2y)) ∴ f(x2y) = xf(y) ∴ f(x) = f(1) x
ิ̎ f(x)x͕૿Ճͨ͠ͱ͖ݮগ͠ͳ͍ t ↦ t + 2f(xt) ҙͷਖ਼ͷ࣮Λͭ ূ໌ɿ Αͬͯy>xʹରͯ͋͠Δt͕ଘࡏͯ͠
f(y) = f(x + t + 2f(xt)) = f(x) + f(t) ≥ f(x)
ఆཧͷূ໌ ͋͠ΔaͰf(a) = 0ͳΒ f(2a) ≤ f(2a + 2f(a2)) =
2f(a) = 0 fݮগ͠ͳ͍͔Βɺf߃తʹ̌ɻ ͦ͏Ͱͳ͍ͱ͢Δɻิ̎ͷূ໌ͱಉ༷ʹ ҙͷy>xʹ͍ͭͯɺ͋Δt͕͋ͬͯy-x = t + f(tx) f(y) = f(x + t + f(tx)) = f(x) + f(t) > f(x) Αͬͯf୯ௐ૿େɻิ̍ΑΓ
ະղܾ f͕ҰൠͷؔͩͬͨΒʁ