[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ17 (1002ﾚｽ)

ガロア第一論文と乗数イデアル他関連資料スレ17 http://rio2016.5ch.net/test/read.cgi/math/1746597368/

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425: 現代数学の系譜 雑談 ◆yH25M02vWFhP [] 2025/05/17(土) 15:35:34.73 ID:y2zepp9J これ 面白い 貼っておきます https://www.researchgate.net/publication/233525067_Modifications_of_Thomae's_Function_and_Differentiability Modifications of Thomae's Function and Differentiability June 2009 The American Mathematical Monthly 116(6):531-535 Kevin Beanland James W. Roberts Craig Stevenson Download full^text Abstract In 1875, K. J. Thomae discovered the now-famous example of a real-valued function that is continuous on the irrationals and not continuous on the rationals. This function is presented in many undergraduate real analysis courses and is known, to some, as the 'popcorn' function. It is not difficult to see that Thomae's function is not differentiable anywhere. The question we examine here is whether it can be modified to be differentiable on some subset of the irrationals. The answer may surprise you—it certainly surprised us. http://rio2016.5ch.net/test/read.cgi/math/1746597368/425

457: 現代数学の系譜 雑談 ◆yH25M02vWFhP [] 2025/05/19(月) 14:46:26.37 ID:q68wgaXf つづき (参考) https://ja.wikipedia.org/wiki/%E3%83%87%E3%82%A3%E3%83%AA%E3%82%AF%E3%83%AC%E3%81%AE%E9%96%A2%E6%95%B0 ディリクレの関数 https://ja.wikipedia.org/wiki/%E3%83%88%E3%83%9E%E3%82%A8%E9%96%A2%E6%95%B0 トマエ関数 https://en.wikipedia.org/wiki/Thomae%27s_function Thomae's function References 1. Beanland, Kevin; Roberts, James W.; Stevenson, Craig (2009), "Modifications of Thomae's Function and Differentiability", The American Mathematical Monthly, 116 (6): 531–535, doi:10.4169/193009709x470425, JSTOR 40391145 (上記 1の表題など から再検索すると 全文が読めるサイトが見つかる（>>425でも貼ったが）) https://www.researchgate.net/publication/233525067_Modifications_of_Thomae's_Function_and_Differentiability Modifications of Thomae's Function and Differentiability ResearchGate 2016/08/05 — ... Modifications of Thomae's Function and Differentiability. June 2009 ... Mathematical Monthly. Kevin Beanland · James W. Roberts · Craig Stevenson. （なお、検索で ”Mathematical Statistics”の補足資料で ”(b) A continuous function is determined by its values on any dense subset of R (in other words: if D is a dense subset of R and if two continuous functions f,g are equal on D, then they must be equal on R, so f = g).” 　と出てくる。突然で不思議な気がする。面白がっているのか？ ；ｐ） https://helios2.mi.parisdescartes.fr/~tleble/teaching/MathStatS19/ Mathematical Statistics - MATH-UA.0234 (Spring 2019) Course description: An introduction to statistics, on the mathematical side. Sessions Jan 29: Logistics and introduction. Definition of a statistical model, a statistic, an estimator. Reminders on probability distributions. Sections 6.1--6.2. A note on the distinction between parametric/non-parametric models (reading is optional).（これか下記のPDF） https://helios2.mi.parisdescartes.fr/~tleble/teaching/MathStatS19/additional/continuousisparametric.pdf (抜粋) （Perhaps surprisingly, the following result is true:） 2. Given a function f in C0(R,R), we may encode it by only keeping track of its values on Q, instead of R. This is because: (a) The rational numbers are dense in R (in other words: every real number is a limit of a sequence of rational numbers). (b) A continuous function is determined by its values on any dense subset of R (in other words: if D is a dense subset of R and if two continuous functions f,g are equal on D, then they must be equal on R, so f = g). (引用終り) 以上 http://rio2016.5ch.net/test/read.cgi/math/1746597368/457

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