現代数学の系譜 工学物理雑談 古典ガロア理論も読む47at MATH
現代数学の系譜 工学物理雑談 古典ガロア理論も読む47
- 暇つぶし2ch533:e, Frantz investigates the Hausdorff dimension of the graphs of f^r. THEOREM 1: If r > 2, then the Hausdorff dimension of the non-differentiability set for f^r is 2/r.” 一方、 ”[18] Richard Brian Darst and Gerald D. Taylor, "Differentiating Powers of an Old Friend", American Mathematical Monthly 103 #5 (May 1996), 415-416. [MR1400724; Zbl 861.26002] Define f:R --> R by f(x) = 0 if x is irrational or zero, and f(p/q) = 1/q for p,q relatively prime with q > 0. They note that the set of points at which f is not continuous is the set of nonzero rational numbers. THEOREM: If 1 < r <= 2, then f^r is differentiable only at zero. If r > 2, then f^r is differentiable almost everywhere (Lebesgue measure).” だから、[18] からすると、If r > 2, then f^r is differentiable almost everywhere (Lebesgue measure).→Hausdorff dimension =1 で、"1 - 2/r(>>285)"ではないのでは? つづく
次ページ続きを表示1を表示最新レス表示レスジャンプ類似スレ一覧スレッドの検索話題のニュースおまかせリストオプションしおりを挟むスレッドに書込スレッドの一覧暇つぶし2ch