Здравейте,
На 5 януари 2026 г. (понеделник) от 14:15 ч. в аудитория 501 на ФМИ ще се проведе сбирка на Семинара по оптимизация.
Докладчик: Cheng-Han Pan, Department of Mathematics and Statistics, Mount Holyoke College, South Hadley, Massachusetts, United States
Тема: Differentiable Monsters and Set of Monstrous Shift
Резюме: “Monsters! An outrage against common sense. An arrogant distraction,and of little use to the subject.” In this talk, we begin with a few
historical remarks on the well-known Weierstrass monster and then breed a
differentiable monster that is at once “rugged” and “smooth.” In particular,
given a strictly increasing differentiable function f : R → R whose derivative
vanishes on a dense subset of R, Ciesielski showed that there is at least a
comeager amount of t ∈ R such that f(x) − f(x − t) is nowhere-monotone.
Moreover, we show that the set of shifts for which the difference is nowhere
monotone is not only comeager but also has full Lebesgue measure in R. Interestingly, we also provide a specific pair of strictly increasing differentiable
functions φ, ψ: R → R such that φ(x)−ψ(x−t) is nowhere-monotone for every
t ∈ R.
Библиография:
[1] Krzysztof Chris Ciesielski, Monsters in calculus, Amer. Math. Monthly 125 (2018), no. 8,
739–744, DOI 10.1080/00029890.2018.1502011. MR3859646
[3] Cheng-Han Pan, Nowhere-monotone differentiable functions and set of monstrous shift, J.
Math. Anal. Appl. 525 (2023), no. 2, Paper No. 127176, DOI 10.1016/j.jmaa.2023.127176.
MR4559372
Каним всички интересуващи се!
С пожелание за светли коледни празници и щастлива и успешна нова година,
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