On One Class of Singular Nowhere Monotone Functions
نویسندگان
چکیده
We construct a continuous nowhere monotone function that depends on infinitely many parameters such the derivative of this is equal to zero almost everywhere (in sense Lebesgue measure). It shown well-defined and monotone. Its differential properties are analyzed, massiveness level sets studied, set maxima minima its structural variational determined.
منابع مشابه
On copositive Lyapunov functions for a class of monotone systems
This paper considers several explicit formulas for the construction of copositive Lyapunov functions for global asymptotic stability with respect to monotone systems evolving in either discrete or continuous time. Such monotone systems arise as comparison systems in the study of interconnected large-scale nominal systems. A copositive Lyapunov function for such a comparison system can then serv...
متن کاملstudy of hash functions based on chaotic maps
توابع درهم نقش بسیار مهم در سیستم های رمزنگاری و پروتکل های امنیتی دارند. در سیستم های رمزنگاری برای دستیابی به احراز درستی و اصالت داده دو روش مورد استفاده قرار می گیرند که عبارتند از توابع رمزنگاری کلیددار و توابع درهم ساز. توابع درهم ساز، توابعی هستند که هر متن با طول دلخواه را به دنباله ای با طول ثابت تبدیل می کنند. از جمله پرکاربردترین و معروف ترین توابع درهم می توان توابع درهم ساز md4, md...
Singular values of convex functions of matrices
Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
متن کاملEverywhere Continuous Nowhere Differentiable Functions
Here I discuss the use of everywhere continuous nowhere differentiable functions, as well as the proof of an example of such a function. First, I will explain why the existence of such functions is not intuitive, thus providing significance to the construction and explanation of these functions. Then, I will provide a specific detailed example along with the proof for why it meets the requireme...
متن کاملFunctions Whose Composition with Baire Class One Functions Are Baire Class One
We study the functions whose composition with Baire class one functions are Baire class one functions. We first prove some characterizations of such functions, then investigate a subclass of such functions which are defined in a natural way.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-05925-6