Related papers: Fonction constante et d\'eriv\'ee nulle : un r\'es…

We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…

We present several Liouville type results for the $p$-Laplacian in $\R^N$. Suppose that $h$ is a nonnegative regular function such that $$ h(x) = a|x|^\gamma\ {\rm for}\ |x|\ {\rm large},\ a>0\ {\rm and}\ \gamma> -p. $$ We obtain the…

In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a…

The aim of this expository article is to present recent developments in the centuries old discussion on the interrelations between continuous and differentiable real valued functions of one real variable. The truly new results include,…

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…

The smooth function reconstruction needs to use derivatives. In 2010, we used the gradually varied derivatives to successfully constructed smooth surfaces for real data. We also briefly explained why the gradually varied derivatives are…

The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with…

We construct an algebra of dimension $2^{\aleph_0}$ consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain…

In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool,…

We prove that convex functions of finite order on the real line and subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some set of zero relative Lebesgue density, are bounded from above…

Godel's theory T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0, the successor function S, and the operator R_tau for primitive recursion on objects of type tau. It is known that…

A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$. This notion provides a basis for an algebraic study of transducers, and was integral to the…

In this paper we consider the question of smoothness of slowly varying functions satisfying the modern definition that, in the last two decades, gained prevalence in the applications concerning function spaces and interpolation. We show,…

We construct and study the class of continuous on $[0, 1]$ functions with continuum set of peculiarities (singular, nowhere monotonic, and non-differentiable functions are among them). The representative of this class is the function…

In this short note we give a proof of Liouville's theorem (every bounded entire complex function is constant) following Peterzil and Starchenko's approach to complex analysis via o-minimality.

The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so…

Existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. In this paper, we…

The purpose of this paper is to introduce the notion of a generalized derivation which derivates a prescribed family of smooth vector-valued functions of several variables. The basic calculus rules are established and then a result derived…

The paper is devoted to the conjecture that an equation is Darboux integrable if and only if it possesses symmetries depending on arbitrary functions. We note that results of previous works together prove this conjecture for scalar partial…