相关论文: On one nearly everywhere continuous and nowhere di…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
Very recently, a new concept called multiplicative differential (and the corresponding $c$-differential uniformity) was introduced by Ellingsen \textit{et al} in [C-differentials, multiplicative uniformity and (almost) perfect…
Given cell-average data values of a piecewise smooth bivariate function $f$ within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. We are interested in an explicit and global (smooth) approach. Bivariate…
We establish an explicit link between depth-3 formulas and one-sided approximation by depth-2 formulas, which were previously studied independently. Specifically, we show that the minimum size of depth-3 formulas is (up to a factor of n)…
The Takagi function is a classical example of a continuous nowhere differentiable function. In this paper we prove that it is nowhere approximately derivable.
{We explore a simple {\it geometric model} for functions between spaces of the same dimension (in infinite dimensions, we require that Jacobians be Fredholm operators of index zero). The model combines standard results in analysis and…
The paper demonstrates the basic properties of the local fractional variation operators (termed fractal variation operators). The action of the operators is demonstrated for local characterization of Holderian functions. In particular, it…
We consider the following conjecture (from Huang, et al): Let $\Delta^+$ denote the upper half disc in $\mathbb{C}$ and let $\gamma = ( - 1, 1)$ (viewed as an interval in the real axis in $\mathbb{C}$). Assume that $F$ is a holomorphic…
Motivated by applications to image reconstruction, in this paper we analyse a \emph{finite-difference discretisation} of the Ambrosio-Tortorelli functional. Denoted by $\varepsilon$ the elliptic-approximation parameter and by $\delta$ the…
A unified fast time-stepping method for both fractional integral and derivative operators is proposed. The fractional operator is decomposed into a local part with memory length $\Delta T$ and a history part, where the local part is…
We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…
In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties…
In a previous paper we produced a complex iteration of a holomorphic function $\phi$ in the immediate basin of a fixed point whose multiplier is a real number and in between zero and one. We further explore this problem, allowing the…
There are many functions which are continuous everywhere but not differentiable at some points, like in physical systems of ECG, EEG plots, and cracks pattern and for several other phenomena. Using classical calculus those functions cannot…
This paper gives the pointwise H\"older (or multifractal) spectrum of continuous functions on the interval $[0,1]$ whose graph is the attractor of an iterated function system consisting of $r\geq 2$ affine maps on $\mathbb{R}^2$. These…
The aim of this paper is to study the problem of existence of remotely almost periodic solutions for the scalar differential equation $x'=f(t,x),$ where $f:\mathbb R\times \mathbb R\to \mathbb R$ is a continuous, monotone in $x$ and…
Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…
We study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have…
Let $\mathcal{V}_p(\lambda)$ be the collection of all functions $f$ defined in the unit disc $\ID$ having a simple pole at $z=p$ where $0<p<1$ and analytic in $\ID\setminus\{p\}$ with $f(0)=0=f'(0)-1$ and satisfying the differential…
In this article we provide existence, uniqueness and regularity results of a degenerate singular elliptic boundary value problem whose prototype is given by \begin{gather*} \begin{cases} -\operatorname{div}(w(x)|\nabla u|^{p-2}\nabla…