Related papers: Detecting discrete integrability: the singularity …
We study open-closed discrete mappings that satisfy the weighted estimate of the distortion of modulus of families of paths. It is proved that the mappings mentioned above have a continuous extension into the isolated point of the boundary,…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
We construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The…
Using Lipman's results on resolution of two-dimensional singularities, we provide a form of resolution of singularities in codimension two for reduced quasi-excellent schemes. We deduce that operations of degree less than two on algebraic…
The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
In reliability-based design, the estimation of the failure probability is a crucial objective. However, focusing only on the occurrence of the failure event may be insufficient to entirely characterize the reliability of the considered…
In this paper a second order dynamical system model is proposed for computing a zero of a maximal comonotone operator in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of a strong global solution of the proposed…
This paper is the second part of a two part paper which introduces the study of the Whitney Equisingularity of families of Symmetric determinantal singularities. This study reveals how to use the multiplicity of polar curves associated to a…
The main question we target is the following: If one fixes a topological type of a complex normal surface singularity then what are the possible analytic types supported by it, and/or, what are the possible values of the geometric genus? We…
This short survey presents the essential features of what is called Painlev\'e analysis, i.e. the set of methods based on the singularities of differential equations in order to perform their explicit integration. Full details can be found…
We develop a monotone, two-scale discretization for a class of integrodifferential operators of order $2s$, $s \in (0,1)$. We apply it to develop numerical schemes, and derive pointwise convergence rates, for linear and obstacle problems…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
We study the non-selfadjoint Dirac system on the line having an non-integrable regular singularity in an interior point with additional matching conditions at the singular point. Special fundamental systems of solutions are constructed with…
Modern autonomous systems with machine learning components often use uncertainty quantification to help produce assurances about system operation. However, there is a lack of consensus in the community on what uncertainty is and how to…
We introduce a series of discrete mappings, which is considered to be an extension of the Hietarinta-Viallet mapping with one parameter. We obtain the algebraic entropy for this mapping by obtaining the recurrence relation for the degrees…