相关论文: Elimination of unknowns for systems of algebraic d…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
In this paper, we consider the problem of local parameter identifiability of a parameter function in a system of ordinary differential equations. Previously, in this problem, the case where the dimensions of a parameter and a solution of a…
Causal functions of sequences occur throughout computer science, from theory to hardware to machine learning. Mealy machines, synchronous digital circuits, signal flow graphs, and recurrent neural networks all have behaviour that can be…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
The criterion of differentiability of functions of quaternion variable is used as the basis of some algebraic field theory. Its necessary consequences are free Maxwell and Yang-Mills equations. The differentiability equations may be…
We study a notion of indecomposability in differential algebraic groups which is inspired by both model theory and differential algebra. After establishing some basic definitions and results, we prove an indecomposability theorem for…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
We describe explicit algorithms for factoring q-difference operators and solving q-difference equations. These are well known results, presented in a "concrete" form. ----- Nous decrivons des algorithmes explicites pour la factorisation…
Given an algebraic difference equation of the form \[\sigma^n(y)=f\big(y, \sigma(y),\dots,\sigma^{n-1}(y)\big)\] where $f$ is a rational function over a field $k$ of characteristic zero on which $\sigma$ acts trivially, it is shown that if…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given property if and only if it has this property with respect to…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…