相关论文: The partial-fractions method for counting solution…

This paper shows how partial differential problems can be solved thanks to cellular computing and an adaptation of the Least Squares Finite Elements Method. As cellular computing can be implemented on distributed parallel architectures,…

We present a method of computing the generating function $f_P(\x)$ of $P$-partitions of a poset $P$. The idea is to introduce two kinds of transformations on posets and compute $f_P(\x)$ by recursively applying these transformations. As an…

Wilf's Sixth Unsolved Problem asks for any interesting properties of the set of partitions of integers for which the (nonzero) multiplicities of the parts are all different. We refer to these as \emph{Wilf partitions}. Using $f(n)$ to…

Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…

We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…

This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…

In this paper, we create a systematic and automatic procedure for transforming the integer factorization problem into the problem of solving a system of Boolean equations. Surprisingly, the resulting system of Boolean equations takes on a…

In this paper, we propose a numerical method of computing a Hadamard finite-part integral with a non-integral power singularity at an endpoint, that is, a finite part of a divergent integral as a limiting procedure. In the proposed method,…

We consider the task of approximating a matrix function $f(A)$, where $A$ is a matrix in which only a relatively small number of (not necessarily consecutive) sub- and superdiagonals contain nonzero entries. Approximating $f$ by a…

In this paper we describe the efficient numerical implementation of Fractional HBVMs, a class of methods recently introduced for solving systems of fractional differential equations. The reported arguments are implemented in the Matlab code…

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

In this paper, we introduce the new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations. We begin…

Recently, fractional differential equations have been investigated via the famous variational iteration method. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to…

The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…

Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…

Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an…

We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…