Related papers: Multiple zeros of nonlinear systems
In this article we examine the multiplicity of non-negative solutions to mixed local-nonlocal equations involving \((-\Delta_p) + (-\Delta^{s}_{q})\) in a bounded smooth domain. The nonlinearity incorporates a parameter \(\lambda > 0\), a…
We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another.…
Root multiplicities encode information about the structure of Kac-Moody algebras, and appear in applications as far-reaching as string theory and the theory of modular functions. We provide an algorithm based on the Peterson recurrence…
In this paper, tall discrete-time linear systems with multirate outputs are studied. In particular, we focus on their zeros. In systems and control literature zeros of multirate systems are defined as those of their corresponding…
The multiplicity of an algebraic curve $C$ in the complex plane at a point $p$ on that curve is defined as the number of points that occur at the intersection of $C$ with a general complex line that passes close to the point $p$. It is…
We investigate the performance of algebraic multigrid methods for the solution of the linear system of equations arising from a Virtual Element discretization. We provide numerical experiments on very general polygonal meshes for a model…
Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea…
In this paper we show some multiplicity estimates theorems for a connected algebraic group (not necessarily commutative) $G$ over an algebraically closed subfield of $\mathbb{C}$. More specifically, under particular assumptions on the…
We describe how to compute topological objects associated to a polynomial map of several complex variables with isolated singularities. These objects are: the affine critical values, the affine Milnor numbers for all irregular fibers, the…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
Let $A$ be an algebra over any field. We do not assume that $A$ has an identity. The \emph{multiplier algebra} $M(A)$ is a unital algebra associated to $A$. If we require the product in $A$ to be non-degenerate (as a bilinear form), the…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
Arclength continuation and branch switching are enormously successful algorithms for the computation of bifurcation diagrams. Nevertheless, their combination suffers from three significant disadvantages. The first is that they attempt to…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
This article discusses the geometric application of the method of multiplier ideal sheaves. It first briefly describes its application to effective problems in algebraic geometry and then presents and explains its application to the…
A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…
F.~Schweiger introduced the fibred system in \cite{Schweiger-MCF}, to unify and generalize many known continued fraction algorithms. An advantage of a fibred system is that it often provides a systematic construction of absolutely…
We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
We consider the problem of multiplicity and uniqueness of radial solutions of a nonlinear elliptic equation of the form \begin{eqnarray*} \begin{gathered} \Delta u +f(u)=0,\quad x\in \mathbb{R}^N, N\geq 2, \lim\limits_{|x|\to\infty}u(x)=0.…