Related papers: Infinitely many solutions for a biharmonic-Kirchho…
We consider the algorithmic problem of finding large \textit{balanced} independent sets in sparse random bipartite graphs, and more generally the problem of finding independent sets with specified proportions of vertices on each side of the…
In this work, we propose and develop efficient and accurate numerical methods for solving the Kirchhoff-Love plate model in domains with complex geometries. The algorithms proposed here employ curvilinear finite-difference methods for…
In many cases, analytic solutions of partial differential equations may not be possible. For practical problems, it is more reasonable to carry out computational solutions. However, the standard grid in the finite difference approximation…
In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices. Precisely, we discuss existence and multiplicity of the…
Let $\{a_t: t \in \mathbb{R}\}< SL_{d}(\mathbb{R})$ be a diagonalizable subgroup whose expanding horospherical subgroup $U < SL_{d}(\mathbb{R})$ is abelian. By the Birkhoff ergodic theorem, for any $x \in…
In this work we introduce a new notion: local mechanisms. These are truthful mechanisms that have an implementation as fast distributed algorithms and non-trivial approximation guarantees. We show how monotone distributed optimisation…
This paper considers the Cauchy problem for the nonlinear dynamic string equation of Kirchhoff-type with time-varying coefficients. The objective of this work is to develop a time domain discretization algorithm capable of approximating a…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
We present a semidefinite programming approach to bound the measures of cross-independent pairs in a bipartite graph. This can be viewed as a far-reaching extension of Hoffman's ratio bound on the independence number of a graph. As an…
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
In this paper we establish the existence of mountain pass and negative energy weak solutions for a Kirchhoff-Schr\"odinger type problem in $\mathbb R^4$ involving a critical nonlinearity and a suitable small perturbation. The arisen…
We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush-Kuhn-Tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the…
There are different definitions of ends in non-locally-finite graphs which are all equivalent in the locally finite case. We prove the compactness of the end-topology that is based on the principle of removing finite sets of vertices and…
In this note, we establish a multiplicity theorem for a nonlocal discrete problem of the type $$\cases{-\left(a\sum_{m=1}^{n+1}|x_m-x_{m-1}|^2+b\right)(x_{k+1}-2x_k+x_{k-1})=h_k(x_k)\hskip 10pt k=1,...,n, \cr & \cr x_0=x_{n+1}=0\cr}$$…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
In this paper we deal with a Kirchhoff type problem driven by a fractional nonlocal integrodifferential operator $-\mathcal L_K$ and involving a critical nonlinearity. For this problem we prove the existence of infinitely many solutions,…
Consider the following $m-$polyharmonic Kirchhoff problem: \begin{eqnarray} \label{ea} \begin{cases} M\left(\int_{\O}|D_r u|^{m} +a|u|^m\right)[\Delta^r_m u +a|u|^{m-2}u]= K(x)f(u) &\mbox{in}\quad \Omega, \\ u=\left(\frac{\partial}{\partial…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…