Related papers: p-Adic Stability In Linear Algebra
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
This paper is devoted to the study of rigidity properties for special solutions of nonlinear elliptic partial differential equations on smooth, boundaryless Riemannian manifolds. As far as stable solutions are concerned, we derive a new…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
We prove unconditional long-time stability for a particular velocity-vorticity discretization of the 2D Navier-Stokes equations. The scheme begins with a formulation that uses the Lamb vector to couple the usual velocity-pressure system to…
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell…
In this work, we determine the general solution of the quinquevigintic functional equation and also investigate its stability of this equation in the setting of matrix normed spaces and the framework of matrix non-Archimedean fuzzy normed…
In this master thesis we have compared different second order stabilized explicit Runge-Kutta methods when applied to the incompressible Navier-Stokes equations by means of a projection method and a differential algebraic approach. We…
We derive algorithms for higher order derivative computation of the rectangular $QR$ and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and reverse mode of algorithmic differentiation (AD) using…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
In this paper, we study the stability of matrix polynomials under structured perturbations of their coefficients. More precisely, we consider a family of matrix polynomials \[…
In this paper, we present a thorough von Neumann stability analysis of explicit and implicit Arbitrary-Lagrangian-Eulerian (ALE) ADER discontinuous Galerkin (DG) methods on classical and degenerate spacetime geometries for hyperbolic…
After reconsidering the theorem of continuity of the roots of a polynomial in terms of its coefficients in the deformation framework, we study the stability of the greater common divisor of two polynomials compared to perturbations on their…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…
In this article we implement a method for the computation of a nonlinear elliptic problem with nonstandard growth driven by the $p(x)-$Laplacian operator. Our implementation is based in the {\em decomposition--coordination} method that…
First we explain the concept of local deformation over a 'parameter' algebra P, in particular the notion of a P-lattice in a Lie group. Purpose of this article is to define the spaces of automorphic resp. cusp forms on the upper half plane…
This paper explores the embedding of lattice structures $L \subseteq \mathbb{R}^n$ into smooth manifolds $M \subseteq \mathbb{R}^n$ through a rigorous mathematical framework. Building upon the foundational results established in "Embedding…
We present an efficient and flexible method for solving the non-linear lasing equations of the steady-state ab initio laser theory. Our strategy is to solve the underlying system of partial differential equations directly, without the need…
We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…