相关论文: Singularity confinement for maps with the Laurent …

Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.

Robert Bryant (Theorie des varietes minimales et applications, 1988, 154: 321-347) proved that an isolated singularity of a conformal metric of positive constant curvature on a Riemann surface is a conical one. Using Complex Analysis, we…

We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax…

We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…

We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory with a variety of matter terms. For some of these models the standard Painlev\'{e} test is sufficient to demonstrate…

We study one parameter deformations of a pair consisting of an analytic singular space $X_0$ and a function $f_0$ on it, in case this defines an isolated singularity. We prove, under general conditions, a bouquet decomposition of the Milnor…

We study the non-selfadjoint Dirac system on the line having an non-integrable regular singularity in an interior point with additional matching conditions at the singular point. Special fundamental systems of solutions are constructed with…

Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we study quantum systems totally confined in space and associated with the discrete Meixner polynomials. We present several…

Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…

We consider here the analytic classification of pairs $(\omega,f)$ where $\omega$ is a germ of a 2-form on the plane and $f$ is a quasihomogeneous function germ with isolated singularities. We consider only the case where $\omega$ is…

Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…

New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…

The Lorenz attractor is one of the best known examples of applied mathematics. However, much of what is known about it is a result of numerical calculations and not of mathematical analysis. As a step toward mathematical analysis, we allow…

We continue the development of the study of the equisingularity of isolated singularities, in the determinantal case. This version of the paper includes a substantial amount of new material (76% larger). The new material introduces the idea…

The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence toward…

The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…

This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatment of variable singular exponents alongside measure-valued…

The aim of this article is to investigate the issues of multiplicative inverses and composition in the set of formal Laurent series. We show the lack of general uniqueness of inverses of formal Laurent series; necessary and sufficient…

A paper of the first author and Zilke proposed seven combinatorial problems around formulas for the characteristic polynomial and the exponents of an isolated quasihomogeneous singularity. The most important of them was a conjecture on the…

The aim of this note is to present some recent results on the structure of the singular part of measures satisfying a PDE constraint and to describe some applications.