Related papers: On the isolated calmness property of implicitly de…

The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a $C^1$ bounded domain, subject to a large external potential $\Phi(x)$…

This article deals with different generalizations of the discrete stability property. Three possible definitions of discrete stability are introduced, followed by a study of some particular cases of discrete stable distributions and their…

High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be…

Explanation methods for machine learning models tend not to provide any formal guarantees and may not reflect the underlying decision-making process. In this work, we analyze stability as a property for reliable feature attribution methods.…

This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…

We derive high-order terms in the asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. Our…

This paper studies a set-theoretic generalization of Lyapunov and Lagrange stability for abstract systems described by set-valued maps. Lyapunov stability is characterized as the property of inversely mapping filters to filters, Lagrange…

We prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of…

This paper presents an extension of the unfolding operator technique, initially applied to two-dimensional domains, to the realm of three-dimensional thin domains. The advancement of this methodology is pivotal, as it enhances our…

This paper is concerned with the strong calmness of the KKT solution mapping for a class of canonically perturbed conic programming, which plays a central role in achieving fast convergence under situations when the Lagrange multiplier…

Monotonicity of a mapping implies its pseudomonotonicity and hence quasimonotonocity, the converse is not true. In this note we intend to study the situations under which quasimono tonicity of a mapping implies its monotonicity. Thus we…

This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen's and Wirtinger's…

We introduce a new geometric characteristic of compact sets on the plane called $r$-convexity, which fits nicely into the concept of generalized convexity and extends essentially the conventional convexity. For a class of subharmonic…

We propose a handful of definitions of injectivity for a parametrized family of maps and study its link with a global nonuniform stability conjecture for nonautonomous differential systems, which has been recently introduced. This relation…

This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…

Recently, Le Donne and the author introduce a notion of intrinsically Lipschitz graphs in metric spaces. The idea of this paper is to investigate about the properties of the intrinsically Lipschitz constants. More precisely, we give the…

Lagrangian generalized Nash equilibriums (LGNEs) were introduced by Rockafellar (2024) for a class of generalized Nash equilibrium problems (GNEPs) in which each player's strategy is subject to conic constraints. This paper investigates the…

A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…

The manuscript is devoted to the boundary behavior of mappings with bounded and finite distortion. We consider mappings of domains of the Euclidean space that satisfy weighted Poletsky inequality. Assume that, the definition domain is…

We study inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold under dimensional reduction. Stability due to different types of effective potentials is analyzed for specific configurations of…