Related papers: On stability of exactness properties under the pro…

Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…

We prove that in a countable theory T fully stable over a predicate P, any complete set A has the existence property. This means that A can be extended to a model of T without changing the P-part. In particular, T has the Gaifman property:…

We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…

We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…

In this paper, we prove stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we construct a category $\mathbf{OrI}(R)$ and prove a Noetherianity theorem for the…

This paper is intended to review recent results and open problems concerning the existence of steady states to the Maxwell-Schr\"odinger system. A combination of tools, proofs and results are presented in the framework of the…

We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows…

New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the…

We study the spaces of locally-finite stability conditions on the derived categories of coherent sheaves on the minimal resolutions of $A_n$-singularities supported at the exceptional sets. Our main theorem is that they are connected and…

In this article we discuss a possibility to implement a well-known scheme of proof for contraction mapping theorems in a situation, when convergence, families of Cauchy sequences, and contractiveness of mappings are defined axiomatically.…

The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…

We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…

In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.

We develop a theory of Finite Element Systems, for the purpose of discretizing sections of vector bundles, in particular those arizing in the theory of elasticity. In the presence of curvature we prove a discrete Bianchi identity. In the…

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…

We apply proof-theoretic techniques in answer Set Programming. The main results include: 1. A characterization of continuity properties of Gelfond-Lifschitz operator for logic program. 2. A propositional characterization of stable models of…

We consider classes of Boolean functions stable under compositions both from the right and from the left with clones. Motivated by the question how many properties of Boolean functions can be defined by means of linear equations, we focus…