Related papers: Openness Stability and Implicit Multifunction Theo…
In this paper we explore solvability of steady-state variational inequalities with multivalued operators. Moreover, we are studying the connections between the class of radially semi-continuous operators with semi-bounded variation and…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
Stimulated by recent problems in the theory of iterated function systems, we provide a variant of the Banach converse theorem for multivalued maps. In particular, we show that attractors of continuous multivalued maps in a metric space are…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
Processes occurring in real open systems are far from equilibrium state and they can lead to synergetic effects, which are caused by coordinated behavior of system units. Traditional methods of analysis often just establish such behavior,…
In this paper, we introduce $n$-variables mappings which are cubic in each variable. We show that such mappings satisfy a functional equation. The main purpose is to extend the applications of a fixed point method to establish the…
It is well known from the seminal Brockett's theorem that the openness property of the mapping on the right-hand side of a given nonlinear ODE control system is a necessary condition for the existence of locally asymptotically stabilizing…
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…
We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…
The Multiscale Law of Requisite Variety is a scientific law relating, at each scale, the variation in an environment to the variation in internal state that is necessary for effective response by a system. While this law has been used to…
We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…
The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular…
In [MaII] Mather proved that a smooth proper infinitesimally stable map is stable. This result is the key component of the Mather stability theorem [MaV], which can be reformulated as follows: a smooth proper map $f: M\to N$ is stable if…
We build on the stability-preserving school choice model introduced and studied recently in [MV18]. We settle several of their open problems and we define and solve a couple of new ones.
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
In an attempt to better understand generalization in deep learning, we study several possible explanations. We show that implicit regularization induced by the optimization method is playing a key role in generalization and success of deep…
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…
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…