相关论文: Discrete mappings with an explicit discrete Lyapun…
In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…
We develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal decrease condition for a Lyapunov function is a new form of…
For discrete-time systems, governed by Kraus maps, the work of D. Petz has characterized the set of universal contraction metrics. In the present paper, we use this characterization to derive a set of quadratic Lyapunov functions for…
We completely describe the asymptotic behaviour of the Riemann mapping function and its derivatives at an analytic cusp. We achieve the same for the inverse of the mapping function.
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
As a basic example in nonlinear theories of discrete complex analysis, we explore various numerical methods for the accurate evaluation of the discrete map $Z^a$ introduced by Agafonov and Bobenko. The methods are based either on a discrete…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
Let X be a Hausdorff quotient of a standard space (that is of a locally compact separable metric space). It is shown that the following are equivalent: (i) X is the image of an irreducible quotient map from a standard space; (ii) X has a…
The discrete Painlev\'e equations have mathematical properties closely related to those of the differential Painlev\'e equations. We investigate the appearance of elliptic functions as limiting behaviours of $q$-Painlev\'e transcendents,…
We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality…
We illustrate the basic notions of {\em additional non-isospectral symmetries} and their interplay with the discrete {\em \DB transformations} of integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili} (\cKP)…
This work is devoted to find the numerical solutions of several one dimensional second-order ordinary differential equations. In a heuristic way, in such equations the quadratic logistic maps regarded as a local function are inserted within…
We define for families of finite metric spaces quantitative assembly map estimates that take into account propagation phenomena for pseudo-differential calculus. We relate these estimates to the Novikov conjecture and we show that they fit…
The maximum principle forms an important qualitative property of second order elliptic equations, therefore its discrete analogues, the so-called discrete maximum principles (DMPs) have drawn much attention. In this paper DMPs are…
This paper presents several experimental findings related to the basic discrete Hilbert transform. The errors in the use of a finite set of the transform values have been tabulated for the more commonly used functions. The error can be…
We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.
We have studied the mappings that satisfy the Poletsky-type inverse inequality in the domain of the Euclidean space. It is proved that the uniform boundary of the family of such mappings is a discrete mapping. We separately considered…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit…