Related papers: Stability and separation in volume comparison prob…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
The behavior of perturbations is studied in cosmological models which consist of two different homogeneous regions connected in a spherical shell boundary. The junction conditions for the metric perturbations and the displacements of the…
We study the Gaussian noise stability of subsets A of Euclidean space satisfying A=-A. It is shown that an interval centered at the origin, or its complement, maximizes noise stability for small correlation, among symmetric subsets of the…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
In the first part, the stability of two-dimensional parallel flow is discussed. A more restrictively general stability criterion for inviscid parallel flow is obtained analytically. In the second part, we report the numerical simulations of…
We construct large velocity vector solutions to the three dimensional inhomogeneous Navier-Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density…
We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete or partial -- of the equations.
We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset $X$ of $\mathbb{R}^d$ from a set $Y$ that is close in the Hausdorff distance. This estimator enjoys a linear rate of convergence as…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ball and upperhalfspace.
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
We use particle dynamics simulations to probe the correlations between noise and dynamics in a variety of disordered systems, including superconducting vortices, 2D electron liquid crystals, colloids, domain walls, and granular media. The…
We consider the problem of comparing the volumes of two star bodies in an even-dimensional euclidean space $\mathbb R^{2n} = \mathbb C^n$ by comparing their cross sectional areas along complex lines (special 2-dimensional real planes)…
We present a new stability result for viscosity solutions of fully nonlinear parabolic equations which allows to pass to the limit when one has only weak convergence in time of the nonlinearities.
We prove a stability version of the Pr\'ekopa-Leindler inequality.
This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Korobov point sets in the unit cube. It was observed recently that this new characteristic allows us to obtain optimal rate of…
This research is focused on linear analysis of a plane-parallel flow stability in a transverse magnetic field (Hartmann flow) within a convective approximation. We derive and solve equations describing the perturbation growth. Perturbation…
The hyperspherical adiabatic expansion method is used to describe correlations in a symmetric boson system rigorously confined to two spatial dimensions. The hyperangular eigenvalue equation turns out to be almost independent of the…
Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…