Search results for "bound"
showing 10 items of 2948 documents
THE TOPOLOGY OF BASIN BOUNDARIES IN A CLASS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS
1996
We will develop new methods to determine the topology of the basin boundary in a class of three-dimensional dynamical systems. One approach is to approximate the basin boundary by backward integration. Unfortunately, there are dynamical systems where it is hard to approximate the basin boundary by a numerical backward integration algorithm. We will introduce topological methods which will provide new information about the structure of the basin boundary. The topological invariants which we will use can be numerically computed.
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
2012
In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
A two-phase problem with Robin conditions on the free boundary
2020
We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an existence and a regularity result for minimizers of the associated variational problem. Finally, in the appendix, we give an example of a class of Steiner symmetric minimizers. peerReviewed
On a class of languages with holonomic generating functions
2017
We define a class of languages (RCM) obtained by considering Regular languages, linear Constraints on the number of occurrences of symbols and Morphisms. The class RCM presents some interesting closure properties, and contains languages with holonomic generating functions. As a matter of fact, RCM is related to one-way 1-reversal bounded k-counter machines and also to Parikh automata on letters. Indeed, RCM is contained in L-NFCM but not in L-DFCM, and strictly includes L-CPA. We conjecture that L-DFCM subset of RCM
Integrability of the one dimensional Schrödinger equation
2018
We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.
Character degrees, character codegrees and nilpotence class of p-groups
2021
Du and Lewis raised in 2016 the question of whether the nilpotence class of a p-group is bounded in terms of the number of character codegrees. In 2020, Croome and Lewis, gave a positive answer to ...
A Multiplicity result for a class of strongly indefinite asymptotically linear second order systems
2010
We prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearity.
Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups
2020
We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $\Gamma$-liminf of the rescaled energy in terms of the horizontal perimeter.
A lower bound for the Bloch radius of 𝐾-quasiregular mappings
2004
We give a quantitative proof to Eremenko’s theorem (2000), which extends Bloch’s classical theorem to the class of n n -dimensional K K -quasiregular mappings.
Roots in the mapping class groups
2006
The purpose of this paper is the study of the roots in the mapping class groups. Let $\Sigma$ be a compact oriented surface, possibly with boundary, let $\PP$ be a finite set of punctures in the interior of $\Sigma$, and let $\MM (\Sigma, \PP)$ denote the mapping class group of $(\Sigma, \PP)$. We prove that, if $\Sigma$ is of genus 0, then each $f \in \MM (\Sigma)$ has at most one $m$-root for all $m \ge 1$. We prove that, if $\Sigma$ is of genus 1 and has non-empty boundary, then each $f \in \MM (\Sigma)$ has at most one $m$-root up to conjugation for all $m \ge 1$. We prove that, however, if $\Sigma$ is of genus $\ge 2$, then there exist $f,g \in \MM (\Sigma, \PP)$ such that $f^2=g^2$, $…