*Correspondence: [email protected] 1Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China Full list of author information is available at the end of the article Abstract By processing the problem through fixed point theory and propagator theory, we investigate the periodicity of solutions to a class of impulsive evolution equations in Hilbert spaces and estab...

The relationship of Choptuik scaling to the scale invariance of Einstein’s equation is explored. Ordinary dynamical systems often have limit cycles: periodic orbits that are the asymptotic limit of generic solutions. We show how to separate Einstein’s equation into the dynamics of the overall scale and the dynamics of the “scale invariant” part of the metric. Periodicity of the scale invariant ...

A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The sec...

This paper considers undiscounted Markov Decision Problems. For the general multichain case, we obtain necessary and sufficient conditions which guarantee that the maximal total expected reward for a planning horizon of n epochs minus n times the long run average expected reward has a finite limit as n -* oo for each initial state and each final reward vector. In addition, we obtain a character...

We analyze the well-posedness and stability properties of a parameter dependent problem that models the reflection and transmission of electromagnetic waves at a thin and rapidly oscillating interface. The latter is modeled using approximate interface conditions that can be derived using asymptotic expansion of the exact solution with respect to the small parameter (proportional to the periodic...

Systems _ x(t) = F(t; x(t); ") depending on a small parameter " are considered. We introduce a concept of convergence of such a system to a system _ x(t) = G(x(t)). Assuming this convergence, we prove that global asymptotic stability for _ x(t) = G(x(t)) implies some notion of \practical stability" for _ x(t) = F(t; x(t); ") if F(; x; ") satisses a periodicity assumption. We apply this theory t...

Introduction 2 1. Self-adjointness of Schrödinger operators 3 1.0. Solving the Schrödinger equation 3 1.1. Linear operators in Hilbert space 7 1.2. Criteria for (essential) self-adjointness 13 1.3. Application to Schrödinger operators 18 2. Hardy-Rellich inequalities 21 2.0. Relative boundedness 21 2.1. Weighted estimates 24 2.2. Explicit bounds 26 3. Spectral properties of radially periodic Sc...

Abstract. We study the diffusion of a particle on a random lattice with fluctuating local connectivity of average value q. This model is a basic description of relaxation processes in random media with geometrical defects. We analyze here the asymptotic behavior of the eigenvalue distribution for the Laplacian operator. We found that the localized states outside the mobility band and observed b...

The Horadam sequence is a direct generalization of the Fibonacci numbers in the complex plane, which depends on a family of four complex parameters: two recurrence coefficients and two initial conditions. In this article a computational matrix-based method is developed to formulate necessary and sufficient conditions for the periodicity of generalized complex Horadam sequences, which are genera...