The long-time asymptotic solutions of initial value problems for the heat equation and the nonlinear porous medium equation are self-similar spreading solutions. The symmetries of the governing equations yield three parameter families of these solutions given in terms of their mass, center of mass and variance. Unlike the mass and center of mass, the variance, or \time-shift," of a solution is ...

The Einstein de Broglie particle-soliton concept is applied to simulate stationary states of an electron in a hydrogen atom. According to this concept, the electron is described by the localized regular solutions to some nonlinear equations. In the framework of Synge model for interacting scalar and electromagnetic fields a system of integral equations has been obtained, which describes the int...

Let M be a compact C1 manifold which is invariant and normally hyperbolic with respect to a C1 semiflow in a Banach space. Then in an -neighborhood of M there exist local C1 center-stable and center-unstable manifolds W cs( ) and W cu( ), respectively. Here we show that W cs( ) and W cu( ) may each be decomposed into the disjoint union of C1 submanifolds (leaves) in such a way that the semiflow...

Assuming that sensors have full local memory, we introduce a novel test for the problem of decentralized change detection that is asymptotically optimum. According to our proposed scheme, sensors perform locally repeated SPRTs and communicate, asynchronously, their one-bit decisions to a fusion center. The fusion center in turn uses the sequentially acquired information to perform a CUSUM test ...

In this paper we investigate the asymptotic structure of a random mapping model with preferential attachment, T ρ n , which maps the set {1, 2, ..., n} into itself. The model T ρ n was introduced in a companion paper [11] and the asymptotic structure of the associated directed graph Gn which represents the action of T ρ n on the set {1, 2, ..., n} was investigated in [11] and [12] in the case w...

Let G be a sofic group, and let Σ “ pσnqně1 be a sofic approximation to it. For a probability-preserving G-system, a variant of the sofic entropy relative to Σ has recently been defined in terms of sequences of measures on its model spaces that ‘converge’ to the system in a certain sense. Here we prove that, in order to study this notion, one may restrict attention to those sequences that have ...

For a market with an atomless continuum of assets, we formulate the intuitive idea of a ‘‘well-diversified’’ portfolio, and present a notion of ‘‘exact arbitrage’’, strictly weaker than the more conventional notion of ‘‘asymptotic arbitrage’’, and necessary and sufficient for the validity of an APT pricing formula. Our formula involves ‘‘essential’’ risk, one based on a specific index portfolio...

We study the spectral geometric properties of the scalar Laplace-Beltrami operator associated to the Weil-Petersson metric gWP on Mγ , the Riemann moduli space of surfaces of genus γ > 1. This space has a singular compactification with respect to gWP, and this metric has crossing cusp-edge singularities along a finite collection of simple normal crossing divisors. We prove first that the scalar...

I provide a background of groups viewed as metric spaces to introduce the notion of asymptotic dimension of a group. I analyze the asymptotic dimension of Z ⊕ Z and the free group on two generators to better understand the concept of asymptotic dimension. The asymptotic dimension of the Heisenberg group, H, asdimH, has been shown to be three using advanced mathematics. I will try to show that a...