Spectral Shift Function in the Large Coupling Constant Limit

In the large-coupling constant limit we obtain an asymptotic expansion in powers of of the derivative of the spectral shift function corresponding to . Here the potential W(x) is positive and near infinity for some δ> n and ω₀ ∈C^∞ (S^n-1). submitted 18/05/05, accepted 19/10/05     

Spectral Shift Function of the Schrödinger Operator in the Large Coupling Constant Limit

The spectral shift function of a Schrödinger operator with a perturbation of definite sign is considered. The asymptotics of the spectral shift function for large coupling constant is studied, and results concerning positive and negative perturbations are compared. A more general case of unperturbed operator given by a function of the Laplacian is discussed. This case explains the dependence of the asymptotics of the spectral shift function on the perturbation potential on the one hand and on the order of the unperturbed operator on the other hand.     

Non-uniform Estimates in Asymptotic Expansions with a Stable Limit Distribution

Under pseudomoment conditions a non-uniform bound is proved for the remainder in asymptotic expansions with a stable limit law, where the quality of the bound with respect to the number of random variables is as good as that with respect to the argument. Further, a theorem for large deviations in the symmetrical problem is obtained.     

Asymptotic Estimates for a Variational Problem Involving a Quasilinear Operator in the Semi-Classical Limit

Let be a domain of ^N . We study the infimum ₁(h) of the functional |u| ^p +h ^–p V(x)|u| ^p dx in W ^1,p () for ||u|| _LP()= 1 where h > 0 tends to zero and V is a measurable function on . When V is bounded, we describe the behaviour of ₁(h), in particular when V is radial and 'slowly' decaying to zero. We also study the limit of ₁(h) when h 0 for more general potentials and show a necessary and sufficient condition for ₁(h) to be bounded. A link with the tunelling effect is established. We end with a theorem of existence for a first eigenfunction related to ₁(h).     

Non-Uniform Estimates and Asymptotic Expansions of the Remainder in the Central Limit Theorem for m-Dependent Random Variables

We study the order structure induced on a rigged Hilbert space ?? ? χ ? ??′by a self-dual cone in χ. Under the assumption that ?? is a semi-reflexive locally convex vector lattice, and a solid subset of ??′ (we speak then of a rigged Hilbert lattice), we show that ??′ is in fact a nondegenerate partial inner product space.     

The Large Time Convergence of Spectral Method for Generalized Kuramoto-Sivashinsky Equations

In this paper we use the spectral method to analyse the generalized Kuramoto-Sivashinsky equations. We prove the existence and uniqueness of global smooth solution of the equations. Finally, we obtain the error estimation between spectral approximate solution and exact solution on large time.     

Spectral Estimates for Degenerate Critical Levels

We establish spectral estimates at a critical energy level for h-pseudo-differential operators. Via a trace formula, we compute the contribution of isolated (nonextremum) critical points under a condition of "real principal type." The main result holds for all dimensions, for a singularity of any finite order and can be invariantly expressed in terms of the geometry of the singularity. When the singularities are not integrable on the energy surface the results are significative since the order w.r.t. h of the spectral distributions are bigger than in the regular setting.     

THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATION (Ⅱ)

1.IntroductionInthepaper[1],westudedthegeneralizedKuramotrySivashinskyequationWeProvedtheexistenceanduniquenessofglobalsolutionforperiodicinitialproblemandgavethelargetimeerrorestimationforthesolutionofcontinuousspectralmethod.Theaimofthispaperistostudyfullydiscretespectralmethodandthelongtimebehaviorofthesolutionofthissystem.In61wegiventhelargetimeerrorestimationforfullydiscretesolutionofspectralmethod.In52weprove-theexistenceofapproximateattractorsAN,4anding3weprovetheconvergenceofapproal…     

The Asymptotic Limit for the 3D Boussinesq System

In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately.     

混合样本时密度估计的渐近正态性

对多元密度函数的最近邻估计和核估计,在样本为不混合的场合下,本文获得了它们的渐近正态性。     

Asymptotic Estimates for Gagliardo–Nirenberg Embedding Constants

Sharp asymptotic information is determined for the Gagliardo–Nirenberg embedding constants in high dimension. This analysis is motivated by the earlier observation that the logarithmic Sobolev inequality controls the Nash inequality. Moreover, one sees here that Hardy's inequality can be interpreted as the asymptotic limit of the logarithmic Sobolev inequality.     

Asymptotic Expansions in the Compound Poisson Limit Theorem

A triangular array of independent infinitesimal integer-valued random variables is considered. Asymptotic expansions for the probability distributions of sums of these variables are investigated in the case of the limiting compound Poisson laws.     

Asymptotic Expansions in Non-central Limit Theorems for Quadratic Forms

We consider quadratic forms of the type

Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times

We consider the Fröhlich model of the polaron, whose path integral formulation leads to the transformed path measure with respect to ℙ that governs the law of the increments of the three-dimensional Brownian motion on a finite interval [−T, T] , and Z_{α, T} is the partition function or the normalizing constant and α > 0 is a constant, or the coupling parameter. The polaron measure reflects a self-attractive interaction. According to a conjecture of Pekar that was proved in [9], exists and has a variational formula. In this article we show that when α > 0 is either sufficiently small or sufficiently large, the limit exists, which is also identified explicitly. As a corollary, we deduce the central limit theorem for under and obtain an expression for the limiting variance. © 2019 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, LLC.     

The Bipolaron in the Strong Coupling Limit

The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr?hlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar–Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum P, provided P is not too large. Tadahiro Miyao: This work was supported by Japan Society for the Promotion of Science (JSPS). Permanent address: The graduate school of natural science and technology, Okayama university, Okayama 700-8530, Japan. Submitted: December 14, 2006. Accepted: March 20, 2007.     

递推数列极限的初等求法和收敛渐近性

借助实例介绍一些非线性递推数列，特别是分式线性递推数列极限的初等求法。就一般分式线性递推数列，明确其收敛渐近性，并通过相关推论展示其应用。