Perturbations and operator trace functions

We study the spectral functional for a suitable function f, a self-adjoint operator D having compact resolvent, and a certain class of bounded self-adjoint operators A. Such functionals were introduce by Chamseddine and Connes in the context of noncommutative geometry. Motivated by the physical applications of these functionals, we derive a Taylor expansion of them in terms of Gâteaux derivatives. This involves divided differences of f evaluated on the spectrum of D, as well as the matrix coefficients of A in an eigenbasis of D. This generalizes earlier results to infinite dimensions and to any number of derivatives.     

Second-order functional differential equations with past, present and future dependence

In this paper we obtain a result on existence of extremal quasisolutions and solutions for second-order functional differential equations with functional boundary conditions and past, present and future dependence. In order to do that, we develop a generalized monotone method in presence of lower and upper solutions. Some examples of application are provided too.     

Analysis of nonlinear BVPs motivated by fluid film flow over a surface

We study a coupled nonlinear boundary value problem which has been shown to have applications to fluid flow and heat transfer in a fluid film over a stretching surface for set values of the model parameters (one of which determines the size of the problem domain). For arbitrary values of these parameters we are able to establish the existence and uniqueness of a class of monotone solutions. Perturbation solutions are then constructed and used to approximate certain invariants for the solutions. We then study a related boundary value problem formed by imposing an additional boundary condition on one of the governing equations (which results in an ill-posed problem), and we arrive at conditions allowing for solutions to this four-parameter problem to agree with the solutions to the three-parameter problem.     

The Nonlinear Schr¨odinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type

The primary goal of this paper is to present a comprehensive study of the nonlinear Schr?dinger equations with combined nonlinearities of the power-type and Hartree-type. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schr?dinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.     

一类宏观经济学中的二阶离散方程的正解的有界性

利用Leray-Schauder延拓定理,使用对角化方法考虑了来源于宏观经济学中的一类二阶差分方程的有界性.     

Self-adjointness of perturbed bi-Laplacians on infinite graphs

We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily bounded. The result allows perturbations that are not necessarily bounded from below by a constant.     

双原子分子非谐振转波函数和能级

从双原子分子简谐势近似波函数出发,运用微扰理论计算出了双原子分子在非谐振转相互作用下的一级、二级近似能级和一级近似波函数.     

薄板声谐振子扰动的声学特征检测研究

为进行快速ＮＤＴ，研究了薄板声谐振子扰动和声学特征变化的关系，用有限元方法分析在睡无缺陷薄板的振动频率和振型。利用数字信号处理技术，实验研究了样品中缺陷对声学特征的影响。实现和理论分析结果一致性很好。研究结果有助于正确利用样品声学特征进行无损检测。     

Perturbation theory for the double sine-Gordon equation

This paper presents a perturbation theory for the double sine-Gordon equation. We obtain a system of differential equations that shows the soliton parameters modification under the influence of the perturbation. For the particular case λ=0 the results transform into the well-known perturbation theory for the sine-Gordon equation.     

Phase Diagram of the Two-dimensional t–t′ Falicov-Kimball Model

The ground-state phase diagram of the two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings has been studied in the perturbative regime where hoppings are small compared with the on-site Coulomb interaction. The phase diagram at fourth-order exhibits a richer structure than the one of the ordinary Falicov-Kimball model. PACS numbers: 71.10.Fd, 71.21.+a, 75.10.Hk, 75.30.Kz