An almost sure central limit theorem for products of sums of partial sums under association

Let be a strictly stationary positively or negatively associated sequence of positive random variables with EX₁=μ>0, and VarX₁=σ²<∞. Denote , and γ=σ/μ the coefficient of variation. Under suitable conditions, we show that

     

Generalized solutions for the Euler-Bernoulli model with distributional forces

We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves discontinuous, and even distributional, coefficients and right-hand side. The general problem is solved by application of functional analytic techniques to obtain estimates for the solutions to regularized problems. Finally, we prove coherence properties and provide a regularity analysis of the generalized solution.     

Regularity, Local and Microlocal Analysis in Theories of Generalized Functions

We introduce a general context involving a presheaf and a subpresheaf ℬ of  . We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as the ℬ-local analysis of sections of  . But the microlocal analysis of the sections of sheaves or presheaves under consideration is dissociated into a “frequential microlocal analysis” and into a “microlocal asymptotic analysis”. The frequential microlocal analysis based on the Fourier transform leads to the study of propagation of singularities under only linear (including pseudodifferential) operators in the theories described here, but has been extended to some non linear cases in classical theories involving Sobolev techniques. The microlocal asymptotic analysis is a new spectral study of singularities. It can inherit from the algebraic structure of ℬ some good properties with respect to nonlinear operations.      

Behaviour of the Landau–Lifschitz equation in a ferromagnetic wire

Following a suggestion from A. Thiaville and J. Miltat, whose work and experiments are about ferromagnetic thin layers and nanowires, we study in this paper the behaviour of the Landau–Lifschitz equation in a straight ferromagnetic wire. As the diameter of the domain and the exchange coefficient in the equation simultaneously tend to zero, we perform an asymptotic expansion to precise the solution for well‐prepared initial conditions and are led to consider 2D exterior problems. Copyright © 2008 John Wiley & Sons, Ltd.     

剔除相关性的最小二乘研究

本文提出了一种新的回归模型,剔除相关性的最小二乘,它有效的克服了变量间的相关性,兼顾到变量的筛选。并与最小二乘、向后删除变量法、偏最小二乘比较分析。发现剔除相关性的最小二乘能很好的处理自变量间多重相关性,对变量进行有效的筛选,克服了回归系数反常的现象。     

Partial regularity of weak solutions for Landau-Lifshitz system with potential

In this note, we prove the partial regularity of stationary weak solutions for the Landau-Lifshitz system with general potential in four or three dimensional space. As well known, in general, since the constraint of the methods, in order to get the partial regularity of stationary weak solution of the Landau-Lifshitz system with potential, we need to add some very strongly conditions on the potential. The main difficulty caused by potential is how to find the equation satisfied by the scaling function, which breaks down the blow-up processing. We estimate directly Morrey’s energy to avoid the difficulties by blowing up. This work was supported by National Natural Science Foundation of China (Grant Nos. 10631020, 60850005) and the Natural Science Foundation of Zhejiang Province (Grant No. D7080080)     

The method of <Emphasis Type="Italic">A</Emphasis>-harmonic approximation and boundary regularity for nonlinear elliptic systems under the natural growth condition

We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.     

非线性时滞双曲型偏泛函微分方程的振动准则

研究一类多滞量非线性双曲型偏泛函微分方程解的振动性,借助广义Riccati变换和微分不等式技巧,获得了该类方程振动的若干新的充分条件,同时也给出了实际应用的例子.     

A short proof of the Zeilberger-Bressoud -Dyson theorem

We give a formal Laurent series proof of Andrews's -Dyson Conjecture, first proved by Zeilberger and Bressoud.

     

Variational solutions for partial differential equations driven by a fractional noise

In this article we develop an existence and uniqueness theory of variational solutions for a class of nonautonomous stochastic partial differential equations of parabolic type defined on a bounded open subset D⊂R^d and driven by an infinite-dimensional multiplicative fractional noise. We introduce two notions of such solutions for them and prove their existence and their indistinguishability by assuming that the noise is derived from an L²(D)-valued fractional Wiener process W^H with Hurst parameter , whose covariance operator satisfies appropriate integrability conditions, and where γ∈(0,1] denotes the Hölder exponent of the derivative of the nonlinearity in the stochastic term of the equations. We also prove the uniqueness of solutions when the stochastic term is an affine function of the unknown random field. Our existence and uniqueness proofs rest upon the construction and the convergence of a suitable sequence of Faedo-Galerkin approximations, while our proof of indistinguishability is based on certain density arguments as well as on new continuity properties of the stochastic integral we define with respect to W^H.