K-强凸空间的一些性质

结合Banach空间的Drop性，利用K维体积给出了K—强凸空间的一个新的定义，同时也给出了K—强光滑空间定义的K维体积表示，然后利用单位圆的切片证明了K—强凸空间是自反空间，进而证明了K—强凸空间与K—强光滑空间是一对对偶空间．最后利用Drop性的切片描述证明了K—强凸空间具有Drop性．     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅲ

More recently, sixteen families of Jacobian elliptic function solutions of mKdV equation have been foundby using our extended Jacobian elliptic function expansion method. In this paper, we continue to improve our methodby using another eight pairs of the closed Jacobian elliptic functions. The mKdV equation is chosen to illustrate theimproved method such that another eight families of new Jacobian elliptic function solutions are obtained again. Thenew method can be more powerful to be applied to other nonlinear differential equations.     

The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

Ergodicity for the Dissipative Boussinesq Equations with Random Forcing

We study the stationary measure for the two-dimensional Boussinesq equation with random forcing. We prove the ergodicity for the two-dimensional stochastically forced Boussinesq equation. We also study the Galerkin truncations of the three-dimensional Boussinesq equations under degenerate stochastic forcing. We follow closely the previous results on the stochastically forced Navier–Stokes equations.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

高维电报方程的对称周期解

讨论n维电报方程的对称周期解．利用Schauder不动点定理，在非共振条件下给出了一个存在性定理．     

A note on strongly π-regular rings

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x ⁿ=x ^{n +1} y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x ^m=x ⁿ. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Patterson–Sullivan Measure for Geometrically Finite Groups Acting on Complex or Quaternionic Hyperbolic Space

The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry.     

Existence and Life Span of Periodic Solutions for the First Order Quasilinear Hyperbolic Equations

g1.IntroductionWeconsiderthefollowingfirstorderquasilinearhyperbolicequationswithinternaIdissipa-tlveterm:U, A(U)U. F(U)=o(1.1)whereUeR2isunknownvectorfunction,A(U)is2X2knownsmoothmatrix,F(U)is2X2knownsmoothvectorfunction.Itiswell-knownthatCauchyproblemoftheequations(l.1)hasbeenwidelystudied(Ll-6J),however,theequations(l.1)withperiedicinitialdatahasbeenhardlystudiedandonesfindthatitiscomplicatedforproblemwithperiodicinitialdata.Becausetheperiodicdis-turbanceLlirectlyinfluencesthebounde…