发展在XLPE电缆绝缘内外侧的电树枝

以XLPE高压电力电缆内外侧绝缘中的电树枝特性为研究对象，通过分析电树枝引发与生长的统计实验规律和采用扫描电子显微镜分析发现，由于不同结晶状态的影响，电缆绝缘内外侧的电树枝特性存在很大的差异.引发于绝缘内侧电树枝引发时间短、生长速度快、电树枝形状具有多样性；起始于绝缘外侧的电树枝不仅引发时间长、生长速度极慢，而且电树枝形状(结构)比较单一.并对这两个位置电树枝的引发和生长机理进行了探讨. 关键词： 电树枝 结晶状态 统计规律 内侧和外侧绝缘层     

Properties of the density for a three-dimensional stochastic wave equation

We consider a stochastic wave equation in space dimension three driven by a noise white in time and with an absolutely continuous correlation measure given by the product of a smooth function and a Riesz kernel. Let pt,x(y) be the density of the law of the solution u(t,x) of such an equation at points (t,x)∈]0,T]×R³. We prove that the mapping (t,x)?pt,x(y) owns the same regularity as the sample paths of the process {u(t,x),(t,x)∈]0,T]×R³} established in [R.C. Dalang, M. Sanz-Solé, Hölder-Sobolev regularity of the solution to the stochastic wave equation in dimension three, Mem. Amer. Math. Soc., in press]. The proof relies on Malliavin calculus and more explicitly, the integration by parts formula of [S. Watanabe, Lectures on Stochastic Differential Equations and Malliavin Calculus, Tata Inst. Fund. Res./Springer-Verlag, Bombay, 1984] and estimates derived from it.     

基于Lascenov多项式零点的(0,2)-插值的正则性

本文给出了基于Ｌａｓｃｅｎｏｖ多项式零点（０，２）－插值正则性的充要条件，并给出基多项式存在时的明显表达式。     

Rigidity and regularity in group actions

Some new results on the rigidity of automorphism groups and the regularity of(?)-Neumann operator in group actions are presented.     

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u = u^k（δu）^α

This paper undertakes a systematic treatment of the low regularity local wellposedness and ill-posedness theory in H^s and H^s for semilinear wave equations with polynomial nonlinearity in u and δu. This ill-posed result concerns the focusing type equations with nonlinearity on u and δtu.     

The affine Plateau problem

In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.

     

Sequential Completeness of LF-Spaces

Any LF-space is sequentially complete iff it is regular.     

Geometric Condition Measures and Smoothness Condition Measures for Closed Convex Sets and Linear Regularity of Infinitely Many Closed Convex Sets

In this paper, we study geometric condition measures and smoothness condition measures of closed convex sets, bounded linear regularity, and linear regularity. We show that, under certain conditions, the constant for the linear regularity of infinitely many closed convex sets can be characterized by the geometric condition measure of the intersection or by the smoothness condition measure of the intersection. We study also the bounded linear regularity and present some interesting properties of the general linear regularity problem.The author is grateful to the referees for valuable and constructive suggestions. In particular, she thanks a referee for drawing her attention to Corollary 5.14 of Ref. 3, which inspired her to derive Theorem 4.2 and Corollary 4.2 in the revision of this paper.     

Fourier series and integral equation method for the exterior Stokes problem

The exterior Stokes problem between two parallel planes that are separated by a prismatic cylinder is extended to the interior of the prism by requiring the continuity of the velocity across the lateral faces. The well‐posedness of the exterior–interior problem is proved in suitable weighted Sobolev spaces. The solution is represented by Fourier series in the z‐variable. The Fourier coefficients, solutions of auxiliary two‐dimensional exterior–interior problems, are analyzed by viewing them as boundary integral equations of potential theory and global regularity of the densities, is established in weighted Sobolev spaces of traces. A boundary element method, with suitably refined mesh size, is implemented for the numerical treatment of the Fourier coefficients. This provides optimal convergent semi‐ and fully‐discrete spectral methods of Fourier–Galerkin type. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008