狄氏型关于狄氏型的扰动

本文在狄氏型扰动的经典意义基础上，首次提出了狄氏型关于狄氏型的扰动的概念，并得到了若干使得扰动后的狄氏型具有拟正则性的条件，最后给出了一些应用。     

一类狄氏型变换及其联系的马氏过程

本文研究一类狄氏型变换.我们给出狄氏型变换后的二次型是拟正则狄氏型的充分条件,分别讨论关于二阶微分算子和伪微分算子所对应的狄氏型的狄氏型变换,得到变换前后拟正则狄氏型对应的马氏过程间的关系.     

广义狄氏型的扰动及其结合的马氏过程

本文研究广义狄氏型的扰动及其结构的马氏过程。我们讨论一般状态空间上的拟正则广义狄氏型ε关于光滑测度的ε的扰动,证明扰动型ε^μ结合m- 胎紧m-特别标准过程。     

半狄氏型的暂留性

本文给出半狄氏型，狄氏型和保正型的暂留性的概念，并讨论它们的有关性质。     

对称马氏过程的Girsanov变换

本文讨论一类对称马氏过程的Girsanov变换,这类Girsanov变换是由该对称马氏过程所联系的狄氏型定义域中的函数来确定的．我们证明了对称马氏过程经变换后还是对称的马氏过程,并且给出经变换后的马氏过程所联系的狄氏型．这些结果将前人的相应结论从有界函数推广到更有应用意义的一类无界函数之上．     

齐次分层垫片上平均值意义下的狄氏型

本文在齐次分层垫片上用平均值方法定义了狄氏型和相关的调和函数,并且证明了它们和点态意义下定义的狄氏型与调和函数具有相同的性质.     

具有无界变差的连续函数研究进展

讨论了具有无界变差的连续函数的结构.首先按照局部结构和分形维数对连续函数进行了分类,给出了相应的例子.对这些具有无界变差的函数的性质进行了初步的讨论.对于新定义的奇异连续函数,给出了一个等价判别定理.基于奇异连续函数,又给出了局部分形函数和分形函数的定义.同时,分形函数又由奇异分形函数、非正则分形函数和正则分形函数组成.相应于不连续函数的情形也进行了简单的讨论.     

拟正则保正型过份函数的积分表示及h-结合过程的轨道性质

本文讨论拟正则保正型α-过份函数的积分表示，证明拟正则保正型（ε，D（ε））的任意α-过份函数u均可表示为εα（u，v）=∫vdμ，v∈D（ε），μ是E上的σ有限测度。并证明（ε，D（ε））的h-结合过程是暂留的和非保守的。     

非对称狄氏型的扰动及其相关的转换等式的注记

利用广义预解方程,本文得到一类特殊的位势项在扰动后的狄氏型定义域中;利用非对称狄氏型的扰动本文还直接地证明了两个常用的转换等式.     

凸函数与半连续函数的关系

通过研究凸函数与半连续函数的关系,给出了凸函数的一个与上半连续性相结合的等价定义.     

Extensions of Lévy-Khintchine formula and Beurling-Deny formula in semi-Dirichlet forms setting

The Lévy-Khintchine formula or, more generally, Courrège's theorem characterizes the infinitesimal generator of a Lévy process or a Feller process on Rd. For more general Markov processes, the formula that comes closest to such a characterization is the Beurling-Deny formula for symmetric Dirichlet forms. In this paper, we extend these celebrated structure results to include a general right process on a metrizable Lusin space, which is supposed to be associated with a semi-Dirichlet form. We start with decomposing a regular semi-Dirichlet form into the diffusion, jumping and killing parts. Then, we develop a local compactification and an integral representation for quasi-regular semi-Dirichlet forms. Finally, we extend the formulae of Lévy-Khintchine and Beurling-Deny in semi-Dirichlet forms setting through introducing a quasi-compatible metric.     

Gauss整环上不可分解的Hermite型

本文给出了构作虚二次域Ｑ（－ｍ）的整数环上不可分解的正定整Ｈｅｒ ｍｉｔｅ型的方法．     

On non-decomposable Hermitian forms over Gaussian domain

Methods are presented for the construction of non-decomposable Hermitian forms over the ring of integers of an imaginary quadratic field.     

Multiplicities of representations in spaces of modular forms

This paper shows that for a given irreducible representation of , the two functions dim( ) and dim( ) of are almost linear functions.

     

Singularity conjecture and constructions of Jacobi forms

This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-typeL-series.     

Classification of quintic eutactic forms

From the classical Voronoi algorithm, we derive an algorithm to classify quadratic positive definite forms by their minimal vectors; we define some new invariants for a class, for which several conjectures are proposed. Applying the algorithm to dimension 5 we obtain the table of the 136 classes in this dimension, we enumerate the 118 eutactic quintic forms, and we verify the Ash formula.

     

Quadratic forms and Pfister neighbors in characteristic 2

We study Pfister neighbors and their characterization over fields of characteristic , where we include the case of singular forms. We give a somewhat simplified proof of a theorem of Fitzgerald which provides a criterion for when a nonsingular quadratic form is similar to a Pfister form in terms of the hyperbolicity of this form over the function field of a form which is dominated by . From this, we derive an analogue in characteristic of a result by Knebusch saying that, in characteristic , a form is a Pfister neighbor if its anisotropic part over its own function field is defined over the base field. Our result includes certain cases of singular forms, but we also give examples which show that Knebusch's result generally fails in characteristic for singular forms. As an application, we characterize certain forms of height in the sense of Knebusch whose quasi-linear parts are of small dimension. We also develop some of the basics of a theory of totally singular quadratic forms. This is used to give a new interpretation of the notion of the height of a standard splitting tower as introduced by the second author in an earlier paper.

     

张拉结构初始几何形状确定的形函数方法

提出了一个确定张拉结构初始几何形状的形状函数.基于该形状函数,通过对结构边界控制点的插值确定张拉结构的初始形状.该结构形状可随结构的双向张力比和边界控制点的坐标而进行自动调整.从而给出了几何上可行,力学上合理的高精度张拉曲面.通过有限元方法检查,大量例子表明该方法确定的初始形状对于实际常用边界及双向等拉或不等拉张结构均十分理想,误差很小.     

方阵的开方问题

运用Jordan标准形理论,完整解决了复数方阵、实数方阵能否开平方、开立方的问题.