Clifford分析中的多周期和准多周期Riemann边值问题

本文考虑了R^n 1空间中椭圆函数和准椭圆函数的一些性质，然后分别讨论了周期和准周期Riemann边值问题，给出了解的表达式和可解条件。     

在局部区域上的奇摄动反应扩散方程初始边值问题

本文是讨论一类在局部区域上的奇摄动反应扩散初始边值问题.利用算子理论和 不动点原理,得到了相应问题解的存在性和唯一性.     

Ratio of Protein Fractions in Cereal Grains Cultivated in Uzbekistan

The glutelin fraction was used as the food value index of local corn. The base-soluble fraction was used as a test of the glassiness of local strains of rice grain. The content of gliadins and glutelins did not change over 24 h after wheat grain cultivated in Uzbekistan was moistened.     

The Elimination of Grains and Grain Boundaries in Grain Growth

The topological changes that occur during coarsening of 2D and 3Dcellular structures, such as polycrystals, areinvestigated. Particular attention is given to the elimination ofgrain boundaries and grains with more than the minimum number oftopological elements. A thermodynamic criterion is introduced tofind out which topological transformations are favoured, based on theevaluation of the Gibbs free energy of the initial and finalconfigurations. In general, elimination of grains is possible only ifthe number of their neighbours is below a critical value, which maybe affected by geometry.     

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…     

胶体颗粒大小的分布——Ⅱ.物理显影中胶体催化剂颗粒大小的分布函数

本文用对数正态分布对物理显影中常用的Au、Ag及Ag_2s胶体催化剂的颗粒大小的实验分布进行了拟合。理论分布与实验分布的比较表明:本实验条件下制备的十二组胶体溶液其颗粒大小都服从了对数正态分布,并且不依赖于胶体的组成、大小及制备方法。因此,它们很可能遵从了同样的成核成长规律。     

A uniqueness theorem for a free boundary problem

In this paper, we prove a uniqueness theorem for a free boundary problem which is given in the form of a variational inequality. This free boundary problem arises as the limit of an equation that serves as a basic model in population biology. Apart from the interest in the problem itself, the techniques used in this paper, which are based on the regularity theory of variational inequalities and of harmonic functions, are of independent interest, and may have other applications.

     

Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors

In this paper we study a free boundary problem modelling the growth of nonnecrotic tumors. The main trait of this free boundary problem is that it is essentially multidimensional, so that its well-posedness is hard to establish by using the usual methods in the classical theory of free boundary problems. In this paper we use the functional analysis method based on the theory of analytic semigroups to prove that this problem has a unique local solution in suitable function spaces. Continuous dependence of the solution on the initial data and regularities of the solution can also be easily obtained by using the argument of this paper.     

Algorithms for finding proper essential surfaces in 3-manifolds

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold.     

Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries

We consider nonnegative solutions of a parabolic equation in a cylinder D×(0,T), where D is a noncompact domain of a Riemannian manifold. Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(M_∂D×[0,T)), where M_∂D is the Martin boundary of D for the associated elliptic operator. We apply it in a unified way to several concrete examples to explicitly represent nonnegative solutions. We also show that [IU] implies the condition [SP] (i.e., the constant function 1 is a small perturbation of the elliptic operator on D).