D-N交替法与Schwartz交替法的收敛关系分析

This paper has demonstrated that the Schwartz alternating process must converge if D-N alternating process has converged. Its technique is that the overlapping regions in Schwartz alternating process are considered as independent domains, then Schwartz alternating process could be transformed into D-N alter-nating process. Finally the convergence estimation of Schwartz alternating process could be obtained. The results show that its convergence rate is same as that of D-N alternating process.     

Periodic solutions of nonlinear impulsive differential inclusions with constraints

In this paper we obtain the existence of periodic solutions for nonlinear ``invariance' problems monitored by impulsive differential inclusions subject to impulse effects.

     

Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ². A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Online publication 23 January 2004.     

Essential domains and two conjectures in dimension theory

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

     

Existence for bounded positive solutions of Schrödinger equations in two-dimensional exterior domains

In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result of bounded positive solutions of Schrödinger equations in two-dimensional exterior domains.     

磁畴形成的原理探索

本文运用量子力学和固体物理学分析铁磁物质及其磁畴形成的原理     

用频域法实现圆环形目标物的计数

研究了用频域法实现圆环形目标物计数的方法。对空域中含有圆环形目标物的二值图像，经傅里叶变换后在频域内进行滤波，再经傅里叶反变换后取一阈值进行处理，则对应于圆环形目标物即变为一个实心体，然后对实心体进行计数即可实现对圆环形目标物的计数。对该方法进行了数学描述，并分别用模拟图像和实际图像进行了实验。结果表明，该方法消除噪声的效果好，对部分封闭圆的检测同样有效，且可用于目标物有粘连的情况。该方法对圆环形目标物的尺寸相差不大的情况更为有效。     

The genetic diversity of cen-tral and peripheral popula-tions of ratlike hamster(Cricetulus triton)

The impact of habitat fragmentation and isolation on the genetic diversity of populations has attracted much attention in studies of meta-population and conservation biology. In this work, using the randomly amplified polymorphic DNA (RAPD) technique, we studied the genetic diversity of central, peripheral and peninsular populations of ratlike hamster, which were collected in five locations of the North China Plain and its surrounding areas, in 1999. The study revealed that, ⅰ) the genetic diversity of central population of Raoyang County＞the sub-central populations of Gu'an County and Taikang County＞the peripheral population of Shunyi District＞the peninsular population of Mentougou District; ⅱ) the genetic diversities of the five populations were positively correlated to the nearest distances to the peripheral line of population distribution; ⅲ) there were significant differences of gene frequencies of some RAPD fragments among the five populations. More RAPD fragments disappeared in peripheral populations than in central or sub-central populations. The frequencies of two RAPD fragments were correlated to the latitude. This study clearly indicated that the variation of the genetic diversities of the five populations was caused by edge effect and frag- mentation through the enhanced inbreeding and genetic drift, and thus supported the view that habitat fragmentation and related edge effect reduce the population genetic diversity.     

凸域内弦的平均长度

本文研究了凸域内弦的平均长度.通过广义支持函数与凸域的弦幂积分,建立了凸域内弦的平均长度的一般公式,并用此公式得出了圆域和矩形域内弦的平均长度.