环形域上的Dirichlet问题

讨论了Laplace方程在环形域上的Dirichlet问题的求解方法,给出了该问题的求解过程和Fourier级数解的结果,并指出了Poisson积分公式在具体求解中的不适应性,对于理解S-L方程在不同边界条件下,特别是自然边界条件和周期边界条件下的本征值问题具有重要意义.     

一类包含Riemann Zeta函数的求和公式

应用广义Dirichlet积分公式得到了一类包含Riemann Zeta函数的求和计算公式．     

一类带有Dirichlet边界值条件的椭圆型方程正解的存在性

利用欧拉变分原理,证明了一类带有Dirichlet边界值条件的椭圆型方程正解的存在性。     

共振的半线性Dirichlet问题解的多重性

使用Z2指标理论获得非线性非自治无界共振的半线性椭圆方程Dirichlet问题解的多重性结果。     

Time gap analysis by the topic model-based temporal technique

This study proposes a temporal analysis method to utilize heterogeneous resources such as papers, patents, and web news articles in an integrated manner. We analyzed the time gap phenomena between three resources and two academic areas by conducting text mining-based content analysis. To this end, a topic modeling technique, Latent Dirichlet Allocation (LDA) was used to estimate the optimal time gaps among three resources (papers, patents, and web news articles) in two research domains. The contributions of this study are summarized as follows: firstly, we propose a new temporal analysis method to understand the content characteristics and trends of heterogeneous multiple resources in an integrated manner. We applied it to measure the exact time intervals between academic areas by understanding the time gap phenomena. The results of temporal analysis showed that the resources of the medical field had more up-to-date property than those of the computer field, and thus prompter disclosure to the public. Secondly, we adopted a power-law exponent measurement and content analysis to evaluate the proposed method. With the proposed method, we demonstrate how to analyze heterogeneous resources more precisely and comprehensively.     

RKPM方法关于非线性椭圆边值问题的的误差估计

通过重构核近似的基本原理简单介绍了重构核质点法(reproducing kernel particle meshfree methods,RKPM),关于非线性椭圆方程的Dirichlet问题,结合重构核近似的理论误差估计,研究了在满足一定条件下的RKPM法对于该类问题的解的误差估计.     

Dirichlet空间上的Toeplitz和小Hankel算子的性质

本文在Dirichlet空间上,对具有符号在H上的Toeplitz算子和小Hankel算子进行研究,考察了其代数性质,并改进了文献[2]中的一些结果．     

泊松方程圆内狄利克雷问题的付氏解

本文应用分离变量法．求出了一个泊松方程圆内狄利克雷问题的付氏解。     

二重多随机Dirichlet级数的收敛性与增长性

本文研究了在一定条件下的二重多随机级数收敛性与全平面的增长性，得到了较好的结果。     

用格林函数法求解双层球面间的非对称电场问题

用格林函数法求出了双层球面间的非对称电场的第一类边值问题的解析解，它概括了常见教材、文献中关于格林函数法往往限于“简单”、“接地”、“轴对称”等特殊情况。