椭圆型方程最大值原理

研究了椭圆型方程的解满足最大值原理的条件,然后对某些定理作了证明,最后探讨了最大值原理在研究解的唯一性以及解的估计中的应用．     

Measuring Parameter Uncertainty by Identifying Fungible Estimates in SEM

Researchers require methods for evaluating whether statistical results are credible and thus, worthy of interpretation. An examination of fungible parameters estimates is a method in which the veracity of inferences can be strengthened or weakened by quantifying the level of support for individual parameter estimates as measured by the likelihood function. This new approach aims to overcome some of the limitations of previous methods and is based on a simplified computational and conceptual understanding of a fungible parameter estimate analysis. Additionally, this computational approach has been implemented in the R package psindex. This package provides a user-friendly, and free method for statisticians and applied researchers to investigate parameter stability in their own models using an analysis of fungible parameter estimates. Finally, an applied example illustrates fungible parameter estimate analysis in practice using the psindex package. General guidelines for interpretation are provided.     

六阶微分方程第二广义谱的含权上界估计

考虑六阶微分方程第二广义谱的含权上界估计,利用算子谱理论、分部积分、测试函数、广义Rayleigh定理和不等式估计等方法,获得了用第一个谱来估计第二个谱的上界的不等式,其估计系数与区间的几何度量无关,其结论是文献[1～3]的进一步推广.     

K层Nekrasov矩阵与广义严格对角占优矩阵的关系研究

K层Nekrasov矩阵的推广矩阵中,K层弱Nekrasov矩阵与广义严格对角占优矩阵存在迭代矩阵和不等式估计等性质,本文针对这几类矩阵与广义严格对角占优矩阵之间的置换关系进行了定义和证明,并根据广义Nekrasov矩阵与弱Nekrasov矩阵的置换不变性,推论出非奇异矩阵的充要条件,将广义K层Nekrasov矩阵和K层弱Nekrasov矩阵的对角阵的奇异性进行了充要性的推论和证明。进而通过构造特殊矩阵和特殊向量改进了广义Nekrasov矩阵研究中的不足。     

多元K_n-近邻密度估计的一致收敛速度

本文在适当的条件下研究了对于一般型式的k_n~_近邻密度估计强一致相合性的收敛速度.     

线性抛物型方程的窄四边形有限元逼近

讨论了各向异性窄四边形元的能量模和零模估计,并利用此单元求解线性抛物型方程,得到了半离散格式和全离散格式的误差估计。     

超球多项式的带权正交性及其应用

本文首先利用幂级数讨论超球多项式的性质并得到超球多项式的一般表这式,其次研究了超球多项式的带权正交性,最后给出超球多项式在Lapalace方程Dirichlet边值问题中的应用。     

一类非线性Schroedinger方程的守恒差分格式

对一类带五次项的非线性Schroedinger方程的初边值问题提出了一个参数型的守恒差分格式,并在先验估计的基础上证明了差分格式的收敛性与稳定性.     

A Walsh function method for a non-linear Volterra integral equation

A new method for the numerical solution of linear and non-linear Volterra integral equations, using the discontinuous wavelet packets known as the Walsh functions, is proposed and investigated. Sufficient conditions for the method to converge are derived and a priori error estimates are obtained. Given sufficient regularity conditions on the integral equation, the method is shown to be locally of order two.     

一类具有非线性边界阻尼和源项的非线性波动方程的解的渐近性

研究一类具有非线性边界阻尼和源项的非线性波动方程的初边值问题，证明在一定条件下其整体广义解的存在、解具有衰减性并给出了解的衰减估计。