n元二次多项式的因式分解

利用二次型的理论．讨论了一般多元二次多项式的因式分解问题。给出了因式分解的判定定理和因式分解的方法。     

D_n上的Cayley图的同构因子分解

证明了素数度的阶为2n 的二面体群 D_n 上的 Cayley 图在 n 为奇,或 n 为2~k,或特征集满足一定条件下是有理的。同时也证明了三度二面体群上的 Cayley 图是有理的。     

Unconstrained parametrizations for variance-covariance matrices

The estimation of variance-covariance matrices through optimization of an objective function, such as a log-likelihood function, is usually a difficult numerical problem. Since the estimates should be positive semi-definite matrices, we must use constrained optimization, or employ a parametrization that enforces this condition. We describe here five different parametrizations for variance-covariance matrices that ensure positive definiteness, thus leaving the estimation problem unconstrained. We compare the parametrizations based on their computational efficiency and statistical interpretability. The results described here are particularly useful in maximum likelihood and restricted maximum likelihood estimation in linear and non-linear mixed-effects models, but are also applicable to other areas of statistics.     

Eisenstein判别法的推广

论述了Eisenstein判别法的若干具有实用价值的推广形式,并把Eisenstein判别法推广到了整环上.     

Graphical models for skew-normal variates

This paper explores the usefulness of the multivariate skew-normal distribution in the context of graphical models. A slight extension of the family recently discussed by Azzalini & Dalla Valle (1996 ) and Azzalini & Capitanio (1999 ) is described, the main motivation being the additional property of closure under conditioning. After considerations of the main probabilistic features, the focus of the paper is on the construction of conditional independence graphs for skew-normal variables. Necessary and sufficient conditions for conditional independence are stated, and the admissible structures of a graph under restriction on univariate marginal distribution are studied. Finally, parameter estimation is considered. It is shown how the factorization of the likelihood function according to a graph can be rearranged in order to obtain a parameter based factorization.     

QR-AMCBFM技术快速分析电磁散射特性

提出了一种新的特征基函数法——自适应修正特征基函数法(AMCBFM),并将其与基于dual-MGS的QR分解技术结合,构造一种新的混合方法——QR-AMCBFM。该方法基于对目标体分块,并按一定的距离关系划分为近、远场两部分,用AMCBFM计算出每一块上的初阶电流。在计算高阶电流时,先对块间互阻抗矩阵进行QR分解以决定远场区的互阻抗可否舍弃;然后计算出高阶基函数以及电流系数。数值结果表明,QR-AMCBFM技术具有相当高的计算效率。     

Computing and approximating multivariate chi-square probabilities

We consider computational methods for evaluating and approximating multivariate chi-square probabilities in cases where the pertaining correlation matrix or blocks thereof have a low factorial representation. To this end, techniques from matrix factorization and probability theory are applied. We outline a variety of statistical applications of multivariate chi-square distributions and provide a system of MATLAB programs implementing the proposed algorithms. Computer simulations demonstrate the accuracy and the computational efficiency of our methods in comparison with Monte Carlo approximations, and a real data example from statistical genetics illustrates their usage in practice.     

A spatial Bayesian semiparametric mixture model for positive definite matrices with applications in diffusion tensor imaging

Studies on diffusion tensor imaging (DTI) quantify the diffusion of water molecules in a brain voxel using an estimated 3 × 3 symmetric positive definite (p.d.) diffusion tensor matrix. Due to the challenges associated with modelling matrix‐variate responses, the voxel‐level DTI data are usually summarized by univariate quantities, such as fractional anisotropy. This approach leads to evident loss of information. Furthermore, DTI analyses often ignore the spatial association among neighbouring voxels, leading to imprecise estimates. Although the spatial modelling literature is rich, modelling spatially dependent p.d. matrices is challenging. To mitigate these issues, we propose a matrix‐variate Bayesian semiparametric mixture model, where the p.d. matrices are distributed as a mixture of inverse Wishart distributions, with the spatial dependence captured by a Markov model for the mixture component labels. Related Bayesian computing is facilitated by conjugacy results and use of the double Metropolis–Hastings algorithm. Our simulation study shows that the proposed method is more powerful than competing non‐spatial methods. We also apply our method to investigate the effect of cocaine use on brain microstructure. By extending spatial statistics to matrix‐variate data, we contribute to providing a novel and computationally tractable inferential tool for DTI analysis.     

Boltzmann方程的意义的探讨

本文试就Boltzmann方程的数学物理内函及其近代物理学的发展,以及为量子力学的建立提供了条件和为统计物理学的发展奠定了基础,从而促使整个物理学的发展进入崭新的革命时期方面来探讨Boltzmann所具有深远意义的物理理论和物理思想,并对Boltzmann方程的意义进行一些粗浅地探讨。     

相对论性理想流体熵密度的计算

求解自引力非辐射体系的熵结构，这个问题很有意义．本文一般地导出相对论性流体热力学第二定律的协变表达式．利用理想流体的熵流守恒和局域能量守恒等基本守恒律推导出熵密度的计算公式．