从能量动量张量T~(ab)讨论熵四矢的散度

为了讨论黑洞的熵结构，本文从能动张量Tab推导出理想流体熵四矢的四维散度特性，其结果散度为零．     

-1/2E~2(?)ε 1/2(?)(E~2τδε/δτ)的物理诠释

本文分析了(-1/2)E~2?ε (1/2)?(E~2τ(?ε)/(?τ))的物理意义,并指出ε在表面处是变量,不能提出积分号外。     

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．     

联络及其在现代物理中的解释

本文从曲线坐标、曲面上向量平移入手,导入了联络,继而引入协变微分、短程线及曲率张量,最后指明联络在广义相对论中的意义。     

f~N电子构型离子的晶场理论

用Racah＝Judd可不约张量方法研究f~N电子构型离子，给出了弱场处理稀土和锕系离子配位场理论的一般方法。     

基张量和张量基的概念及其分析

通常张量有整体表示式和分量（指标）表示式，但这二者尚不是全面而完整的。因此，须将矢量中的基矢量和矢量基的概念推广到基张量和张量基。为此，需以基矢量及张量外积为基础，导出基张量和张量基，任一张量可表达为诸基张量的线性和。据此，可以阐明并矢正是二矢量的外积，并建立了其与张量的对应关系，这样的认识对于物理定律的张量方程及其应用有着重要的意义。     

对偶基矢量组在张量分析中的作用与意义

在数学上将客观定律用量的分量形式表达为对坐标系具有不变性的方程，是张量分析所要解决的核心问题，为此，需从单一一的基矢量组发展为对偶的两个基矢量组，文中给地偶基几何意义解释的新证明，进一步阐明了“同变”与“逆变”的含义，说明“同变”较为现在广泛使用的     

Testing for additivity and joint effects in multivariate nonparametric regression using Fourier and wavelet methods

We consider the problem of testing for additivity and joint effects in multivariate nonparametric regression when the data are modelled as observations of an unknown response function observed on a d-dimensional (d 2) lattice and contaminated with additive Gaussian noise. We propose tests for additivity and joint effects, appropriate for both homogeneous and inhomogeneous response functions, using the particular structure of the data expanded in tensor product Fourier or wavelet bases studied recently by Amato and Antoniadis (2001) and Amato, Antoniadis and De Feis (2002). The corresponding tests are constructed by applying the adaptive Neyman truncation and wavelet thresholding procedures of Fan (1996), for testing a high-dimensional Gaussian mean, to the resulting empirical Fourier and wavelet coefficients. As a consequence, asymptotic normality of the proposed test statistics under the null hypothesis and lower bounds of the corresponding powers under a specific alternative are derived. We use several simulated examples to illustrate the performance of the proposed tests, and we make comparisons with other tests available in the literature.