A template of rat brain based on fMRI T*2 imaging

The development of functional magnetic resonance imaging (fMRI) technology has made it possible to carry out functional brain imaging experiments in small animals. Usually, group data is required to form the assessment of population, which can not only increase the sensitivity of the overall experiment, but also allow the generalization of the conclusion to the whole population. In order to average the signals of functional brain images from different subjects, it is necessary to put all the mapping images into the same standard space (template image). However, up to now, most animal brain templates remain unavailable and it must be done by ourselves. In this study, a template image based on the brains of eight male Wistar rats is obtained, and it is successfully used in our present Alzheimer disease (AD)-like rat model studies as template for spatially normalizing images to the same stereotaxical space. The fMRI results processed with statistical parametric mapping (SPM99) software are in agreement with the results from immunohistochemical experiment, which proves that this method is universally applicable to the pathologic models of other small animals and to human brain lesion studies.     

关于相对拓扑性质的某些探讨

本文对相对正规性，可弱连续嵌入以及潜在紧空间等几个相对拓扑性质进行了初步研究，分别给出了正规空间在更大的拓扑空间中正规的条件和Tychonoff空间可弱连续嵌入到更大的Tychonoff空间的条件．同时证明了拓扑空间的潜在紧性是拓扑不变量。     

三维水动力学模型高精度差分格式和解法研究

采用高精度差分格式对三维水动力学问题的时均化Navier-Stokes方程进行了数值模拟，进而采用广义共轭剩余法（GCR方法）求解压力泊松方程，并采用显式三级二阶Runge-Kutts格式模拟了时间步进过程。傅立叶分析表明，文中所采用的三阶迎风紧致差分格式具有较高的精度，数值实验进一步验证了上述数值模型的准确性和有效性。     

Compact difference approximation with consistent boundary condition

For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.     

一类差分方程的Cm解的存在性和惟一性

讨论了一类较广泛的差分方程G(x,f(x),f(x 1),……,f(x n)=n,x∈R，其中G∈C^m（R^n 2,R),n≥2)，通过采用小挪动映射逼近不动点的方法，对任一整数m≥0，在较弱的条件下证明了该方程的C^m解的存在性和惟一性。     

低热固相法合成纳米(NH4)3PMo12O40·4H2O及其机理的研究

通过低热固相反应合成了纳米(NH4)3PMo12O40*4H2O,XRD、31P NMR研究发现,在此固相反应的4个步骤中(扩散,反应,成核,生长),反应的速率控制步骤是产物的成核.     

关于算子紧空间

在算子开集理论中提出了算子紧空间、算子可数紧空间、算子Lindeloef空间的概念，同时指出算子紧空间是紧空间、s-紧和强紧等空间的推广，并对这类空间所具有的性质进行了一些有益的讨论。     

群的s*-拟正规性及其性质

称群G的子群H为G的s^-拟正规子群，如果G中存在p-Sylow子群与H可换，其中p为|G|的任意素数因子．本讨论了s^-拟正规子群的性质并给出一个群为可解群的一些条件．     

具有混合边界条件的地下水污染模型的强解存在性

给出具有混合边界条件的地下水污染模型的弱解和强解定义，用积分估计法得到了强解（如果存在）的先验一致估计，利用半－Ｇａｌｅｒｋｉｎ方法和紧性原理证明了上述方程组强解的局部存在性     

紧Lie群上的高阶Riesz变换

讨论了紧Ｌｉｅ群上的高阶Ｒｉｅｓｚ变换并给出了高阶Ｒｉｅｓｚ变换的奇异积分表示．