四元六次对称多项式不等式探讨

对四元六次对称多项式不等式的分拆进行了初步探讨；证明了若干拆分基不等式和含参不等式；最后提出了若干问题。     

求解大型对称特征值问题的改进块Jaeobi—Davidson方法

块Jacobi—Davidson方法是求解对称矩阵重或密集特征值问题的一种有效方法．为了提高其整体收敛速度,应用动态压缩技术,提出了动态压缩的块Jacobi—Davidson方法;为了计算大型对称矩阵的内部特征对,本文将调和Rayleigh—Ritz方法与块Jacobi—Davidson方法结合,提出了调和块Jacobi—Davidson方法,并将动态压缩技术应用于调和块Jacobi—Davidson方法,给出了动态压缩的调和块Jacobi—Davidson方法．数值结果表明,动态压缩的块Jacobi—Davidson方法优于块Jacobi—David—son方法,动态压缩的调和块Jacobi—Davidson方法能有效计算大型对称矩阵的内部重或密集特征值．     

对称三对角矩阵的QL方法论

QL(QR) method is an efficient method to find eigenvalues of a matrix. Especially we use QL(QR) method to find eigenvalues of a symmetric tridiagonal matrix. In this case it only costs O( n^2) flops, to find all eigenvalues. So it is one of the most efficient method for symmetric tridiagonal matrices. Many experts have researched it. Even the method is mature, it still has many problems need to be researched. We put forward five problems here. They are: (1) Convergence and convergence rate; (2) The convergence of diagonal elements; (3) Shift designed to produce the eigenvalues in monotone order; (4) QL algorithm with multi-shift; (5) Error bound. We intoduce our works on these problems, some of them were published and some are new.     

辐射场包围Schwarzschild黑洞的稳态球对称度规

由于黑洞具有Hawking辐射,它对时空必有影响（所谓反作用）。本文结合用热力学方法研究黑洞反作用问题所得结果,应用求解考虑辐射场存在时的半经典受因斯坦场方程,得出由辐射场包围Schwarzschild黑洞的稳态球对称度规。由此度规度的到黑洞的辐射能量密度与径向压强的关系同平直时空的关系一致。     

射影空间上的等参子流形

讨论了复射影空间ＣＰｎ和四元数射影空间ＨＰｎ上的等参子流形．利用ＣＰｎ上等参子流形的分类定理［１０］,证明了ＣＰｎ上等参子流形的刚性定理．同时,还得到了四元数射影空间ＨＰｎ上等参子流形的例子．     

两类矩阵方程有亚半正定解的充要条件

本文给出了矩阵方程（Ⅰ）AXAT＋BYBT＝C,（Ⅱ）（ATXA,BTXB）＝（C,D）有亚半正定解的充要条件．     

非对称通信网络中易变数据的广播调度

Recent advances in wireless sensor networks and GPS have made constantly-evolving data a new type of data which bring a new challenge to traditional data processing methods. Data broadcasting is an effective means for data dissemination in asymmetric communication networks, such as wireless networks. In this paper, definition of the mean uncertainty ratio of data is presented and a broadcasting scheme is proposed for constantly-evolving data dissemination. Simulation results show that the scheme can reduce the uncertainty of the broadcasted constantly-evolving data effectively at the cost of minor increase in data access time, in the case of no transmission error, transmission errors present, and multiple broadcast channels. As a result it benefits the qualities of the query results based on the data.     

关于实对称矩阵的惯性定理

从实对称矩阵与实二次型的联系、实对称矩阵与实线性空间的对称双线性函数的联系以及将实对称矩阵作为研究主体这三个角度,介绍实对称矩阵的惯性定理的三种证明,以期加深对实对称矩阵的惯性定理的理解.     

二次曲线分类的一个标准

作者证明了点C(x0 ,y0 )是二次曲线的对称中心的充要条件是点C(x0 ,y0 )满足对称中心方程组 ,从而得到了对称中心是二次曲线分类的一个标准 ,进一步论证了按下面的思路讲解二次曲线分类的科学性 :二次曲线的对称中心方程组 - -二次曲线的分类。     

局部纯正半群的一个注记

本文证明了局部纯正半群的正则子半群、同态像和直积是局部纯正半群, 以及带与完全单半群的Pastijn 积是一个局部纯正半群。