线性流形上矩阵方程BTXB=F的双对称最小二乘解

1引言令R~(n×m)、OR~(n×n)、SR~(n×n)(SR_0~(n×n))分别表示所有n×m阶实矩阵、n阶实正交阵、n阶实对称矩阵(实对称半正定阵)的全体,A~ 表示A的Moore-Penrose广义逆,I_k表示k阶单位矩阵,S_k表示k阶反序单位矩阵。R(A)表示A的列空间,N(A)表示A的零空间,rank(A)表示矩阵A的秩。对A=(a_(ij)),B=(b_(ij))∈R~(n×m),A*B表示A与     

四元数矩阵方程AX-YB=C的最佳逼近解

本利用四元数矩阵的广义Frobenius范数建立一个关于四元数矩阵的实函数，并讨论了它的极值问题．然后在四元数矩阵方程AX-YB=C的解集合中导出了与给定矩阵的最佳逼近解的表达式．     

上协边类纤维丛表示的若干性质

本文研究了底空间为实射影空间时上协边类纤维丛表示的若干性质．     

实验模型的模态综合技术

本文将结构传递函数概念引入模态综合技术之中,提出了一种有利于实验模型的模态综合解案。文中通过结构传递函数导出了结构高阶剩余模态,为实验模型引入模态综合之中奠定了基础。同时,本文进一步讨论了将实验模型引入模态综合之中所必然出现的转角模态问题,并采用曲线拟合技术解决了这一问题。     

无限维空间中的实零点定理

在本文中，我们建立了无限维空间中的实零点定理，同时从仿射空间的拓扑结构和域的序结构两个方面，分别刻划了适合无限维实零点定理的序域．此外，本文有例子表明，对任意的基数α，确实存在适合α维实零点定理的序域．     

CALCULUS ON CANTOR TRIADIC SET （Ⅱ）—EXCEPTIONAL SET

In this paper the derivative and its exceptional set according to the alternatively jumping function and self-similar function respectively are discussed. And in the appendix, a proof of the statement 1.2(2) of “Calculus on Cantor triadic set (Ⅱ)—derivative” which is important to the discussion of exceptional set is given.     

Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with Pareto Individual Claim Distributions

In this paper we first consider a risk process in which claim inter-arrival times and the time untilthe first claim have an Erlang (2) distribution.An explicit solution is derived for the probability of ultimateruin,given an initial reserve of u when the claim size follows a Pareto distribution.Follow Ramsay,Laplacetransforms and exponential integrals are used to derive the solution,which involves a single integral of realvalued functions along the positive real line,and the integrand is not of an oscillating kind.Then we showthat the ultimate ruin probability can be expressed as the sum of expected values of functions of two differentGamma random variables.Finally,the results are extended to the Erlang(n) case.Numerical examples aregiven to illustrate the main results.     

On the Extension of Isometries between Unit Spheres of E and C（Ω）

In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too.     

K2里德堡态新分类

根据里德堡轨道的nl? 特性，对理论计算和实验观察到的钾分子电子态进行了分类．这些态被划分为实贯穿和实非贯穿里德堡态．这种分类更能从本质上解释和预测实验结果．比较了这种分类法对K2的应用和对Na2、Li2的应用．     

The relationship between acoustic radiation modes and structural modes and its applications

Both acoustic radiation modes and structural modes play an important role in the field of structure-borne sound, however, little work has been done for inherent relations between these two kinds of modes. This paper is focused on the relationship between the radiation modes and structural modes and its physical mechanisms. First, a governing equation for relating the radiation mode and structural mode is given based on the characteristics of the modes. Then, using the symmetric or anti-symmetric properties of two kinds of modes, the corresponding relations are presented. And then, numerical examples are given to verify the theoretical investigations, and it has been shown that, for a simply supported rectangular panel vibrating at low frequencies, the first radiation mode is dominant corresponding to (odd, odd) structural modes; the following radiation modes are respectively dominant corresponding to (even, odd), (odd, even), and (even, even) structural modes. Finally, such relations are applied to active acoustic structural control and provide a direct help for the design of active control strategy and arrangement of the secondary forces.