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．     

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.     

广义矩阵函数及其指标

本文推广了广义矩阵函数及对称张量的一些定理，给出了广义矩阵函数指标的若干关系式．     

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．     

两例对数即时定义赏析

<正>一、基于对数性质的新定义运算【例1】已知a_n=log_n+1（n+2）（n∈N^*）,观察下列运算a₁×a₂=log₂ 3×log₃4=lg3/lg2×lg4/lg3=2,a₁·a₂·a₃·a₄·a₅·a₆=log₂3·log₃4……log₆7·log₇8=lg3/lg2·lg4/lg3……lg7/lg6·lg8/lg7=3,……     

逆p·n·p·矩阵的表征

一个n阶实方阵A,若其各阶主子式皆非正,则称A为p.n.p.矩阵,记作A∈PNP;特别地,若A∈NP且各阶主子式皆负,则称A为p.n.矩阵,记作A∈PN进一步,若n阶实方阵A非奇异,且A^-1∈PNP,则称A为逆p.n.p.矩阵,记作A∈IPNP;特别地,若A^-1∈PN,则称A为逆p.n.矩阵,记作A∈IPN。     

广义Jacobi矩阵的逆特征问题

本文主要讨论广义Jacobi阵及多个特征对的广义Jacobi阵逆特征问题.通过相似变换将广义Jacobi阵变换为三对角对称矩阵,其特征不变、特征向量只作线性变换,再应用前人理论求得广义Jacobi阵元素ai,|bi|,|ci|有唯一解的充要条件及其具体表达式.