ND阵列加权乘积和的完全收敛性

设（Xni：1≤i≤n,n≥1）为行间ND阵列,g（x）是R^＋上指数为α的正则变化函数,{αni：1≤i≤n,n≥1}为满足条件max1≤i≤n｜ani｜=0（（g（n））^-1）的实数阵列．本文采用截尾的方法,得到了使ND随机变量阵列加权乘积和完全收敛的条件,并推广了以前学者的结论．     

The valuation of convertible bonds with numeraire changes

The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market. We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper. A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time. We also consider a special case when the asset price follows GBM （Geometric Brownian Motion） and interest rate follows Vasicek＇s model.     

Ring graphs and complete intersection toric ideals

We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideals are minimally generated by Gröbner bases. We prove that any graph can be oriented such that its toric ideal is a complete intersection with a universal Gröbner basis determined by the cycles. It turns out that bipartite ring graphs are exactly the bipartite graphs that have complete intersection toric ideals for any orientation.     

Perpendicular Dissections of Space

For each pair (Q _i ,Q _j ) of reference points and each real number r there is a unique hyperplane h \perp Q _i Q _j such that d(P,Q _i ) ² - d(P,Q _j ) ² = r for points P in h . Take n reference points in d -space and for each pair (Q _i ,Q _j ) a finite set of real numbers. The corresponding perpendiculars form an arrangement of hyperplanes. We explore the structure of the semilattice of intersections of the hyperplanes for generic reference points. The main theorem is that there is a real, additive gain graph (this is a graph with an additive real number associated invertibly to each edge) whose set of balanced flats has the same structure as the intersection semilattice. We examine the requirements for genericity, which are related to behavior at infinity but remain mysterious; also, variations in the construction rules for perpendiculars. We investigate several particular arrangements with a view to finding the exact numbers of faces of each dimension. The prototype, the arrangement of all perpendicular bisectors, was studied by Good and Tideman, motivated by a geometric voting theory. Most of our particular examples are suggested by extensions of that theory in which voters exercise finer discrimination. Throughout, we propose many research problems. Received July 20, 2000, and in revised form September 29, 2001, and October 12, 2001. Online publication March 4, 2002.     

关于线性子空间交的基

给出求两个子空间交的基的一般方法     

A tripling construction for mutually orthogonal symmetric hamiltonian double Latin squares

We provide two new constructions for pairs of mutually orthogonal symmetric hamiltonian double Latin squares. The first is a tripling construction, and the second is derived from known constructions of hamilton cycle decompositions of when is prime.     

多期完全信息博弈中的自我控制现象：一个基于双重自我模型的分析框架

现有文献对双重自我的研究仅限于对单人决策问题的探讨. 基于Fudenberg 和 Levine (American Economic Review, 2006, 96(5): 1449-1476) in 2006 的理论框架,建立将单人决策拓展至多人博弈的双重自我模型,以更准确地刻画和研究人们在现实生活中的互动行为. 利用该模型对某一完全信息下的两期多重均衡博弈展开分析,并与其他无双重自我个体的经济学模型进行对比. 双重自我模型在与Fudenberg-Levine 模型的公理假设保持一致的基础上,提出了更具一般性的体现多人互动特征的自我控制成本概念.     

完全多部图的无符号Laplacian特征多项式(英文)

For a simple graph G,let matrix Q（G）=D（G） + A（G） be it’s signless Laplacian matrix and Q G （λ）=det（λI Q） it’s signless Laplacian characteristic polynomial,where D（G） denotes the diagonal matrix of vertex degrees of G,A（G） denotes its adjacency matrix of G.If all eigenvalues of Q G （λ） are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K（n₁,n₂,···,n_t）.We prove that the complete t-partite graphs K（n,n,···,n）t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K（m,···,m）s（n,···,n）t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K（m,···,m,）s1（n,···,n,）s2（l,···,l）s3.     

Busemann-Petty问题的对偶均质积分形式

本文主要建立了凸体几何中Busemann-Petty问题的一个对偶均质积分形式,并将Funk截面定理推广到了对偶均质积分形式．     

A counterexample concerning line-free groups and complete Erdos space

We present a weakly closed, one-dimensional, line-free subgroup of the separable Banach space that is not homeomorphic to complete Erdos space. The existence of this example disproves a conjecture of Dobrowolski, Grabowski, and Kawamura.