ON EQUILIBRIUM PRICING AS CONVEX OPTIMIZATION

We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets： 1. A mixed Fisher and Arrow- Debreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex opti- mization by an interior-point algorithm in polynomial time.     

拟调和球的不存在性

证明了当N的万有覆盖上存在一个多项式增长的非负严格凸函数时,不存在从R~3到N的非平凡拟调和球.于是在dim M=3时推广了Eells-Sampson的定理.     

一类非对称结构线性方程组的子结构预处理子(英文)

针对一类具结构的非对称线性方程组提出了一类子结构预处理子,该预处理子只保留了约束条件的一半项.研究表明,预处理矩阵只有三个离散的特征值.为了避免计算Schur补的逆,还给出了正则化的子结构预处理子,同样对预处理矩阵进行了谱分析.这些结果将Zhou和Niu(Zhou J T,Niu Q.Substructure preconditioners for a class of structuredlinear systems of equations.Math.Comput.Model.,2010,52:1547-1553)的结果推广到非对称结构线性方程组.数值算例验证了提出的子结构预处理子的有效性.     

Magnetoabsorption spectra of magnetoexciton transitions in GaAs/Ga0.7Al0.3As quantum wells

The internal transitions and absorption spectra of confined magnetoexcitons in GaAs/Ga0.TA10.aAs quan- tum wells have been theoretically investigated under magnetic fields along the growth direction of the semiconductor heterostructure. The magnetoexciton states are obtained within the effective-mass ap- proximation by using a variational procedure. The trial exciton-envelope wavefunctions are described as hydrogeniclike polynomial functions. The internal transition energies are investigated by studying the allowed magnetoexcitonic transitions using terahertz radiation circularly polarized in the plane of the quantum well. The intraexcitonic magnetoabsorption to 2p^± like magnetoexciton states as functions of the coefficients are obtained for transitions from 1s-like applied magnetic field.     

A new class of multi-wavelet bases: V-system

The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.     

n次单位根在代数问题中的应用

主要论述n次单位根在一些组合数求和、多项式的整除、因式分解中的应用,说明了n次单位根法可拓宽解题思路,是一种方便、快捷的数学解题方法.     

有理插值型求积公式的存在性与收敛性

构造两种奇点预先给定的有理插值型求积公式(RIQFs),在一定条件下证明其存在唯一性和收敛性,结果推广了普通的插值型求积公式和Gauss型求积公式.     

矩阵广义对角化的探讨

利用子空间关于矩阵的最小多项式研究了矩阵可广义对角化的充要条件,给出了矩阵可广义对角化的一种算法.     

IMPORTANCE MEASURE OF CORRELATED VARIABLES IN POLYNOMIAL OUTPUT

为了解决一般工程问题中输出量为多项式情况下相关正态输入变量的贡献识别问题，以二次不含交叉项的多项输出量为例，利用多维相关正态分布及其条件分布的性质，解析地推导了相关正态输入变量对输出量总方差的独立贡献及相关贡献，采用算例验证了所推导的解析表达式的正确性．文中所推导的相关正态变量独立贡献和相关贡献的表达式可直接用于输出量为二次不含交叉项多项式或一次多项式情况下的输入变量贡献的识别，并且为其他新的算法提供了对照解，另外此方法亦可以推广至含交叉项的高阶多项式，解决更为复杂输出量情况下输入量的贡献识别问题．     

简证一道自主招生考试题

题目(2010年五校联考自主招生考试)设u是方程x3-3x+10=0的根,f(x)是系数为有理数的二次多项式,且α=12(u2+u-2),f(α)=u,