素超代数上超导子的线性组合

In the paper, we give some results about a linear combination of superderivations on prime superalgebras and generalize a result of Niu Feng-wen.     

基于灰色线性回归组合模型的长沙、武汉房地产投资预测研究

本文通过对长沙、武汉2001-2007年房地产投资额的历史数据进行分析,分别建立了两市的灰色线性回归组合模型.模型较好地拟合了长沙、武汉的房地产投资情况,运用该模型得到了两市2008、2009年的预测值,并对其房地产投资发展趋势的异同进行比较分析,对房地产市场的发展具有一定的指导意义.     

求不定二次规划全局解的一个新算法

本文提出了一个求不定二次规划问题全局最优解的新算法.首先,给出了三种计算下界的方法:线性逼近法、凸松弛法和拉格朗日松弛法;并且证明了拉格朗日对偶界与通过凸松弛得到的下界是相等的;然后建立了基于拉格朗日对偶界和矩形两分法的分枝定界算法,并给出了初步的数值试验结果.     

K-Drop凸空间与局部K-Drop凸空间

引入了Banach空间的局部k-drop凸性质，研究了k-drop凸与局部k-drop凸的一些性质以及两者之间的关系，并用单位球的切片统一而简洁地处理了这两个性质．     

Variational Inequality with Fuzzy Convex Cone

In this study, we discuss one type of variational inequality problem with a fuzzy convex cone , denoted by VI( , f). Different classes of fuzzy convex cones which are considered in different context of the problems will be discussed. According to the existence theorem, an approach derived from the concepts of multiple objective mathematical programming problems for solving the VI( , f) is proposed. An algorithm is developed to find its fuzzy optimal solution set with complexity analysis.     

The Median Stabilization Degree of a Median Algebra

The median stabilization degree (msd, for short) of a median algebra measures the largest possible number of steps needed to generate a subalgebra with an arbitrary set of generators. We determine the value of msd of a graphic n-cube Qn and we derive an estimation of msd for the natural median operator of Rn which is sharp up to one or two units. Interestingly, msd of Qn and of Rn grows like log1.5n. Finally, we characterize median algebras and median graphs of msd 1 in terms of forbidden subspaces.     

Application of Upper Hemi-Continuous Operators on Generalized Bi-quasi-variational Inequalities in Locally Convex Topological Vector Spaces

Let and be Hausdorff topological vector spaces over the field , let be a bilinear functional, and let be a non-empty subset of . Given a set-valued map and two set-valued maps , the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point and a point such that and for all and for all or to find a point a point and a point such that and for all . The generalized bi-quasi-variational inequality was introduced first by Shih and Tan [8] in 1989. In this paper we shall obtain some existence theorems of generalized bi-quasi-variational inequalities as application of upper hemi-continuous operators [4] in locally convex topological vector spaces on compact sets.     

Approximation to Probabilities Through Uniform Laws on Convex Sets

Let P be a probability distribution on ^d and let be the family of the uniform probabilities defined on compact convex sets of ^d with interior non-empty. We prove that there exists a best approximation to P in , based on the L ₂-Wasserstein distance. The approximation can be considered as the best representation of P by a convex set in the minimum squares setting, improving on other existent representations for the shape of a distribution. As a by-product we obtain properties related to the limit behavior and marginals of uniform distributions on convex sets which can be of independent interest.     

Cyclic Just-In-Time Sequences Are Optimal

Consider the Product Rate Variation problem. Given n products 1,...,i,...,n, and n positive integer demands d ₁,..., d_i,...,d_n. Find a sequence =₁,...,_T, T = _i=1 ⁿ d _i, of the products, where product i occurs exactly d _i times that always keeps the actual production level, equal the number of product i occurrences in the prefix ₁,..., _t, t=1,...,T, and the desired production level, equal r _i t, where r _i=d_i/T, of each product i as close to each other as possible. The problem is one of the most fundamental problems in sequencing flexible just-in-time production systems. We show that if is an optimal sequence for d ₁,...,d_i,...,d_n, then concatenation ^m of m copies of is an optimal sequence for md ₁,..., md_i,...,md_n.     

一类具约束选址模型的组合算法

针对一般具闭凸集约束的单址选址模型,提出具全局收敛性的组合算法．算法在迭代中先采用信赖域技巧,当出现“内循环”时,则改用不做线搜索的梯度法．该算法既具有信赖域算法的优越性,又避免了出现“内循环”时速成的隐迭代．同时,该算法通常不需进行线搜索,较之其它组合算法更加简捷实用．