Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems

In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions.  

复亚正定矩阵的一些性质

复亚正定矩阵是正定Ｈｅｒｍｉｔｅ矩阵的推广，本文讨论了这一类矩阵张量积的性质，并将实对称矩阵的Ｓｃｈｕｒ定理、华罗庚定理和Ｍｉｎｋｏｗｓｋｉ不等式推广到较为广泛的复矩阵类．  

Generalized Chi Square Method for the Estimation of Weights

This paper presents a generalized chi square method for the estimation of weights in the analytic hierarchy process and studies its desirable properties such as invariance under transpose, harmony, and rank preservation. A convergent iterative algorithm is given and its practicality is shown by a numerical example.  

模糊推理全蕴涵算法及其还原性

模糊推理是模糊控制的逻辑基础,然而通用的模糊推理CRI算法却缺乏严格的逻辑依据,近期问世的模糊推理全蕴涵三I算法有效地改进了CRI算法。本文研究了全蕴涵三I算法的一般计算公式及其还原性问题,并且得到了一些新的算法,也提出了一些新的观点,文献中已有的结果大多数是本文结果的特例。从而为模糊推理提供了一种新方法。  

Coordination of a Supply Chain with One-Manufacturer and Two-Retailers Under Demand Promotion and Disruption Management Decisions

Increasingly, customer service, rapid response to customer requirements, and flexibility to handle uncertainties in both demand and supply are becoming strategic differentiators in the marketplace. Organizations that want to achieve these benchmarks require sophisticated approaches to conduct order promising and fulfillment, especially in today’s high-mix low-volume production environment. Motivated by these challenges, the Available-to-Promise (ATP) function has migrated from a set of availability records in a Master Production Schedule (MPS) toward an advanced real-time decision support system to enhance decision responsiveness and quality in Assembly To Order (ATO) or Configuration To Order (CTO) environments. Advanced ATP models and systems must directly link customer orders with various forms of available resources, including both material and production capacity. In this paper, we describe a set of enhancements carried out to adapt previously published mixed-integer-programming (MIP) models to the specific requirements posed by an electronic product supply chain within Toshiba Corporation. This model can provide individual order delivery quantities and due dates, together with production schedules, for a batch of customer orders that arrive within a predefined batching interval. The model considers multi-resource availability including manufacturing orders, production capability and production capacity. In addition, the model also takes into account a variety of realistic order promising issues such as order splitting, model decomposition and resource expediting and de-expediting. We conclude this paper with comparison of our model execution results vs. actual historical performance of systems currently in place.  

Structure of Degenerate Block Algebras

Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map : A A F, we define a Lie algebra = (A, ) over F with basis {e_x | x A/{0}} and Lie product [e_x,e_y] = (x,y)e_x+y. We show that is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der of is a complete Lie algebra. We describe the double extension D( , T) of by T, where T is spanned by the locally finite derivations of , and determine the second cohomology group H²(D( , T),F) using anti-derivations related to the form on D( , T). Finally, we compute the second Leibniz cohomology groups HL²( , F) and HL²(D( , T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee.  

ON JENSEN’S INEQUALITY FOR g-EXPECTATION

Briand et al. gave a counterexample showing that given g, Jensen's inequalityfor g-expectation usually does not hold in general. This paper proves that Jensen'sinequality for g-expectation holds in general if and only if the generator g(t,z) issuper-homogeneous in z. In particular, g is not necessarily convex in z.  

环上矩阵的Moore-Penrose逆

本文研究环上矩阵的广义逆,得到其存在的充要条件,给出它的表达式,推广了以往文献的相应结果。  

非线性随机效应模型的异方差性检验

随机效应模型广泛应用于刻画重复测量数据的特征．在该模型中,随机误差的方差包括受试群体内部及受试群体之间两项方差．Ｚｈａｎｇ和 Ｗｅｉｓｓ ２０００年研究了线性随机效应模型的异方差检验,本文对非线性随机效应模型,分别讨论了群体内、群体间和多变量的异方差性的检验问题,得到了检验的ｓｃｏｒｅ统计量,并讨论了三种情形下,相应的ｓｃｏｒｅ函数之间的关系．最后给出一个数值例子说明上述方法的有用性．  

N-环Von-Neumann正则性

环R称为N-环，如果R的素根N(R)=｛r∈R｜存在自然数n使rⁿ=0}.本文不仅对N-环进行了刻划，而且还研究了N-环的VonNeumann正则性.特别证明了：对于N-环R，如下条件是等价的：(1)R是强正则环；(2)R是正则环；(3)R是左SP-环；(4)R是右SF-环；(5)R是MELT，左p-V-环；(6)R是MERT，右p-V-环.因此推广了文献[4]中几乎所有的重要结果，同时也改进或推广了其它某些有关正则环的有用结果.