Worst-case analysis for flow shop scheduling problems with an exponential learning effect

A real industrial production phenomenon, referred to as learning effects, has drawn increasing attention. However, most research on this issue considers only single machine problems. Motivated by this limitation, this paper considers flow shop scheduling problems with an exponential learning effect. By the exponential learning effect, we mean that the processing time of a job is defined by an exponent function of its position in a processing permutation. The objective is to minimize one of the four regular performance criteria, namely, the total completion time, the total weighted completion time, the discounted total weighted completion time, and the sum of the quadratic job completion times. We present heuristic algorithms by using the optimal permutations for the corresponding single-machine scheduling problems. We also analyse the worst-case bound of our heuristic algorithms.     

Erdos-Ko-Rado Theorems of Labeled Sets

For k = (k1, ··· , kn) ∈ Nn, 1 ≤ k1 ≤···≤ kn, let Lkr be the family of labeled r-sets on k given by Lkr := {{(a1, la1), ··· , (ar, lar)} : {a1, ··· , ar} ■[n],lai ∈ [kai],i = 1, ··· , r}. A family A of labeled r-sets is intersecting if any two sets in A intersect. In this paper we give the sizes and structures of intersecting families of labeled r-sets.     

Parameter identification and optimization algorithm in microbial continuous culture

In this study, a novelty mathematical model is established to formulate the continuous culture of glycerol to 1,3-Propanediol (1,3-PD) by Klebsiella pneumoniae, in which the inhibition of 3-hydroxypropionaldehyde (3-HPA) to cells growth and activity of some enzymes (such as glycerol dehydratase (GDHt) and 1,3-PD oxidoreductase (PDOR)), and the passive diffusion and active transport of glycerol and 1,3-PD across cell membrane are all taken into consideration. Taking the mean relative error between the experimental data and calculated values as the performance index, a parameter identification model involving multiple nonlinear dynamic systems is presented. The identifiability of the parameter identification model is also proved. Finally, an improved particle swarm optimization (PSO) algorithm is constructed to find the optimal parameters for the systems under substrate limitation and excess conditions, respectively. Numerical results not only show that the established model can be used to describe the continuous fermentation reasonably, but also the improved PSO algorithm is valid.     

Periodic solution of a chemostat model with variable yield and impulsive state feedback control

In this paper, a chemostat model with variable yield and impulsive state feedback control is considered. We obtain sufficient conditions of the globally asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.     

Further results on planar DO functions and commutative semifields

It is proven that any Dembowski–Ostrom polynomial is planar if and only if its evaluation map is 2-to-1, which can be used to explain some known planar Dembowski–Ostrom polynomials. A direct connection between a planar Dembowski–Ostrom polynomial and a permutation polynomial is established if the corresponding semifield is of odd dimension over its nucleus. In addition, all commutative semifields of order 3⁵ are classified.     

多圆盘Hardy空间的不变子空间(英文)

设M是多圆盘Hardy空间H²（Tⁿ）的不变子空间.R_zi是以坐标函数z_i（i=1,2,…,n）为符号的乘法算子在M上的限制.本文作者证明了,存在一个内函数q,使得M=qH²（Tⁿ）当且仅当对i≠j,R_ziR_zj^*=R_zj^*R_zi.     

3标度层次分析法下盘锦人口预测方法的优选

基于目前我国人口数量预测方法繁多,优缺点不一的现状,以盘锦市1978～2008年人口数据为基础,分别采用曲线回归、GM(1,1)与等维递补灰色模型、BP神经网络与RBF神经网络、马尔萨斯模型与费尔哈斯模型、宋健模型与Leslie矩阵方法分别对盘锦市2030、2050、2070、2090年人口进行预测,并根据预测结果设置了盘锦市人口预测方法的多目标定量优选体系,并采用Matla,b2009b软件运用3标度层次分析法方法进行了预测方法的优选.优选结果显示在盘锦市人口预测中,径向基网络(RBF)为最优方案.     

客户知识管理—概念与量表开发

通过文献分析,将客户知识管理的定义划分为三类。从客户知识管理的概念和客户知识活动的特性入手,以文献研究和已有相关问卷、量表为基础,结合半结构化问卷和人员访谈所获得的资料,编制客户知识管理量表。研究结果表明,客户知识管理具有多维度结构,其量表的开发具有较好的可信度和可靠性,客户知识管理包括五个维度,即客户知识获取、客户知识整合、客户知识共享、客户知识使用和客户知识创新。本文对概念的界定以及量表的开发可以为企业进行客户知识管理提供参考和借鉴。     

Infinite domain potential problems by a new formulation of singular boundary method

This study proposes a new formulation of singular boundary method (SBM) and documents the first attempt to apply this new method to infinite domain potential problems. The essential issue in the SBM-based methods is to evaluate the origin intensity factor. This paper derives a new regularization technique to evaluate the origin intensity factor on the Neumann boundary condition without the need of sample solution and nodes as in the traditional SBM. We also modify the inverse interpolation technique in the traditional SBM to get rid of the perplexing sample nodes in the calculation of the origin intensity factor on the Dirichlet boundary condition. It is noted that this new SBM retains all merits of the traditional SBM being truly meshless, free of integration, mathematically simple, and easy-to-program without the requirement of a fictitious boundary as in the method of fundamental solutions (MFS). We examine the new SBM by the four benchmark infinite domain problems to verify its applicability, stability, and accuracy.     

Branched Coverings and Embedded Surfaces in Four-manifolds

In this paper, we get a lower bound on the genera of surfaces re, presenting certain divisible classes in some 4-manifold X with Hi（X; Z） finite.