An Inventory Model with an Inventory-Level-Dependent Demand Rate and Relaxed Terminal Conditions

This paper investigates an inventory system with an inventory-level-dependent demand rate followed by a constant demand rate. The analysis previously conducted on this model imposed a terminal condition of zero inventory at the end of the order cycle. This condition is not warranted for systems with inventory-level-dependent demand rates, even for deterministic models. This paper relaxes this restriction, and an appropriate model is developed.     

Fejér不等式加强形式的推广

通过建立积分恒等式,将一个关于4阶可微函数的Fejér不等式的加强形式推广到关于2n-1(n≥2)阶可微函数的Fejér型不等式.对此新推广的不等式还给出了若干误差估计.     

Revised proof of a theorem concerning an involution with local Engel or power commuting condition

This paper is a correction paper concerned with an important theorem about an involution with Engel condition.     

A NOTE ON THE GLOBAL SOLUTIONS OF A SEMILINEAR REACTION DIFFUSION SYSTEM

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Demand during Lead Time for Normal Unit Demand and Erlang Lead Time

We obtain an expression for the probability density function of demand during lead time when the distributions of demand and lead time are, respectively, normal and Erlang. This probability density function is then used to derive expressions for the protection level and potential lost sales. This paper may be considered an extension and also a clarification of a paper by Burgin that appeared in 1972.     

On optimizing functions which are defined in part by an approximation process

This paper studies an optimization problem in which the objective function can not be completely given in closed form. In particular, we assume that some part of the objective function must be computed by an approximation process. This paper develops a technique for solving a class of such problems. Examples demonstrating the technique and problem areas in which it has been successfully applied are also given.     

Uncertain random programming with applications

Uncertain random variable is a tool to deal with a mixture of uncertainty and randomness. This paper presents an operational law of uncertain random variables, and shows an expected value formula by using probability and uncertainty distributions. This paper also provides a framework of uncertain random programming that is a type of mathematical programming involving uncertain random variables. Finally, some applications of uncertain random programming are discussed.     

Fuzzy inventory problems for perishable commodities

This paper considers an inventory control model for a single perishable product with a fuzzy shortage cost and a fuzzy outdating cost. This model is a single-period horizon model. Due to fuzziness of shortage and outdating costs, an expected profit function is represented with a fuzzy set. The purpose of this paper is to find the solution maximizing the expected profit function. After defining a nondominated ordering quantity based on fuzzy max order, we seek some of them and investigate an effect of the fuzziness on the obtained solutions.     

Constructing a rhombus through paper folding

This paper presents an example of how paper folding can be used in a geometry class to support conceptual understanding. Specifically, it explains an activity that constructs a rhombus and explores its attributes by using paper folding. The steps of constructing a rhombus are described and some discussion questions are given to consolidate understanding.     

考虑缺货的闭环供应链选址-库存-路径集成优化

再制造是企业实现环境友好、提升经济效益的重要策略之一;再制造的发展推动了新商业模式的出现,即产品服务系统;高效的再制造物流网络对于成功实施再制造十分重要。本文研究了基于产品服务系统下的再制造物流网络集成优化问题,即闭环供应链的选址-库存-路径的集成优化决策问题,且在库存策略中允许库存出现缺货的情况;论文基于产品服务系统模式构建了混合非线性规划模型来最小化生产、选址、配送、库存以及缺货成本,并采用了改进的禁忌搜索算法进行求解。通过与传统禁忌搜索算法的计算结果进行对比,表明本文中的算法能在可接受的时间内得到较优解。通过算例的敏感性分析得出,企业所服务的顾客如果接受再制造产品,提高回收率可以节约成本;在回收率一定时,客户在缺货情形下的制造和再制造批量比不允许缺货时要大,企业总成本比不允许缺货时要小。     

On one question of the kourovka notebook 1

This paper answers the open question 12.73 in “Unsolved Problems in Group Theory, The Kourovka Notebook, 1995“. This paper give an example to show that this question has a negative solution, and give a condition under which the conclusion of the question is correct.     

关于无界连续函数逼近

§ 1 .　Introduction　　Itisaveryimportantstudytoapproximatenonboundedcontinuousfunctionsdefinedonalargerange.Aneffectivemethodcalledthemethodofmultiplierenlargementhasbeenputfor wardandgreatlydevelopedbyHSULCandWANGReng Hong [1— 3].Thesecondauthorofthispaperinparticularhasprovedin [2 ]almostuniformlythatanynonboundedcontinuousfunctionsdefinedonawholerealaxiscanbeapproximatedbypolynomialoperators.We’llgen eralizeinthispaperthebasicprincipleofthismethod,andasanexample,Bernsteinpolynomial…     

Membership functions and operational law of uncertain sets

Uncertain set is a set-valued function on an uncertainty space, and attempts to model “unsharp concepts” that are essentially sets but their boundaries are not sharply described. This paper will propose a concept of membership function and define the independence of uncertain sets. This paper will also present an operational law of uncertain sets via membership functions or inverse membership functions. Finally, the linearity of expected value operator is verified.     

A Two-product,Single-machine,Storage-constrained Production Problem

This paper considers a two-product, single-machine production scheduling problem where there is an added constraint on the amount of finished stock that can be held. The need for a ratio of the cycle times of the two products is a feature both of two-product production scheduling problems contained on one machine and two-product inventory problems with constraints on storage capacity. This means an easy solution algorithm is possible for the problem addressed in the paper which has both types of constraints.     

A retelling of Newton’s work on Kepler’s Laws

This paper details an investigation into Kepler’s Laws. Newton’s technique for deducing an inverse-square law from Kepler’s Laws is given a modern presentation, with necessary background material included. Kepler’s Laws are then deduced from the assumption of an inverse-square law. This is done in a geometric style, inspired by Newton’s work. Finally, a problem involving planetary orbits is stated and solved using the earlier results of the paper.     

Evaluating electronic workshops through analysing the ‘brainstormed’ ideas

This paper explores how participants work in a new format of brainstorm, called an ‘incubated gathering’. The paper explores brainstorm-type activities, where senior managers share occupational knowledge in the generation of a solution to a problem in which they have an embedded interest. The findings suggest that participants perceive great worth in the incubated gathering, and (compared to other formats of gathering) it allows participants to consider a significantly wider range of issues, and in more detail. They also suggest that an outcome from an incubated gathering will be informed by a more rich consideration of the pertinent issues than that from other formats of brainstorming. This paper substantiates these claims with evidence from a suite of new approaches to gauge the ability of participants to share knowledge during group brainstorming-type activities.     

一个修正的Newton法之改进

众所周知,多项式方程的求解有很多应用背景,而Newton法是一种常用的数值方法,因此有不少文献讨论Newton法的各种改进,包括用于求解多项式方程时的变形[1-7],在文[1]中,Ehrlich,L.W.提出了一个同时决定n次多项式的n个单根的迭代法.对方程     

A finitely convergent procedure for facial disjunctive programs

This paper addresses an important class of disjunctive programs called facial disjunctive programs, examples of which include the zero-one linear integer programming problem and the linear complementarity problem. Balas has characterized some fundamental properties of such problems, one of which has been used by Jeroslow to obtain a finitely convergent procedure. This paper exploits another basic property of facial disjunctive programs in order to develop an alternative finitely convergent algorithm.     

REMARKS ON BRUALDI＇S THEOREM FOR SPECTRUM INCLUSION REGION OF AN IRREDUCIBLE MATRIX

This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi‘s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.     

浅析构造思想在高等数学中的应用

本文对高等数学中的构造思想进行了一定程度的探究,主要分析说叫了构造思想在高等数学中的重要地位及其应用,重点沦述了反例的构造,为高等数学教学提供了一个有效的辅助方法。