关键词： timetabling   class scheduling   mixed-integer programming   employee scheduling   gender policies  

摘要： This paper presents mathematical programming models for assigning faculty members to classes including, among typical academic class scheduling issues, certain specialized central policies at Kuwait University. The time-slots for classes are initially assumed to be given and an integer programming model (CFAM) is constructed to solve the resulting problem, which aims to minimize the individual and collective dissatisfaction of faculty members in a fair fashion, where dissatisfaction is measured by a function of the assignment of faculty members to time-slots and specific classes. In order to enhance the quality of results obtained in practice, the model is modified (ECFAM) so that the time-slots for the classes can be changed, however, with restrictions related to efficient facility utilization and permitting an administratively regulated maximum number of changes. Gender-based modeling considerations are also introduced in order to maintain desirable class offering patterns. Computational results are presented based on solving the models directly by the CPLEX-MIP (version 7.5) package and also using a specialized LP-based heuristic. The faculty schedules generated via the proposed approach based on a number of case studies related to the Department of Mathematics and Computer Science at Kuwait University reveal that this approach yields improved schedules in terms of fairness and enhanced satisfaction levels among faculty members. (c) 2005 Elsevier B.V. All rights reserved.

关键词： active-set algorithm   branch-and-bound method   complementarity   disjunctive cuts   global optimization  

摘要： In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, NP-hard Linear Complementarity Problems, and Hinge Fitting Problems are presented to highlight the efficacy of the procedure in determining a global minimum for different classes of MPECs.

关键词： computer algebra   numerical integration   numerical differentiation   multistep methods  

摘要： An useful application of computer algebra systems is the generation of algorithms for numerical computations. We have shown in Gander and Gruntz (SIAM Rev., 1999) how computer algebra can be used in teaching to derive numerical methods. In this paper we extend this work, using essentially the capability of computer algebra system to construct and manipulate the interpolating polynomial and to compute a series expansion of a function. We will automatically generate formulas for integration and differentiation with error terms and also generate multistep methods for integrating differential equations.

关键词： posets   combinatorics   Birkhoff's theorem  

摘要： A combinatorial problem usually requires enumerating, counting or ascertaining existence of structures that satisfy a given property B in a set of structures L. This paper describes a technique based on a generalization of Birkhoff's theorem of representation of finite distributive lattices that can be used for solving such problems mechanically and efficiently. Specifically, we give an efficient (polynomial time) algorithm to enumerate, count or detect structures that satisfy B when the total set of structures is large but the set of structures satisfying B is small. We illustrate our techniques by analyzing problems in integer partitions, set families, and set of permutations. (C) 2006 Elsevier B.V. All rights reserved.

关键词： 模糊算法   闪点   温度  

摘要： 在智能闪点仪中应用基于模糊算法的温度控制方法,可以有效地控制升温过程。文中给出了具体的模糊计算过程。

关键词： 高中数学课程标准   算法   算法教学  

摘要： 算法是当前高中数学课程改革中引入的新内容.经过对实验区师生的调查访谈发现,课程改革中有关算法的理念得到了广大师生的赞同.但是还存在以下问题:(1)学生对于算法概念的理解不够全面;(2)算法在计算机和相关数学内容中的应用很差;(3)教师在教学中获得的支持不足.这些问题主要是由于课程自身、教师观念,课程资源和教师培训几方面的原因造成的。

关键词： 军械物资紧急调运   多需求点   单货种   运力限制   多目标决策  

摘要： 军械物资调运是军械保障工作的一个十分重要的环节,关系到军械保障工作能否快捷有效地完成。考虑到战时状况下军械物资调运的复杂性、快速性和危险性等特点,建立了不同时间要素规定情况下多需求点、单货种军械物资有运力限制条件的紧急调运的2种优化模型。通过严格的数学逻辑推导,对这2种模型给出了解析算法,并通过具体的算例表明了模型的正确性及算法的有效性。

关键词： algebraic grid generation   algebraic mixed methods   grid quality measures   condition numbers   grid optimization  

摘要： In this paper we present an algorithm able to provide geometrically optimal algebraic grids by using condition numbers as quality measures. In fact, the solution of partial differential equations (PDEs) to model complex problems needs an efficient algorithm to generate a good quality grid since better geometrical grid quality is gained, faster accuracy of the numerical solution can be kept. Moving from classical approaches, we derive new measures based on the condition numbers of appropriate cell matrices to control grid uniformity and orthogonality. We assume condition numbers in appropriate norms as building blocks of objective functions to be minimized for grid optimization. This optimization procedure improves the mixed algebraic grid generation method first discussed in [C. Conti, R. Morandi, D. Scaramelli, Using discrete uniformity property in a mixed algebraic method, Appl. Numer. Math. 49 (4) (2004) 355-366. [3]]. The whole algorithm is able to cheaply generate optimal algebraic grids providing optimal location of the control points defining a small set of free parameters in the tensor product of the mixed algebraic method. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： embedding   generic points   homotopy continuation   irreducible components   multiplicity   numerical algebraic geometry   polynomial system   primary decomposition  

摘要： Let F-1, F-2,..., F-t be multivariate polynomials (with complex coefficients) in the variables z(1), z(2),..., z(n). The common zero locus of these polynomials, V (F-1, F-2,..., F-t) = {p is an element of C-n vertical bar F-i (p) = 0 for 1 <= i <= t}, determines an algebraic set. This algebraic set decomposes into a union of simpler, irreducible components. The set of polynomials imposes on each component a positive integer known as the multiplicity of the component. Multiplicity plays an important role in many practical applications. It determines roughly "how many times the component should be counted in a computation". Unfortunately, many numerical methods have difficulty in problems where the multiplicity of a component is greater than one. The main goal of this paper is to present an algorithm for determining the multiplicity of a component of an algebraic set. The method sidesteps the numerical stability issues which have obstructed other approaches by incorporating a combined numerical-symbolic technique. (c) 2006 Elsevier Inc. All rights reserved.

关键词： 统计信号处理   非多尺度分解   EM算法   图像融合  

摘要： 在非多尺度分解的框架下,针对像素级的图像融合,提出了一种基于统计信号处理图像融合算法。该算法从一个直观的图像融合模型出发,即所获得的原始图像是模糊因子乘理想的融合图像与噪声进行非线性累加所得,应用模糊数学的原理和统计信号处理的EM算法,递推求出噪声的各项参数和对应的模糊因子,最终导出所求的融合图像。试验表明,应用该算法融合后的图像取得了满意的效果。