关键词： 复杂刀具   优化设计   数学模型   算法   改进  

摘要： 　目的　建立复杂刀具优化的数学模型,提高优化算法速度.方法　采用优化设计与CAD相结合的方法.结果与结论　解决了传统刀具设计的缺点,改进后的算法速度大幅度提高.

关键词： 开发型驾驶模拟器   17自由度   算法   汽车动力学   仿真   数学模型   结构特征   初始平衡  

摘要： 文中对17自由度汽车动力学仿真的数学模型进行了分析,具体描述了该汽车动力学仿真模型微分—代数方程组的结构特征,并针对该结构特征提出了一种适用于在开发型驾驶模拟器上运行的求解算法。仿真实践证明,这种算法快速准确,并可应用到具有类似结构的汽车动力学仿真模型或其它多体系统微分—代数方程组的求解中。

关键词： 投资组合   数学模型   算法研究   有效边缘   遗传算法   效用函数  

摘要： 投资组合理论是现代金融理论的核心,它起始于Markowitz1952年所发表的开创性论文\"证券组合选择\".经过四十余年来的发展,投资组合理论已取得一些突破性成果,例如CAPM模型、APT理论、Black-Scholes公式等.该文系统深入地研究了投资组合的一些新理论和新算法.主要内容包括:第一章介绍现代投资组合理论的历史与研究现状,罗列该论文研究所需要的一些相关基础知识.第二章在有限分散情况下,讨论了均值方差有效证券组合的选择问题.第三章讨论投资者如何配置资产问题.第四章建立了Markowitz模型的一种修正模型,并讨论了它的算法实现.第五章讨论基于可能性分布的投资组合模型.第六章主要讨论了连续时间投资组合问题.第七章讨论了一类特殊的投资组合问题,即虚拟企业管理中的伙伴选择问题.

关键词： ALGORITHMS   ALGEBRA  

摘要： We propose an algorithm for isolating the real solutions of semi-algebraic systems, which has been implemented as a Maple-program realzero. The performance of realzero in solving some examples from various applications is presented and the timings are reported. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： UMDA(c)   linear functions   quadratic functions   tournament selection   mathematical modeling   EDAs  

摘要： This paper presents a theoretical study of the behaviour of the univariate marginal distribution algorithm for continuous domains (UMDA(c)) in dimension n. To this end, the algorithm with tournament selection is modelled mathematically, assuming an infinite number of tournaments. The mathematical model is then used to study the algorithm's behaviour in the minimization of linear functions L(x) = a(0) + Sigma(i=1)(n) a(i)x(i) and quadratic function Q(x) = Sigma(i=1)x(i)(2), with x = (x(1),...,x(n)) is an element of R-n and a(i) is an element of R, i = 0, 1,...,n. Linear functions are used to model the algorithm when far from the optimum, while quadratic function is used to analyze the algorithm when near the optimum. The analysis shows that the algorithm performs poorly in the linear function L-1(x) = Sigma(i=1)(n)x(i). In the case of quadratic function Q(x) the algorithm's behaviour was analyzed for certain particular dimensions. After taking into account some simplifications we can conclude that when the algorithm starts near the optimum, UMDA(c) is able to reach it. Moreover the speed of convergence to the optimum decreases as the dimension increases. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： pollutant ranking   Microtox((R))   bioavailability   mixture effects  

摘要： In order to evaluate sediment toxicity, a mathematical algorithm was developed to compute the toxicity of multiple component mixtures acting in an additive manner. A statistical approach was devised to determine the presence of potential interactive effects among mixture components. The algorithm uses three kinds of data to obtain an integrative approach to sediment toxicity assessment: Microtox((R)) toxicity data (EC50 values), sediment pollutant concentration measurements, and sequential extraction (SEQ) data to investigate metal partitioning. To simplify the analysis of complex mixtures using a prioritization scheme based on intrinsic toxicity and relative abundance, a toxicity index (TI) was employed as an indicator of adverse ecological impact. In general, the ranking of contaminants using the TI approach was found to be most efficient in reducing computational time, and concentrations using bioavailability data from SEQ was found to be the best theoretical predictor of the experimental mixture toxicity value. Only a few pollutants that were present at the greatest abundance were needed to provide a good approximation of the calculated EC50 found when all components were included. Not only does this substantially reduce the computational time needed to determine the EC50, it could in some cases dramatically reduce the pollutant monitoring effort required to track toxicity effectively. This approach would have substantial implications for both risk assessment and for remediation strategies, making them more efficient by focusing on the priority pollutants identified. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： algebraic multigrid   interpolation operator   convergence   linear system of equations  

摘要： In this paper, efficient algorithms for the algebraic multigrid (AMG) method are advanced, and AMG methods are proposed for improving the convergence rate. A new convergence theorem of AMG is given, and a complete theoretical study of new algorithms is subsequently presented. Various numerical results demonstrate the efficiency of the new approaches.

关键词： broadcast communication   sorting   conflict resolution   Euler's summation formula  

摘要： We study three algorithms for sorting under the broadcast communication model. Two algorithms are based on the maximum finding and the loser selection strategy, the third one is the naive strategy based on loser selection only. While a precise description of the algorithms can be found in the paper [15], we concentrate here on the mathematical aspects of the analysis. From these elementary considerations it follows that the average time complexities of the non-naive algorithms are circle minus(n). We give precise expressions for the constants involved by writing them as contour integrals involving zeta functions. The numerical evaluation via residues leads to slowly converging series, and the acceleration of them is a non-trivial task that is done in a slightly more general fashion in order to fit all the applications. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： 工业裂解炉   数学模拟   加速算法   乙烯   裂解过程   能量平衡关系式   管壁温度   管长   石油化工  

摘要： 乙烯裂解炉裂解过程模拟是一个复杂的迭代试算过程 ,现有模拟方法计算时间冗长 ,难以用于在线优化。为此提出的加速算法把裂解过程中的能量平衡关系式作适当简化 ,把反应管管壁温度的求解转换为解一元四次方程的根 ,从而直接得到温度沿管长的微分方程式 ,再结合反应物料和压力沿管长的微分方程式 ,使得裂解过程由一套新的、完整的微分方程组来描述 ,并在模拟过程中对能量关系式的简化作了逐步改进的处理。工业实例表明该算法避免了复杂的迭代计算 ,模拟计算的速度比以前的算法提高约 1/18。

关键词： vector finite-element method   algebraic domain decomposition   CG   BCG  

摘要： This Letter, proposes an algebraic domain decomposition algorithm (ADDA) to solve large sparse linear systems derived from the vector finite-element method (FEM) for 3D electromagnetic field problems. The proposed method segments the problem into several smaller pieces, solves each subproblem by direct methods, and then reassembles the subproblem solutions together to get the global result. Block LU factorization and multifrontal method are applied to solve each subproblem for the generation of the reduced system, and iterative methods are applied to solve the reduced system. It is shown that if combined with ADDA, biconjugate gradient method (BCG) converges more rapidly than the conjugate gradient method (CG), and both of them are faster than the conventional CG method. The simulation results demonstrate that the proposed algorithm can efficiently solve large and sparse linear equations arising from the finite-element method for the electromagnetic problems involving complex media such as perfectly matched layers (PMLs), which often make the linear equation ill-conditioned. (C) 2002 Wiley Periodicals, Inc.