一些组合地图新算法的实现

本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.     

Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modi ed direct algebraic method

In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.     

Sign-based Test for Mean Vector in High-dimensional and Sparse Settings

In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.     

Multiple Positive Solutions for One Dimensional Third Order p-Laplacian Equations with Integral Boundary Conditions

In this paper,we consider the one dimensional third order p-Laplacian equation■u^′′(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.     

中国数学会举行第十次全国代表大会

中国数学会第十次全国代表大会暨2007学术年会11月2日在北京航空航天大学开幕,这是中国数学会历史上规模最大的一次全国代表大会.教育部副部长吴启迪、中国科协书记处书记冯长根、北京航空航天大学校长李未及中科院、科技部等单位的相关领导、嘉宾出席开幕式.     

Bayesian Approach for Recovering Piecewise Constant Viscoelasticity from MRE Data

This paper deals with an inverse problem for recovering the piecewise constant viscoelasticity of a living body from MRE(Magnetic Resonance Elastography)data.Based on a scalar partial differential equation whose solution can approximately simulate MRE data,our inverse coefficient problem is considered as a statistical inverse problem of reconstructing the posterior distribution of unknown viscoelastic modulus.For sampling this distribution,one usually can use the Metropolis-Hastings Markov chain Monte Carlo(MHMCMC)algorithm.However,without an appropriate"proposal"distribution given artificially,the MH-MCMC algorithm is hard to draw samples efficiently.To avoid this,a so-called slice sampling algorithm is introduced in this paper and applied for solving our problem.The performance of these statistical inversion algorithms is numerically tested basing on simulated data.     

RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.     

Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|²-2uv-τu(|u|²)x=0 vtt+vxx-β(|u|^x)xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.     

RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.     

Indefinite Least Squares Problem with Quadratic Constraint and Its Condition Numbers

In this paper,we consider the indefinite least squares problem with quadratic constraint and its condition numbers.The conditions under which the problem has the unique solution are first presented.Then,the normwise,mixed,and componentwise condition numbers for solution and residual of this problem are derived.Numerical example is also provided to illustrate these results.     

基于期权的树形供应链应急模型与仿真

在多级树形供应链网络环境下,基于实物期权策略并引入中断风险成本,建立了树形供应链应对中断风险的保护与应急模型,通过求解模型得到最优策略并进行了数值仿真分析.仿真结果表明该模型能够显著降低树形供应链系统的中断风险成本与系统中断时间,从而提高供应网络的鲁棒性.     

单链需求扰动下竞争供应链决策模型研究

突发事件经常导致需求扰动,致使供应链运营出现失调.以两条竞争供应链组成的供应链系统为研究对象,建立了供应链竞争基准模型.引入偏差惩罚成本,构建了竞争供应链应对单链需求扰动的均衡模型,给出了不同扰动程度下生产数量及零售价格的应对策略.研究发现,在一定的扰动程度内,原生产计划都具有鲁棒性,鲁棒性范围依赖于价格交叉弹性系数和偏离惩罚成本,其大小与需求扰动源无关.     

Analysis of a two-party supply chain with random disruptions

We study a continuous-review inventory problem of a two-echelon supply chain with random disruptions, identify properties of the optimal cost function, compare the optimal order quantity with the classical economic order quantity, analyze the sensitivity of the optimal solution, and explore the conditions under which zero-inventory ordering policy is preferred.     

双渠道供应链协调及价值扰动

本文研究了消费者选择行为给出的需求模型下双渠道供应链的协调与价值扰动问题.利用Stackelberg博弈对系统建模及其应急管理方法考虑价值扰动问题,获得了扰动前的Stackelberg博弈系统的均衡解和中心决策系统的最优解对价值扰动具有一定的橹棒性的结果,推广了供应链中的应急管理研究结果.     

树形供应链中断风险应急模型研究

基于战略应急库存与实物期权组合策略,设计了树形供应链中断风险应急模型,并通过求解模型得到系统最优策略.应急模型既考虑了风险防范与应急供应所引发的成本,同时考虑了供应链系统中断导致的损失收益.最后进行了仿真分析,结果表明应急模型能够显著降低树形供应链系统的中断风险成本与系统中断时间.     

相容工件系统的最小化最大延迟与误工和的重新排序

在单机重新排序问题中,一个原始工件集已经排好顺序,使得给定的目标函数最小．当一个新的工件集到来时就会产生一些错位,决策者需要插入新工件到原来排序中而还不能过分打乱它们的顺序．该论文首先研究了当工件加工时间和工期相容时,在错位量限制的条件下最小化最大延迟问题;也研究了当工件加工时间相同或工件工期相同时,在错位量限制的条件下最小化误工和问题．对这些问题,给出了好的算法．     

供应中断下零售商的最优定价和最优分批订购策略

考虑了由两个可靠性不同的供应商,一个零售商和一个竞争零售商组成的供应链系统,研究了以双垄断市场为背景,在供应中断条件下,建立了零售商的最优定价模型,给出了最优销售价格和分批订购策略.最后通过数值算例就零售商和竞争零售商价格对竞争零售商的采购成本在不中断和中断情形下做了比较.     

绿色混合产品市场下制造企业应对成本突增的策略

在绿色产品和非绿色产品并存的市场环境下,针对绿色产品和非绿色产品的生产成本突增的情况,研究了制造企业的生产调整策略.首先给出了常规环境下,制造企业对绿色产品和非绿色产品的生产策略;接着,研究了绿色产品和非绿色产品生产成本突然增加的情况下,制造企业的生产调整策略.最后,采用数值分析进一步证明了结论的正确性.研究表明:1)常规下的生产策略具有一定的鲁棒性,当突发事件引起生产成本扰动比较小时,应保持常规下的生产策略不变.2)当产品的生产成本突然增加时,会减少产品的市场规模,导致企业的利润受损.3)当产品的生产成本增加幅度比较大时,应该首先适度上调产品的销售价格,同时还要适度调整产品的产量:当其中一类产品的生产成本增加比较大,而另一类产品的生产成本增加比较小(扰动幅度在一定的范围内)时,对成本增加幅度大的产品,应减少产量;对成本增加幅度比较小的产品,应保持常规下的产量不变.随着两类产品的生产成本进一步增加,对成本增加幅度比较大的产品,应进一步减少产量,对成本增加幅度比较小的产品,应适度增加产量.当两类产品的生产成本增加都比较大时,不仅应增加两类产品的销售价格,而且还要减少两类产品的产量,尽管如此,企业的利润还是会大幅度减少.研究结论进一步丰富发展了企业应急管理的理论基础,为企业有效应对突发事件提供了理论指导的作用.     

回购契约下突发事件影响供应商的生产响应策略

在分析基准回购契约协调模型基础上,建立突发事件后影响供应商生产能力回购契约协调模型,研究在供应商生产成本增加的前提下供应商选择增产和不增产两种响应策略及相应的满足条件,同时给出突发事件后供应商为增产生产成本合理上限以及零售商合理销售价格的下限,最后通过算例验证了该模型的科学性和可行性.     

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.