基于时域有限差分方法求解薛定谔方程

时域有限差分(finite difference time domain, FDTD)方法广泛应用于电磁场仿真领域,并与量子力学理论相结合来求解时域薛定谔方程,然而数值计算中的稳定性研究缺少理论方面的探讨。基于冯·诺依曼的稳定性分析方法得到了时域薛定谔方程的一维以及多维的稳定性条件,并且讨论了在不同势能情况下该稳定性条件的表现形式。数值结果充分证明了结论的正确性。     

解析与数值的意义及所描述的世界

基本科学规律一般指动力学规律即状态时间变化的微观规律,呈现为“边界条件＋动力学方程”形式。动力学方程是潜无限意义下的微分方程,少数简单情况下有解析解,初等连续函数形式的解析解描述的是一个确定性、连续性的世界;多数情况下没有解析解,那是一个不确定性和非线性放大机制并存的世界;潜无限动力学方程不能完全描述的是实无限的连续性世界。在运动学层面,无论有无解析解也无论存不存在动力学方程,都可以用数值方法研究动力学现象的运动学行为,数值解描述的是有限性、确定性、离散性、历史性的世界。     

Establishing formal state space models via quantization forquantum control systems

1.INTRODUCTION Quantumtheoryisoneofthemostimportantachieve mentsinthe20thcentury,anditdisclosesthestruc tures,characteristicsandmotionlawsofmatterinthe microcosmicfieldandleadsusfromthemacroscopical worldintomicrosystems.Aseriesofnewphenomena whicharedifferentfromclassicalsystemshavebeen discovered,suchasquantumentanglement,quantum coherenceanduncertainty.Meanwhile,quantum theoryandquantummethodsarealsowidelyusedin differentfieldssuchaschemicalreaction,geneticen gineering,atomicphysicsandi…     

THE COMPARISON-NUMBER METHOD FOR FINDING MAJOR OPTIMAL SOLUTIONS AND MAJOR EFFICIENT SOLUTIONS OF THE DISCRETE MULTIOBJECTIVE PROGRAMMING

In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions to discrete multiobjectiveprogramming is given.     

一类2人合作交叉规划的s-最优联合解

提出并研究了一类 2人合作交叉规划问题。引进了具有相同联合值的s 最优联合解 ,它作为 2人合作交叉规划的一种公平解 ,比Nash均衡解要更好 ,并得到了它的若干有关性质 ,证明了可以通过求解一个等价的数学规划问题的最优解来作为交叉规划的s 最优联合解。最后 ,讨论了具有不同联合值的s 最优联合解。 2人合作交叉规划可以广泛用于讨论许多具有或不具有冲突的多人决策问题 ,如生产计划控制、工程、计算机等领域中的网络冲突问题。     

EXISTENCE OF THE VALUE FOR A DIFFERENTIAL GAME WITH SWITCHING STRATEGIES IN A BANACH SPACE

A two-player zero-sum differential game in some Banach space is studied.Positiveswitching costs are associated with each player.By regularizing the game and combining thenotion of viscosity solutions for Isaacs-Bellman equation,we obtain the existence of the Elliot-Kalton value of the game under suitable conditions.     

ON THE NONEXISTENCE OF PERIODIC SOLUTIONS FOR LIENARD-TYPE EQUATIONS

1.IntroductionConsiderthefollowinggeneralizedLi6nardtypeequationwhereshallowing[1],thisequationwillbecalledasaLi6nard-typeequationofordern.Whenn=1,theequation(1.1)canbewrittenasthefollowingformClearly)whenfi(x)=j(x),f200=0,theequation(1.3)isreducedtothewellknownLi6nardequationx j(x)x g(x)=0.(1.4)Recently,theequation(1.3)hasalreadybeenstudiedwithparticularemphasisontheex-istenceanduniquenessofperiodicsolutionsbyseveralauthors.Forexample,needmanandKuangll],GuidorizzilZ],ZhouJinI3],andJiangJ…     

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS

ＥＸＩＳＴＥＮＣＥＯＦＮＯＮＴＲＩＶＩＡＬＳＯＬＵＴＩＯＮＳＦＯＲＣＲＩＴＩＣＡＬＳＥＭＩＬＩＮＥＡＲＢＩＨＡＲＭＯＮＩＣＥＱＵＡＴＩＯＮＳ￥ＧＵＹｏｎｇｇｅｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅ...     

多属性决策的TOPSIS夹角度量评价法

推广了决策矩阵的几种规范化方法及与此相应的理想和负（反）理想解（点）的确定法。简化了新双基点法所用的与理想点的贴近度。利用被评价方案与理想解和负理想解的夹角，定义了一种新的与理想解的贴近度，据此给出了一种新的综合排序法，并将此法与ＴＯＰＳＩＳ法做了对比，得到了好结果.     

ON THE UNIQUENESS THEOREMS FOR THE UNBOUNDED CLASSICAL SOLUTION OF THE MAGNETIC BNARD SYSTEM

1.IntroductionItiswellknownthatitissufficientt0consideronlytheeffect0ftemperaturegradientinB6nardsystem,butinthemagneticB6nardsystemthestrength0ftheimpressedmagneticfieldhasanimportanteffect.Thereforeitisnecessaryt0considerMaJxwell'sequationcoupledwiththeheatconvectionequationwiththeBoussinesqapproximati0ninthemagneticB6nardsysteml1-3],i.e.,whereu=(u1,u2lu3),h=(h1,h2,h3),e,Pdenotethevelocity,themagneticfiuid,thetem-peratureandpressurefieldrespectively;pisthedensityoffluid,pthemagneticpermeab…     

二层线性规划的有效解

在容许集有界且二层线性规划存在最优解是相应双目标规划有效解的假设下，证明了有效最优解可在容许集的顶点达到。给出了二层线性规划的解的更为合理的有效化方法，并用算例对各种有效化方法所得的有效解进行了比较。     

BOUNDARY SOLUTIONS OF OPERATOR EQUATIONS IN PARIAL ORDERING SETS WITH APPLICATIONS TO SYSTEMS OF FUNCTIONAL

1.IntroductionThepaPers[l-5]studythecoupledfixedp0intsofmixedmonotoneoperatorsinBanachspaces;theyshowusgeneralizationsofthefixedpoillttheoremsonincreasingoperatorsanddecreasingoperators.Applicationsoftheseresultsmaybefoundinmanyfieldsofmathematicssuchasnonlineaxdifferentialequations,illtegralequationsanddynamicprogrammingtheories.Inthispaper,westudytheekistenceofsolutionsandboundarysolutionstoasystem0foperatorequationsinpartialorderingsets.Wegeneralizeandimproveonsomeresultsaboutthecoupledfix…     

基于Hamilton系统理论的SFS模型分析

从明暗恢复形状(SFS)是计算机视觉中三维形状恢复问题的关键技术之一。本文从Hamilton系统理论角度解释了SFS问题的动力学本质,简要介绍了求解相应Hamilton-Jacobi方程的三种经典方法,即特征线方程法、粘稠解方法以及等值线求解方法,并分析了各方法的优缺点。     

求解群体多目标决策问题的一种方法

引进了群体多目标决策问题的一种新的最优解概念──s-最优平衡解,它的实际意义是对于每个决策者而言在每个目标下都给出一个让步值.证明了求解s-最优平衡解等价于求解一个对应的单目标优化问题,并在一定条件下s-最优平衡解总是存在的.讨论了具有不同让步值的s-最优平衡解.数值例子表明这个方法对解决群体多目标决策问题具有一定的有效性.     

A REMARK ON PERIODIC SOLUTIONS OF SINGULAR HAMILTONIAN SYSTEMS WITH SUBLINEAR TERMS

In this paper,we prove the existence of multiple periodic solutionsfor a class of singular Hamiltonian systems with sublinear terms via variationalmethods.     

NON-CLASSICAL GENERALIZED SOLUTIONS FOR SOME HYPERBOLIC SYSTEMS

1.IntroductionThemostspecialfeatureofconservationlawsofhyperbolicsystemsisthattheirsolutionsalwayshavediscolltinuities.ThiskindofdiscontinuityrepresentstheshoCkwavephenomena.Sopeopleintroducetheideaofgeneralizedsolutionwhichsatisfiesequationsinthesenseofdistribution.Underthisdefinition,alotofachievementshavebeenobtainedsince1950'sinthisfield.However,inrecelltyears,manyauthors(see[l--6])discoveredthatthereisnoexistenceanduniqllenessofsolutionstoRiemannproblemsforsomeconservationlaws.Bynumeric…     

Primary Structural and Quantitative Analysis of Infeasible Solution to Job shop Scheduling Problem

1　IntroductionTheJobShopSchedulingProblemisawell-knownNP-hardproblem,whichattractslotsofmathematiciansallovertheworldspendingmuchtimeandenergyinthisfield.Uptonowtherearemanyefficientheuristicalgorithms,whichhadalreadybeendeveloped,buttheinfeasiblesolutioncertainlypossessesthemajorityofsearchspacewhichhasinfluencedtheefficiencyofthesealgorithms.Atthemoment,noonehasbeenfoundtobededicatingtothequantitativeanalysisoftheinfeasiblesolutionproblem.InthispaperthestructureofinfeasiblesolutiontoJSS…     

NONTRIVIAL PERIODIC SOLUTIONS OF A SEMILINEAR WAVE EQUATION WITHOUT ASSUMPTION OF MONOTONICITY

In references,some authors have succeeded in obtaining existence re-sults of the superlinear wave equation without the assumption of monotonicity forthe nonlinear term.In this paper,we present existence results for this problem byusing local linking idea and improve some previous results.     

A Nonlinear Age-Structured Forest EvolutionSystem

ＡＮｏｎｌｉｎｅａｒＡｇｅ－ＳｔｒｕｃｔｕｒｅｄＦｏｒｅｓｔＥｖｏｌｕｔｉｏｎＳｙｓｔｅｍＡＮｏｎｌｉｎｅａｒＡｇｅ－ＳｔｒｕｃｔｕｒｅｄＦｏｒｅｓｔＥｖｏｌｕｔｉｏｎＳｙｓｔｅｍ￥ＷＡＮＧＤｉｎｇｊｉａｎｇ（ＰｉｎｇｄｉｎｇｓｈａｎＴｅａｃｈｅｒ＇...     

ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS

In this paper,we use the contraction principle and the Leray-Schauder principleto deal with the existence of periodic solutions of the Volterra integral differential equation.Some new existence criteria and unique existence criteria are obtained.