THE RATIONALITY OF THE DISCRETE ORDINATES METHOD FOR TIME DEPENDENT NEUTRON TRANSPORT EQUATION

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NEUMANN SERIES SOLUTION TO A NEUTRON TRANSPORT EQUATION OF SLAB GEOMETRY

This paper deals with the solution to an energy, dependent stationary neutrontransport equation of slab geometry. In L~p space, the equation is converted into an equiva-lent integral equation. By the study of the corresponding integral operator and its spectralradius, results of Neumann series solution are obtained, and an easy-verified condition thatthe transport equation has a nonnegative solution is given.     

THE MULTIPLICITY OF ZERO AND LIMIT CYCLES FOR ABEL EQUATIONS

In [1], AlwaSh and Lloyd investigated the nUmber of hot cycles surrounding a critical pointof focus take for polynOInial two dimensional systems. Under polar coordinates, the discussedsystems can be transformed into Abel equstion of the form:2 = a(t)z' g(t)z' 7(t)z, (1)with periodic boundary condition:z(0) = z(W). (2)When multiplicity p of solution z = 0 for equation (1) is larger than one, without lOss ofgeneralityt we can assume 7(t) = 0 for t E [0, w]. Let pm denote the m~ multiplic…     

Solving the State Equation of a System by Walsh Function

In this paper, We deal with the solution of the state equation of a system by the Walsh function, that is, we shall find the solution of a matrix differential equation by the Walsh function, and introduce a solution of the higher-order matrix differential equation. First, after a certain transform, we turn the higher-order matrix differential equation into a state equation. Then we find the solution of the state equation by the Walsh function. Finally after a certain transform, we obtain a solution of the higher-order matrix differential equation.     

FRACTIONAL ORDER EVOLUTION EQUATIONINTERPOLATING BOTH HEAT AND WAVE EQUATION

1.IntroductionInthispaperweconsidertheCauchyproblemforthefollowingintegrodifferentialequationHerewedenotebyrtheGammafunction,byb(t)theDiracfunction.Equation(1.1)describestheheatconductionwithmemory12'3'4].Wesaythatacolltinuousfunction*Thisresearchissuppor…     

REDUCED FORM OF YANG-MILLS EQUATION OFSU(2) ON R~(3,1)

1.NotationsLetR3,1betheMinkowskifour-dimensionalspacewithcoordinatesx=(x')x',x',x').ThemetricdsZ=Zgijdx'dxjofR3'1isgivenbygll=gab=gb3=l,g'=--1,andgij~0fori/j.Letgi(2)betheLiealgebraofgroupSU(2).Theanti-Hermitianrepresentationsofabasisofgi(2)aretakenasfollows:inwhichi=n.Theconnectionisa1-forminwhichThereare12unknownfunctionsA,Thecurvaturetensorsaregivenbyinwhichoj=0/oxj,j=l,2,3,4.TheYang-MillsequationofSU(2)onR3)1is(see[1])TheYang-Millsequationconsistsof12equationsYMjk=0,j~1,2,3,4,k~…     

一种寻求退化型运输问题最优解方法研究

文献[3]和文献[4]都对运输问题最优解的改进作了讨论,但对退化型运输问题是否存在最优解却作了回避.对于出现退化情形而又无法用位势法或闭回路法调优的运输问题,给出了一种寻求最优方案的方法--零数字格转移定理.该定理不仅为退化型运输问题的处理提供了理论基础,而且也为这类特殊的运输问题提供了一种简便可行的表上作业求解方法.     

A MULTI－PARAMETER SPLITTING EXTRAPOLATION AND A PARALLEL ALGORITHM FOR PARABOLIC PROBLEM

ＡＭＵＬＴＩ－ＰＡＲＡＭＥＴＥＲＳＰＬＩＴＴＩＮＧＥＸＴＲＡＰＯＬＡＴＩＯＮＡＮＤＡＰＡＲＡＬＬＥＬＡＬＧＯＲＩＴＨＭＦＯＲＰＡＲＡＢＯＬＩＣＰＲＯＢＬＥＭＬＩＵＸｉａｏｑｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｎｇｔａｎＴｅａｃｈ...     

SOLITON AND ELLIPTICAL PERIODIC SOLUTIONS TO THE MODIFIED NONLINEAR SCHRODINGER EQUATION

1.IntroductionAsiswellknown,theNLSE.02 ac Iql:q=0(1)'N Zap Iql:q=0(1)describesthepropagationofpicosecondOPticalpulseinamonomodeOPticalfiber,whereq(',T)istocomplexpulse,'represelltsthedistancealongthedirectionofpropagation,Trepresentsthetimeinthegroupvelocityframeandrs=11.TheNLSEhasbrightsolitonsolutionwhend==1,anddarksolitonsolutionwhena=11.Inthisnotewehaveobtainedthedarksolitonsolutionwhena~1.However,recentworkshaveshownthattheNLSEisnotsufficieDttodescribethepropagationoffemtosecond…     

THE FINITE ELEMENT PROBABILITY COMPUTATIONAL METHOD FOR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

1.IntroductionThefiaiteelementprobabilitycomputationalmethodisakindofnumericalcalculationtecboqueofauniquestyle.Themethodshavebeendevelopedduringthefiftiestosixesforuseindeferencemethodll'2'3)andforsolvingsystemofalgebraicequations.Inengineeringandphysicsproblems,oftenwehavetosolvetheconcelltratedloadproblem.Inthiscase,weneedonlytoknowthevaluesofthefunctionatafewnodalpoilltsofthedomain.Itwillwastealotoftimetocomputetheunnecessaryvaluesofthefunctionbythefiniteelemelltmethods(ordeferencemethods…     

OBSERVING THE HEAT EQUATION ON A TORUS ALONG A DENSE GEODESIC

Several authors have considered observability problems for the heat equation and relatedpartial differential equations.A basic problem is to determine what kinds of sampling providesufficient information to uniquely determine the initial heat distribntion.We address the case wherethe temperature is measured while travelling along a curve.We consider the special case where the space is a flat torus(of arbitrary dimension)and thecurve is a geodesic.It is shown that,in this case,the observed temperature is sufficient informationto uniquely determine the initial heat distribution if and only if the geodesic is dense in the torus.In the case of a torus,Fourier analysis techniques can be used to write down the solution of theheat equation.This allows us to derive an explicit representation of the observed temperature interms of the initial distribution.We use this representation and some ideas from the theory ofalmost periodic functions to show that the Fourier coefficients of the initial distribution can berecovered from the observation.     

A Nonlinear Age-Structured Forest EvolutionSystem

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跳跃-扩散模型的首达时研究

考虑跳跃-扩散风险模型,研究盈余达到下界L的首达时T的特性.利用更新论证得到关于(u)=E[e-rT|U(0)=u]的更新方程.对于下跳模型,若索赔额为相互独立且具有相同的指数分布,得到更新方程解的解析表示;对于上跳模型,则解析表示的推出不需要指数分布的假定.作为应用,得到了首达时T的均值和方差的表达式.最后给出了数值计算和随机模拟的实例.     

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.     

THE HOPF BIFURCATION DIRECTION OF A FOUR DIMENSIONAL ELECTRONIC NEURAL NETWORK SYSTEM

1.IntroductionCurrentlybifurcationtheoryiswidelyusedinmanymathematicalmodelsofvariousfieldssuchasbiologyjmechanics,medicalscience,managementofnaturalresourcesandthetheoryofneuralnetowrks.Inadifferentialdynamicalsystem,averyimportalltproblemistheexistencea…     

CLASSICAL TIME DEPENDENT SOLUTION FORNEUTRON TRANSPORT IN A SLAB WITHGENERALIZED BOUNDARY CONDITIONS

1.IntroductionSincethepioneeringworkofLehner,WingandJorgens['3],thetimedependentneutrontransportproblemhasbeentreatedbymanyinvestigators,andtheliteratureonthissubjectisconsiderable.Variousmethods,theCO-semigroupmethodin[2,3],theNeumannseriesexpansionmetho…     

A Class of Jump-Diffusion Stochastic Differential System Under Markovian Switching and Analytical Properties of Solutions

Our article discusses a class of Jump-diffusion stochastic differential system under Markovian switching(JD-SDS-MS). This model is generated by introducing Poisson process and Markovian switching based on a normal stochastic differential equation. Our work dedicates to analytical properties of solutions to this model. First, we give some properties of the solution, including existence,uniqueness, non-negative and global nature. Next, boundedness of first moment of the solution to this model is considered. Third, properties about coefficients of JD-SDS-MS is proved by using a right continuous markov chain. Last, we study the convergence of Euler-Maruyama numerical solutions and apply it to pricing bonds.     

THE POPULATION DYNAMICS WITH N-INTERSECTIONS

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GLOBAL SUPERCONVERGENCE FOR A MIXED FINITE ELEMENT METHOD FOR THE WAVE EQUATION

1.IntroductionWeconsiderthesecondorderhyperbolicequationwithinitialconditionswhereaCRZisaboundeddomainwithboundariesparalleltotheaxes.Forconvenience,weassumehomogeneousDirichletboundaryconditions'Weassumethatthefunctionsailandfareuniformlyboundedandmeasurable,andthespatialoperatorisuniformlyellipticinthesensethatthereexistpositiveconstantsorandPsuchthatInamixedfiniteelementformulationbothdisplacementsandstressesareapproximatedsimultaneously.ThispropertyisimportantincomputingDarcyvelocitieso…     

THE SINGULAR PERTURBATION OF NONLOCAL BOUNDARY VALUE PROBLEMS FOR NONLINEAR ELLIPTIC EQUATION OF FOURTH ORDER

Chenandothersstudiedaclassofsingularlyperturbedboundaryproblems[1--3].NowweconsiderthefollowingsingUlarlyperturbednonlocalboundaryvalueproblemforthenonlinearellipticequationoffourthorder.whereEisapositiveparameter,bistheLaplacian,ndenotesaboundedregi...