NUMERICAL APPROXIMATIONS OF A SEMI-LINEAR ELLIPTIC PROBLEM

1IntroductionConsidertl1eparameterdependentequationwhereA,ltERarepara1ueterandf:R-RandS:R-RaresinoothoddfunctionwithLetS1:u(x)-u(T-x),r={S1,I}then(l.1)isr-equivariant.Tl1eequality(1.2a)isjustanormalizatiolloffatx=o.Otherwise,onelllayreseektl1eparameterxtoensure(1.2a).To8implifyanalysisweintroduceaSobolevspaceX:=Hl(o,1)anddefilleamappingT:gEL'(o,T)-lL:=TgEXimp1icitly:for(Tg)'V'dx=-jorgl)dx,VvEX,aweakformof(1.1)inXxR2isDuetof(o)=O,theproblem(1.3)(resp.(1))hasatrivialsolutioncurvesC…     

EXISTENCE AND GLOBAL STABILITY OF POSITIVE PERIODIC SOLUTION IN A LOGISTIC INTEGRODIFFERENTIAL EQUATION WITH FEEDBACK CONTROL

1IntroductionThelogisticequation([8],l12])isoneoftheelementaryandmathematicallysimplemodelsusedtodescribethetempora1evolutionofasinglespeciespopulationinaconstantenvironment,inwhichaand5arepositiveconstants;aisrelatedtothereproductionofthespecieswhilebisrelatedtothecapacityofenvironmenttosustainthepopu1ation.Itisknownthatsoltitionsof(1.1)aremonotonicfunctionsoftwithlimN(t)=tifN(o)>o.Ithasbeenfoundthatsuchamonotonict-ooconvergencetofheequilibriumisnotrealisticincertainlaboratorypopulationsinte…     

SOLVABILITY OF m-POINT SINGULAR BOUNDARY VALUE PROBLEMS

1IntroductionInthisarticletheexistentresultsforthesecond-orderdifferentia1equationI,x=q(t)f(t,x(t),x'(t)) c(t),tE(O,1)(1.1)subjecttooneofthefollowingboundaryvalueconditions:arepresented,whereqEC(o,1),ff[o,1]xR2-Risacontinuousfunctionandc:[O,l1-RisafunctioninL'(o,1),crf6RWithallofthecrishavingthesamesign,(f6(o,l),i=1,2,...,m-2,o<(l<(2<..-相似文献   

MULTISTEP METHODS FOR A CLASS OF HIGHER ORDER DIFFERENTIAL PROBLEMS:CONVERCENCE AND ERROR BOUNDS

1.IntroductionHigherorderdifferentialsystemsoftheformY(')(t)=f(t,Y(t)),a5tSb,Y(')(a)=fliEor"q,o5t5r-1,r22(1.1)arefrequentinavarietyofmodelsinphysics.ThesesystemsariseforexamplemodelingthemotionofasystemofparticlesasdeterminedfromthelawsofclassicaJmechanicssuchastheinteractionofatomsandmolecules[2l16,17],themotionofthesolarsystemandspacecapsules[3,21jandtheevolutionofstarclusterl5].Other8ituationswheresystem8ofthetype(1-1)appearinanaturalwaymaybefoundinoptics[8],quantumtheoryofscatteringI']o…     

Infinitely Many Sign-changing Solutions for a Schr(o)dinger Equation in RN

We consider the existence of infinitely many sign-changing solutions for the nonlinear timeindependent schr(o)dinger equations of the form {-△u+Vλ(x)u=f(u), u∈H1(RN), (1.1) where Vλ(x) = λα(x) + 1.     

ON A CELL ENTROPY INEQUALITY OF THE RELAXING SCHEMES FOR SCALAR CONSERVATION LAWS

1.IntroductionIn[1],JinandXinconstructedaclassofthelocalrelaxationapproximation--TheRelaxingSchemesforsystemsofnonlinearcollservationlawsorsinglenonlinearconservationlawson,dofi(u)~ ;ac~0,(1l)otMoxil=1zwithinitialdatau(0,x)~"o(x),x~(xl,...,-cd),byusingtheideaofthelocalrelaxationapproximation[1--4].Theschemeisobtainedinthefollowingway:firstalinearhyperbolicsystemwithastiffsourcetermisconstructedtoapproximatetheoriginalsystem(1.1)withasmalldissipativecorrection;Then,thenewlinearhyperbolicsyste…     

SMALL SAMPLE PROPERTIES OF THEPOWER FUNCTION OF F TESTS IN TWO-WAYERROR COMPONENT REGRESSION

1.IntroductionThetwcawayerrorcomponentregressionmodelmsybeexpressedasif=o

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GLOBAL EXISTENCE OF SMOOTH SOLUTION FOR BOLTZMANN-POISSON SYSTEM WITH SMALL DATA

1IntroductionThebasicequationinsemiconductorkinetictheoryistheBoItzmannEquation.Iftherelevantphysicsconstantsaretakenasone,theBoltzmannEquationin3D,undertheattractforce,canbewrittenas:o,f vV.f-E.V.f=Q(f),xER',vER',t>o,(1.1)wheref(t,x,v)isadistributionfunction,itrepresentsthefractionofoccupiedstatesattimetE[o,oo),atthepoint(x,v)eR'xR3oftheposition-velocityspace.E(f,x)ER'istheelectricfield-IfthepotentialcorrespondingtotheelectricfieldE(f,x)isdenotedbyV(t,x),thenAndV(t,x)satisfiesthePoi…     

A LEGENDRE PSEUDOSPECTRAL METHOD FOR SOLVINGNONLINEAR KLEIN-GORDON EQUATION

1.IntroductionAsweknow,theKlein-Gordonequationisanimportantmathematicalmodelinquantummechanics.Itisoftheformwherefi=(--1,1)",x=(xl,x25'jx.),bisarealnumber.AssumethatU000=UI(x)=0onOnandAsin[1],itcanbeshownthatifUOEHI(n)nH(n),UIEL'(fl)andfEL'(o,T;L'(n)),then(1.1)hasuniquesolutionUELoo(o,T;Hi(n)nH(fl)).oftheotherhand,somefinitedifferenceschemeswereproposedin12,31withstrictproo]ofgeneralizedstabilityandconvergence.TheirnumericalsolutionskeepthediscretEconservations.Oneofspecialcases(…     

A TOBIN-TYPE ESTIMATE OF CENSORED LINEAR MODELS

1IntroductionConsiderthelinearregressioumodelcensoredfromtheleft:K=m{K,0}=rnax{Z:W ei,0},1Si5n,(1.1)whereZi=(1,X:),,15i5n,7o=(ac,P6)'(1'2)ThedimensionalityofXiisd21.WeobBerve(Xi,K)',1SiSn.Basedontheseobservations,wetrytogivesomeestimationofac,ortesthypothesisonit.Themodelwasfirstconsideredbycabin[llundertheassumptionthatelfe2,''arelid.withacommonnormaldistributionN(0,rs:).HedefinedtheMLEof7o,whichnowisusuallyknownastheTobinestimator.TheconsistencyOfthisestimatorwasestablishedbyAmend…     

A new constraint qualification condition

We introduce a new constraint qualification condition in mathematical programming which encompasses the Mangasarian-Fromovitz's condition and the constant rank condition of Janin. Contrarily to the Mangasarian-Fromovitz's condition, our condition is still satisfied when one translates equalities as double inequalities. It relies on the fact that linearization stability is easier to check with equalities than with inequalities.     

Necessary Condition for a Strong Relative Minimum for Singular Optimal Control

A necessary condition is developed for a strong relative minimum for a first-order singular optimal control. It is shown that the strong condition is identical with the existing weak condition, namely, the generalized Legendre-Clebsch condition. It is conjectured that the strong condition for a second-order singular control will be the same as the corresponding weak condition.     

On global quadratic growth condition for min-max optimization problems with quadratic functions

Second-order sufficient condition and quadratic growth condition play important roles both in sensitivity and stability analysis and in numerical analysis for optimization problems. In this article, we concentrate on the global quadratic growth condition and study its relations with global second-order sufficient conditions for min-max optimization problems with quadratic functions. In general, the global second-order sufficient condition implies the global quadratic growth condition. In the case of two quadratic functions involved, we have the equivalence of the two conditions.     

用条件(Pw)刻画的幺半群

本文引入了条件（P_w）,讨论了条件（P_w）与条件（P）、条件（P_E）之间的关系,刻画了幺半群上S-系的平坦性.     

Subdivision Schemes and Irregular Grids

The present paper deals with subdivision schemes associated with irregular grids. We first give a sufficient condition concerning the difference scheme to obtain convergence. This condition generalizes a necessary and sufficient condition for convergence known in the case of uniform and stationary schemes associated with a regular grid. Through this sufficient condition, convergence of a given subdivision scheme can be proved by comparison with another scheme. Indeed, when two schemes are equivalent in some sense, and when one satisfies the sufficient condition for convergence, the other also satisfies it and it therefore converges too. We also study the smoothness of the limit functions produced by a scheme which satisfies the sufficient condition. Finally, the results are applied to the study of Lagrange interpolating subdivision schemes of any degree, with respect to particular irregular grids.     

KKT系统结构条件数与条件数的比较

本文讨论Karush-Kuhn_Tucker(KKT)系统的条件数．首先利用单参数展开方法建立了Byers型不等式,然后讨论结构条件数与条件数的定性比较,结果表明,在极端情形,条件数与结构条件数之比可以任意大．     

A new necessary condition for optimality of systems with time delay

A new necessary condition for optimality of nonsingular control problems with time delay is developed. This condition accounts for the interaction of the different delays in the control vector. A necessary condition for optimality of singular control problems with time delay is also obtained as a corollary of the new condition.     

BCQ条件和广义限制域最佳一致逼近的特征

研究了广义限制域的最佳一致逼近问题,在允许有有限个节点的情况下,引入次强内点条件的概念,并将优化理论中的BCQ条件等概念应用到本文所研究的问题中,刻划了次强内点条件、BCQ条件和最佳一致逼近的特征之间的关系.     

THE ASYMPTOTIC PROPERTIES OF SUPERCRITICAL BISEXUAL GALTON-WATSON BRANCHING PROCESSES WITH IMMIGRATION OF MATING UNITS

In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L1 convergence are given for the process with the suitably normed condition.     

Asymptotic analysis of the differences between the Stokes-Darcy system with different interface conditions and the Stokes-Brinkman system

We consider the coupling of the Stokes and Darcy systems with different choices for the interface conditions. We show that, comparing results with those for the Stokes-Brinkman equations, the solutions of Stokes-Darcy equations with the Beavers-Joseph interface condition in the one-dimensional and quasi-two-dimensional (periodic) cases are more accurate than are those obtained using the Beavers-Joseph-Saffman-Jones interface condition and that both of these are more accurate than solutions obtained using a zero tangential velocity interface condition. The zero tangential velocity interface condition is in turn more accurate than the free-slip interface boundary condition. We also prove that the summation of the quasi-two-dimensional solutions converge so that the conclusions are also valid for the two-dimensional case.