ON THE SPECTRUM OF THE LINEAR TRANSPORT OPERATOR IN L~P SPACE

InthispaperweinvestigatethespectrumofthetransportoperatorA:Aam=Bac KegwhereBac=--aam(x,v,p)--vZ(x,v)op(x,v,p),Keg=11,joank(x,yip;V',p')op(x,v',p')dp'dy',D(A)={op(x,v,p)ELP(G):;;:t--:,y::op(a,v,--p)=0,for0相似文献   

ASYMPTOTIC STABILITY OF SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR SCALAR VISCOUS CONSERVATION LAWS CORRESPONDING TO RAREFACTION WAVES

1.IntroductionWeconsidertheinitial-boundaryvalueproblem(IBVP)forscalarviscousconservationlaw(ut f(u).=uxx,xE(0, co)=R ,t>0,o,(n \--9,ifI~9,f~M(IBVP){u(0't)=u~(t)-1~i---t:7),[u(x,0)=u000={=:0)f:LO .,wheref"(u)>0foralluunderconsideration,andu--u (1.1),andu~(t)~u~EL'(R ),U'(t)EL'(R ).(1.2)Undercondition(1.l)or(l.l)',thecorrespondingRiemannproblem{;;ot:<:>;i,>=x{,:3'f:,:(13)yieldstherarefaCtionwavesolution(u~)x5f'(u~)t,r"(X,t)=17j,)~1(…     

STRONG CODING THEOREM AND ASYMPTOTICERROR EXPONENT OF ARBITRARILY VARYING SOURCE WITH A FIDELITY CRITERION

1.IntroductionLetXbeafiniteset.Adiscretememorylesssource(DMS)withsourcealphabetXisasequenceofi.i.drandomvariableswithsourcedistributionP={p(x):xEX}.LetYbeanotherfinitesetcalledreproductionalphabet,andd'XxY-- [0, co)beagivendistortionmeasure.Thedistortionbetweensequencesx"EX"andy"6Y"isdefinedasd(x",y")=n--1Z:=,d(x,,yi).AsubsetBgY"iscalledasourcecode.Therateofthecodeisdefinedas.--ilogIBI.Inthispaper,alllogarithmsandexponentsaretakentobase2.Forx"EX",defined(x",B)=minbneBd(x",b").Given…     

POINCARE BIFURCATIONS IN POLYNOMIAL DIFFERENTIAL SYSTEMS

1.IntroductionForagivenunperturbedplanarsystemwithafamilyofclosedorbits,considerthecreationofisolatedclosedorbits--limitcyclesbyperturbationofthesystem.ThatiscalledthePoillcar6bifurcation.Therearewell-knowntheoreticalresultsaboutPoincar6bifllrcati()11,seeforexam-Ple[1],[2].InthecasewheretheunperturbedsystemisHamiltonian,thepertllrbedsystemcanbewrittenasinwhichweassumethatp(x,y,0)=Q(x,U,(i)~0,and(1)A--ohasafamilyofclosedorbitsgivenbytheHamiltonianintegralnfH(x,y)=h,0相似文献   

FURTHER RESULTS ON THE ASYMPTOTIC BEHAVIOUR OF MINIMUM AVERAGE HAMMING DISTANCE FOR BINARY CODES

1.IntroductionLetFZnbethen-dimensionalvectorspaceoverthebinaryfieldF2.Anon-emptysubsetACFZniscalledacode.TheaverageHa~ngdistanceofacodeAisdefinedby1\d(A)=IAIz,ZZdH(x,y)ahApeAwhereIAIisthenUmberofcodewordsinA,dH(x,y)istheHammingdistancebetweenxandy.ForallaE{1,2,'',2"}andn21,wedefinetheminimumaverageHammingdistanceasda(a)=^.gle^l=.d(A).AlilswedeandAlthofer[1]provedthefollowingtheorem.Theorem1illLetan(15anS2"),n=1,2,'',beasequenceOjpositiveintegers.Ijforsomeconstanto(0相似文献   

UPPER AND LOWER SOLUTIONS METHODS FOR EXISTENCE OF PERIODIC SOLUTIONS OF DUFFING EQUATION

1.IntroductionandNotationsInthispapertwestudytheexistenceofsolutionstothefollowingperiodicboundaryvalueproblemforthesecondorderDuffingequationwheresisarealparameter,g:[0,TIxR~RisaCarath6odoryfunctionandkER\{0}.Werecall(forexample,see[1])thatg:[0,TIxR~RiscalledaCarath6odoryfunctionifg(.,x)ismeasurableforallxERandg(t,.)iscontinuousfora.e.tE[0,TI.Theexistenceproblemfor(1.1)--(1.2)byusingtheupperandlowersolutionsmethodhasbeenstudiedbyFabryetal.in[2]foramoregeneralcasewhereacontinuousdampin…     

THREE-POINT BOUNDARY VALUE PROBLEMSFOR A CLASS OF THREE ORDER DIFFERENTIAL INCLUSIONS

1.IntroductionandLemmasThree-pointboundaryvalueproblems(BVPforshort)forthreeorderdifferentialequationsareveryusefulincertainpracticalworkandattractcloseattentionextensively,see[l--41.Recently,in[11,GuptaandLakshmikanthamstudiedthefollowingthree-pointBVP:U"'(x)=f(x,ulU',U")--e(x),(l)u(0)=u(n)=u(1)~0,(2)wheref:[0,1]xR3-RdoesnothavetobecontinuousandnE(0,1).ThemainresultisthefollowingTheoremLetfsatisfyCarntheodory'sc.nditions[1]andthefollowingconditions:i)3a,b,cER,or(x)ELI[0,1],suchthatfo…     

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

1.INTRODUCTION Considerthefollowingdelaydifferentialequations(DDEs)y′(x)=f(x,y(x),y(x-τ(x))),a≤x≤b y(x)=φ(x),xmin≤x≤a(1)wherey,f,φaren vectorfunctions,φ(x)isinitial valuefunction,τ(x)≥0isdelayfunction.Definition1DDEs(1)issingularatthepoint xαifthelagsatisfiesτ(xα)=0.Ifthereisnosuch pointxα∈[a,b],thentheDDEs(1)isnon singular.InthenumericalsolutionofDDEs(1)byacon tinuousexplicitRunge Kuttamethod,wesuppose thatwehaveanapproximationyntoy(x)atxnand wishtocomputeanapproxima…     

GLOBALLY TOPOLOGICAL EQUIVALENCE OF NONAUTONOMOUS SYSTEMS

1.IntroductionInthispaper,weshalldiscussthefollowingnonautonomoussystem:wheref,WEC'(R xR",R"),R =[T, co),andf(t,0)=0,W(t,0)~0,tER .Thetopologicalequivalenceisanequivalelltrelation.Wecanuseittotopologicalclassificationfordifferentialequations.So,topologicalequivalencebecomesacentralquestionofdifferentialdynamicsystems.K.J.Palmerhasintroducedandstudiedgloballytopologicalequlvalenceandstructuralstabilityfornonautonomouslinearsystems(see[1,2]).ShiJinlin[3]andZhengZuohuan[4]haveintroducedth…     

EQUIVALENT CONDITIONS FOR THE UNIFORM CONTINUITY OF DUALITY MAPPING

InII],T.Katogaveasufficientconditionfortheuniformcontinuityofdualitymapping,in[2],MaShaoqinpointedoutthattheconversepropositionofthisresultholdstoo.[3]gotthattheuniformcontinuityofdualitymappingF(x)isequivalenttothat(F(x ty),y),(F(x),y),(t~0)uniformlyforx…     

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…     

THE SINGULARLY PERTURBED NONLINEAR ELLIPTIC SYSTEMS

Mostudiedaclassofsingularlyperturbedboundaryvalueproblemsforellipticequationsin{3--8].Nowweconsiderthefollowingsingularlyperturbedproblemeisapositiveparameter,x=(xl,x2,'')x.)Ea,t]denotesaboundedregioninR",onsignifiesthepiecewisesmoothboundaryofa.Thispaperisconcernedwiththesingularlyperturbedproblem(1)--(2),andweconstructtheasymptoticexpansionsofsolution,anddiscusstheirasymptoticbehavior.Weneedthefollowinghypotheses:[HI]ThecoefficientsofL,fiandgiaresufficientlysmoothfunctionswithregardtothei…     

Class of numerical methods for differential-algebraic systems with discontinuous right-hand sides

1.INTRODUCTION Differential algebraicsystemswithdiscontinuous right handsides My′=f(t,y),a≤t≤b,　y(t0)=y0(1) discontinuitiesoff(t,y)aredeterminedbythestate ofswitchingfunctionφ(t,y).Adiscontinuityissaid tooccuratt whenφ(t ,y(t ))=0.Theex pressionoff(t,y)is f(t,y)=f-(t,y)φ(t,y)<0f+(t,y)φ(t,y)≥0(2) tistheindependentvariableofsystem,y=( y1, y2, …, yn)Tisstatevariableofndimensions,f=(f1, f2,…,fn)T,somefiisdiscontinuousfunction,M= [m1,…,mn]n×nisann×ndiagonalmatrix,thedi …     

EXISTENCE AND UNIQUENESS OF POSITIVE EIGENVALUES FOR CERTAIN EIGENVALUE SYSTEMS

1.IntroductionLetnbeaboundeddomaininR"withsmoothboundaryoa,A.denotethep-Laplaciandefinedbya.~div(IVuIP--'Vu),forpE(1,co),andop.(u)=]nip--'if.ItiswellknownthattheeigenvalueproblemhasauniquepositiveeigenvalueAcforwhichtheeigenvalueproblerll(1.1)possessespositiveeigenfunctions.Infact,andtheeigenfunctionsforAcaretheminimizersofthefunctionalMoreover,suchaminimizerofo6Wt3'(n)existsandisuniqlle11ptoascalarmultiple,andofo6Lab(~);wenormalizeitbyjaba(x)lgholpdx~1andofo2:0inD.Thenalsoofo>0inDandcp…     

EXISTENCE, MULTIPLICITY AND BIFURCATION FOR CRITICAL POLYHARMONIC EQUATIONS

1.IntroductionLetfibeaboundeddomaininR"withn23andoffbesufficientlysmooth.WeareconcernedwiththesemilinearellipticequationofhigherordersinvolvingcriticalSobolevexpelwhere,andthroughoutthispaper,gistheunitoutwardnormaltooff,25Zm相似文献   

A CLASS OF SINGULARLY PERTURBEDBOUNDARY VALUE PROBLEMS FOR NONLINEARDIFFERENTIAL SYSTEMS

Considerthesingularlyperturbednonlinearproblemfory=(y1,…,yn)oftheformwhereεisasmallpositiveparameter,f=(f1,…,fn),g=(g1,…gn),fi(x,y')≡fi(x,y'1,…,y'n),gi(x,y')≡gi(x,y'1,…,y'n),A=(A1,…,An),B=(B1,…,Bn).ManyauthorssuchasHowes[1],O'DonnelllZ],Lin[3],Mo[4--7]andothershavediscussedthisproblemundervarioussituationsusingthemethodofdifferentialinequalities.Thispaperconcernsaclassofboundaryvalueproblemsfornonlineardifferentialsystemsusingtheiterationmethodandthetheoryofdifferentialinequaliti…     

DETERMINATION OF THE SIGN OF DIVERGENCE OF A QUADRATIC SYSTEM AT CRITICAL POINTS

Todeterminethesignofdivergenceatcriticalpointsisanimportantstepininvestigatingthestabilityofseparatrixloopsandthatoflimitcyclesgeneratedfromsuchloops(see[1--3]).JiangI4]hassolvedthisproblemforthequadraticsystemoftype(II)andaspecialboundedsystem.Thispaperwillcompletelysolvethisproblemforthegeneralcase.Themethodusedhereissimplerthanthatin[4].Considerthefollowingquadraticsystemoftype(ill):x=--y 6x lxa mad y',gi~x(l ax by),(1)whereb/0.Weconsiderthecasea/0,andwithoutlossofgenerality,wemadassumea<…     

THE DISTRIBUTION OF LIMIT POINTS OFINCREMENTS OF LOCAL TIME OF THE WIENER PROCESS

ThisresearchissupportedbythePostdoctoralGrantofChina.1.IntroductionLetW(t)for05t相似文献   

An Impulse Weakly Observability of Generalized Linear Systems

1.INTRODUCTIONConsiderthelineartime-invariantsystemsWhereE,AeRI"",BERI"",CeR"""jDERrxm.Vt6R :=to' OO),x(t)ER",u(t)6Re,y(t)6R",Herenoregularityassumptionofthepencil[E,A]ismade,i.e.,detIsE--AImaybeZero'polynomial.SincetheworkofRosenbrock[if,alotofcontributionhasbeenmadetosuch.systems,whichhJD=B=0,thestructuresofinfiniteandfinitezerosarecharacterized[21,observabilityandstrongobser.vabilityareanalyzed[3].TothecaseofD=0,regularizabilityofsingularsystemsisproved[61,interiorgeometr…     

考虑到时滞与结构演化的动态投入产出模型

自Leontief关于投入产出的静态平衡系统x(k)=Ax(k)+y(k)提出以来,一方面它相当成功地用以描写生产、消费系统,另一方面它又被改造成为考虑到投资、再生产的动态系统 x(k)=Ax(k)+B[x(x+1)-x(k)]+y(k) (1.1) 由于投资系统矩阵B通常是奇异的,所以有些研究工作者曾设法解决此问题。再则,由投资开始到投产往往有时间上的延迟(时滞),所以如何表达时滞于模型中并设法求解也是研究中的一个方面。上