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…     

SOME NEW RESULTS ON THE CONFIDENCELIMITS FOR RELIABILITY PARAMETERS IN THECASE OF NO FAILURES

1.IntroductionDenotethelifelengthofanyitemofsomekindofproductbyX.ThedistributionfunctionofXisF(t)(F(0)=0).Asiswellknown,themostimportantreliabilitypametersare:(1)R(t)=1--F(t)(reliatiility);(2)tR=tR(F)=sup{t:R(t)2R}(reliablespan);(3)M=M(F)=/ootdF(t)(averagelife).]0Inreliabilityengineeringoneofthemostimportanttasksistoestimatethesereliabilityparameters,especiallytogivegoodlowerconfidencelimitsforthem.Whenitemsofsuchaproductareputintoareliabilitytestitoftenhappensthatnofailureismet.Example…     

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…     

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(…     

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…     

A CHARACTERIZATION OF REALCOMPACT STONIAN SPACES X AND EXTENDED RIESZ HOMOMORPHISMS ON C~∞(X)

1. IntroductionBy R(= [--co, co]) we denote the two-point compactification of the real line R. The rulesfor addition and multiplication are extended to boo in the usual wad, i.e., for ally af A E Rand A > 0, we define a (f co) ~ boo, (boo) (loo) = boo, A. (boo) = boo, (--A). (boo) =Too, (boo).(~oo) = co and (loo).(Too) = --co, where it is understood that the multiplicationobeys 0' (boo) ~ (loo)' 0 = 0. For any p) q E R, we say that p q makes sense whenever thecase of p ~ co and q…     

Guaranteed Quadratic Stabilization of Certain Time-Varying Large-Scale Delay It Stochastic Systems

1. INTRODUCTIONIn this paper, we investigate the decentralized stabilization of the large-scale delay It6 stochastic system, aswhere fi E Rut is state vector of the ith subsystem, m e Rmi is input vector of the ith subsystem: Al(t), Fi.(t) E R"' xni I Bi(t) E Rut xos are bounded and piecewise continuous matrixm mhmctions, aAi E R"i"', FBi e R"'"m', ac = al ZNi = N; r(.) E RP, P(.) E Rqj~1 i=1are Lebesgue measurable; W(t) ~ (Wll(t),'' I WIN, (t),'' Wml(t),..., WANd (t))" …     

POSITIVE SOLUTIONS OF SINGULAR SUBLINEAR SECOND ORDER BOUNDARY VALUE PROBLEMS

1.IntroductionBoundaryvaluepr0blemsconcerningthegeneralizedEmden-F0wlerequationsx" p(t)x'=O,(1)wherep(t)eC(O,1),p(t)20f0rtE(O,1),AER,havebeenstudiedbymanyauthors(see[1-51andthereferencestherein).InthispaperwetreattheDirichletproblem(1)withax(0)-bx'(0)=O,c…     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

ON A NONLINEAR DEGENERATE PARABOLIC EQUATION

1.IntroductionInthispaperwedealwiththeexistenceofweaksolutionsofnonlineardegenerateparabolicinitial-boundaryvalueproblemonthespaceX=LP(0,T,V)whereQ~ax(0,T),V=Wb'~(~,n)whichisaweightedSobolevspace(seeSection2).Thedegenerationisdeterminedbyavectorfunctionv(x)(yi(x),yi(x),''9VN(x))withpositivecomponentsyi(x)inasatisfyingcertainintegrabilityassumptions.Nondegenerateparabolicequationsindivergentformhavebeenconsideredbyseveralauthorse.g.F.E.Browderll],R.Landes[2].Parabolicfunctionaldifferen…     

Robust stability for stochastic interval delayed Hopfield neural networks

A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) WIf(t,u(t)) WIτf7τ(uτ(t)] dt σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.     

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 …     

ON THE BOUNDARY STABILIZATION OF WAVE EQUATION WITH VARIABLE COEFFICIENT

1.IntroductionLetfibeaboundedopendomaininR"(n22)withsmoothboundaryr,u~u(s)betheoutwordnormalofrats.GivenavectorxoER",denotem(x)gx--xo(x6R"),Rgsup{lm(x)fjxCfi}.SetLndsupposer nrAI~0.Weconsiderthefollowingwaveequationonfiwithboundaryfeedback:whereK=(m'u)k,L…     

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…     

ON THE ONE-SIDED LOGARITHMIC LAW FOR ARRAYS

1.IntroductionLet{X.,n2l}beasequenceofindependentandidenticallydistributed(i.i.d.)randomvariables.TheHartmanandWintner,sllllawoftheiteratedlogarithmstatesthatifEXI~0andEX7=1Moreover,itisprovedin[2]and[3]that(1)holdsifandonlyifEXI~0andEX7=1.Nowlet{Xnk,k=1,2,''tntn~1,2,'.}beanarrayofi.i.d.randomvariables.FOreveryn21setS.~Z:--,X.k'ThealmostsureconvergenceofSahasbeenstlldiedbyHu,MoriczandTaylor[41,HuandWeb.rls]andQi[6].HuandWeber[5]showedundertheconditionsEXll=0,EX7,=1andEXt,相似文献   

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 CHARACTERISTIC OF EVENTUALLYUNIFORMLY CONTINUOUS C0 SEMIGROUPSON A HILBERT SPACE

1.IntroductionA.Pazy[1]hastwicepointedoutthat"sofar,therearenoknownnecessaryandsufficientconditions,intermsofAortheresolventR(A;A),whichassurethecontinuityfort>0ofT(t)intheuniformoperatortopology".Dr.PengfeiYaol2]hasobtainedthecharacteristicconditionsofaCOsemigroupT(t)onaHilbertspace,whichassurethecontinuityofT(t)fort>0intheuniformoperatortopology.InthispaperweconsiderthecharacteristicconditionsofaCOsemigroupT(t)onaHilbertspace,whichassurethecontinuityofT(t)fort>to(to20)intheuniformoper…     

A Note on the Tu-Deng Conjecture

Abstract Let k be a positive integer.For any positive integer x=∑∞i=0x i2i,where x i=0,1,we define the weight w(x)of x by w(x):=∑∞i=0x i.For any integer t with 0t2k-1,let S t:={(a,b)∈Z2|a+b≡t(mod 2k-1),w(a)+w(b)k,0≤a,b≤2k-2}.This paper gives explicit formulas for cardinality of S t in the cases of w(t)≤3 and an upper bound for cardinality of S t when w(t)=4.From this one then concludes that a conjecture proposed by Tu and Deng in 2011 is true if w(t)≤4.     

THE DIRICHLET PROBLEM AND NEUMANN PROBLEM FOR NONLINEAR PARABOLIC SYSTEMS OF SECOND ORDER EQUATIONS WITH MEASURABLE COEFFICIENTS IN A HIGHER DIMENSIONAL DOMAIN

1 Formulation of Dirichlet Problem and Neumann Problem fOrParabolic SystemsLet O be a bounded domain in Rn and the boundary On E C2. Denote Q = g x I,I =0 < t 5 T, 0 < T < ool 0Q = Sl U S2 is the parabolic boundary where S1 = a x {t = 0} is thebottom and S2 = an x I is the lateral boundary. We consider the nonlinear parabolic systemof second order equationsFh(t, xl ut D.u, D:u) -- Hukt = 0 in Q, k = 1, 2,'',m. (l.l)Under certain conditions, system (1.1) can be reduced to the fOrmw…     

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

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