简介：Theauthorsinvestigatetheexistenceandtheglobalstabilityofperiodicsolutionfordynamicalsystemswithperiodicinterconnections,inputsandself-inhibitions.Themodelisverygeneral,theconditionsarequiteweakandtheresultsobtainedareuniversal.

简介：这篇文章处理微分系统的思考功能。结果被使用讨论这些微分系统的稳定性。

简介：Inthispaper,westudyaclassofdynamicalsystemsinRn-idealsystemsandgiveanexistencecriterionofquasi-connectingorbitsforsuchsystems.Also,anexistencecriterionofconnectingorbitsforgeneralsystemsisgiven.

简介：TheexistenceofatleasttwohomoclinicorbitsforLagrangiansystem(LS)isproved,wheretheLagrangianL(t,x,y)=1/2∑aij（x）yiyi-V(t1x),inwhichthepotentialV(t,x)isgloballysurperquadraticinxandT-periodicint.TheConcentration-CompactnessLemmaandMinimaxargumentareusedtoprovetheexistences.

简介：AparallelhybridlinearsolverbasedontheSchurcomplementmethodhasthepotentialtobalancetherobustnessofdirectsolverswiththeefficiencyofpreconditionediterativesolvers.However,whensolvinglarge-scalehighly-indefinitelinearsystems,thishybridsolveroftensuffersfromeitherslowconvergenceorlargememoryrequirementstosolvetheSchurcomplementsystems.Toovercomethischallenge,weinthispaperdiscusstechniquestopreprocesstheSchurcomplementsystemsinparallel.Numericalresultsofsolvinglarge-scalehighly-indefinitelinearsystemsfromvariousapplicationsdemonstratethatthesetechniquesimprovethereliabilityandperformanceofthehybridsolverandenableefficientsolutionsoftheselinearsystemsonhundredsofprocessors,whichwaspreviouslyinfeasibleusingexistingstate-of-the-artsolvers.

简介：Thispaperdealswithabsorbingboundaryconditionsforhyperbolicsystemsinoneandtwospacedimensions.Weprovethestrictwell-posednessoftheresultinginitialboundaryvalueproblemin1D.AfterwardsweestablishtheGKS-stabilityofthecorrespondingLax-Wendroff-typefinitedifferencescheme.Hereby,wehavetoextendtheclassicalproofs,sincethe(discretized)absorbingboundaryconditionsdonotfitthestandardformofboundaryconditionsforhyperbolicsystems.

简介：Theauthorsinvestigatetheglobalpropertiesofgeneralautonomoussystemsontheplaneandestablishcriteriaforthenonexistence,existenceanduniquenessoflimitcycles.Asapplicationexamples,thelimitcyclesforsomepolynomialsystemsarestudied.

简介：Triangularsystemsplayafundamentalroleinmatrixcomputations.Ithasbecomecommonplacethattriangularsystemsaresolvedtobemoreaccurateeveniftheyareill-conditioned.Inthispaper,wedefinestructuredconditionnumberandgivestructured(forward)perturbationbound.Inaddition,wederivetherepresentationofoptimalstructuredbackwardperturbationbound.

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简介：InthispaertheinequalityofLemma1of[1]isextended.BymeansofourinequalityandthemethodofLyapunovfunctionwestudythestabilityoftwokindsoflargeseatedifferentialsystemswithtimelagandthestabilityofahigher-orderdifferentialequationwithtimelag.Thesufficientconditionsforthestability(S.),theasymptoticstability(A.S.),theuniformlyasymptoticstability(U.A.S)andtheexponentialasymptoticstability(E.A.S.)ofthezerosolutionsofthesystermsareobtainedrespectively.

简介：Inmechanics,bothclassicalandquantum,onestudiestheprofoundinteractionbetweentwotypesofenergy,namely,thekineticenergyandthepotentialenergy.Theformercanbeorganizedasthekinematicmetricontheconfigurationspacewhilethelattercanberepresentedbyasuitablepotentialfunction,suchastheNewtonianpotentialincelestialmechanicsandtheCoulombpotentialinquantummechanicsofatomicandmolecularphysics.Inthispaper,theauthorstudiesthekinematicgeometryofn-bodysystems.Themainresultsaxe(i)theintroductionofacanonicalcoordinatesystemwhichrevealsthetotalamountofkinematicsymmetrybyanSO(З)×O(n-1)actioninsuchacanoniealcoordinaterepresentation;(ii)anindepthanalysisoftheabovekinematicsystembothinthesettingofclassicalinvarianttheoryandbythetechniqueofequivarjantRiemanniangeometry;(iii)aremarkablysimpleformulaforthepotentialfunctioninsuchacanonicalcoordinatesystemwhichrevealsthewell-fittingbetweenthekinematicsymmetryandthepotentialenergy.

简介：<正>Inthispaperwegivethenecessaryandsufficientconditionsforallfinitecriticalpointsofquadraticdifferentialsystemstobeweakfoci,andsolveanopenproblemproposedbyYanqianYe.

简介：Inthispaper,thediscrete-timeneuralnetworkmodeloftwoneuronswithpiecewiseconstantargumentisconsidered.Somesufficientconditionsunderwhicheverysolutioniseitherperiodicorconvergentareobtained.

简介：Amaximumprincipleisprovedforsemilinearstochasticevolutionsystems.Themaincontributionofthisworkisthatinourproblem,theinfinitesimalgeneratorofthesemigroupofthesystemsneednottobeelliptic.ThisgeneralizesaresultofA.Bensoussanin1983.

简介：Borderedlinearsystemsarisefrommanyindustrialapplications,suchasreservoirsimulationandstructuralengineering.TraditionalILUpreconditionerswhichthrowawaytheadditionalequationsareoftentoocrudeforthesesystems.WedescribeapracticalimplementationofILUpreconditionerswhicharemoreaccurateandmorerobust.Theemphasisofthispaperisonimplementationratherthanontheory.

简介：Inthispapertheauthordiscussesthevectorfieldssatisfyingtheconditions(C1)and(C2)andprovessometheoremsforthenumberoflimitcyclesoftheplaneautonomoussystems.Someapplicationsofthetheoremsandlemmasin§1aregivenin§2.

简介：Ahybridtriplesystemofordervandindexλ,denotedbyHTS(v,λ),isapair(X,B)whereXisav-setandBisacollectionofcyclictriplesandtransitivetriplesonX,suchthateveryorderedpairofXbelongstoλtriplesofB.AnoverlargesetofdisjointHTS(v,λ),denotedbyOLHTS(v,λ),isacollection{(Y\{y},Ai)}i,suchthatYisa(v+1)-set,each(Y\{y},Ai)isanHTS(v,λ)andallAisformapartitionofallcyclictriplesandtransitivetriplesonY.Inthispaper,weshalldiscusstheexistenceproblemofOLHTS(v,λ)andgivethefollowingconclusion:thereexistsanOLHTS(v,λ)ifandonlyifλ=1,2,4,v≡0,1(mod3)andv≥4.

简介：LetGbeasecondcountablelocallycompactgroupoidwithHaarsystem{λuH},HbeaclosedsubgroupoidcontainingG^0withHaarsystem{λuH}.T.MasudaintroducedtheC^*-Groupoiddynamicsystem(G,A,α)anditsreducedcrossedproductCrea(G,A)in[2]：whereAisC^*-algebraαisthekomomorphismG→Aut(A).InthispapertheauthorintroducestheC^*-groupoiddynamicsystems(H,A,α/H)and(H\G2,A,^-α)inducedby(G,A,α)andprovesthatC*red(H,A)andC^*red(H\G^2,A)arestronglyMoritaequivalentMoreovertheinducedrepresentationfromC^*red(H,A)toC^*red(G,A)isgot.

简介：Singularlyperturbedproblemsforthenonlineardliptiesystemsinastripdomainareconsidered.Undersuitablaconditions,byusingthecomparisontheorem,theexistenceandasymptoticbehaviorofsolutionfortheboundaryvalueproblemsarestudied.

简介：Itisprovedthatthequadraticsystemwithaweakfocusandastrongfocushasauniquelimitcyclearoundoneofthetwofoci,ifthereexistssimultaneouslylimitcyclesaroundeachofthetwofociforthesystem.