On the Decomposition of Hopf Module Coalgebra

In1969,Sweedler[1]giventhedecompositiontheoreyofcoalgebraswhicharecocommu-tative.In1975,Kaplansky[2]showedthatanycoalgebracanbeuniquelydecomposedintoadirectsumofitsindecomposablesubcoalgebras.From1978to1992,Shudo[3]andXu[4]consructuredtheindecomposabledirectsumcomponentsofacoalggebra,viadefineequivalenceralationforthesetofsimplesubcoalgebras.Asweknow,themodolecoalgebraisthennaturalgeneralizationofcoalgebra.AndittakesplayanimportentroleintheDrinfelddouble.Inthispaper,wediscussthedecompositio…     

The Pointwise Characterizations of Fuzzy Ideals and Fuzzy Prime Ideals

TheconceptofthefuzzysubgroupsintroducedinRosenfeld[l],wasappliedtogeneralizesomeofthebasicconceptsofalgebra.In[2,3,4]LuWangjindefinedfuzzysubringsandfuzzyideals,introducedtheoperationsonfuzzyidea1s.In[5]theautherdiscussedaboutthenatureoffuzzysubringsbythenestedsubring.Butthepointwisedefinitionsoffuzzysubgroupsandfuzzysubringsarerare.Inthispaper,theautherprogramsanddiscussesthefuzzysubrings,fuzzyidealsandfuzzyprimeidealsbyfuzzyPoints..5l.PreliminariesLetusrecallsomeconceptsoccurrjnginthe[2,3…     

Existence of non-trivial solution for superlinear system of integral equations and its applications

1.IntroductionTherearealotofresultsaboutHammersteinintegralequations(see[1]),butsupen-linearproblemsaredifficult;thereareonlyafewresultsaboutit.In[2,3]theauthorsstudysuperliniearintegralequations;in[4]theauthorsstudysystemofsuperlinearintegralequatio...     

TWO ALGORITHMS FOR LC~1 UNCONSTRAINED OPTIMIZATION

1. IntroductionThe LCI optimization problems exist extensively in various optimization problems.FOr example, the problems from nonlinear complementarity) variational inequality andCd nonlinear programming can be formed as LCI optimization problems. In addition,LCI optimization problems also arise from the extended linear-quadratic programmingproblems, nonlinear minimax problems, stochastic optimization problems and somesemi-infinite programs. See [6] [9] [11] [13] [14] [151 [17] [21].In t…     

GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM NON-DEGENERATE QUADRICS

1. IntroductionThe geometry of quadrics in finite-dimensional projective spaces has been studiedby E.J.F. Primrose[1], D.K. Ray-ChaudhUxi[','] and I.M. Chakravarti[4]. In 1993, 1.M.Chakravartils] derived some association schemes from nondegenerate and degenerate Hermitian varieties. In [6], we constructed association schemes from the set of isotropic points inpseudthsymplectic spaces. In this paper) we will construct three-class association schemesfrom nolldegenerate quadrics.Let Fi be …     

On the Blowing-up and Quenching Problems for Semilinear Heat Equation

In recent years due to investigations on some practical problems it is found solutions of initial or initial-boundary value problems for semilinear heat equation and other equations may blow up or quench. See, for example, [1]-[9]. In [1] S. Kaplan discussed general parabolic equation     

CHAOS AND ORDER OF INVERSE LIMIT SPACE FOR A GRAPH MAP

1.IntroductionIntherecentyearsthereisagrowinginterestininvestigatingtheconnectionbetweenthedynamicsofacontinuousmapofafinitegraphandthetopologicalstructureoftheinverselimitspaceusingthemapasasolebondingmaptsincesomeattractorofadynamicalsystemcanbeshowntobetheinverselimitspaceofacontinuousmapofafinitegraph["](seeforinstance[1,4,7,8,12]).In[1]BargeandDiamondprovedthatapiecewisemonotonecontinuousmapofafinitegraphhastopologicalentropyzeroifandonlyiftheinverselimitspaceusingthismapasasolebondingmap…     

PERMANENCE OF A NONAUTOMONOUS POPULATION MODEL

1.IntroductionPersistenceofpopulationsplaysanimportantroleinmathematicalecology.Inrecentyears)muchattentionhasbeengiventothepersistenceofnonautomonouspopulationmodelsll--6].[1]proposedtheconceptofpersistenceinthemeanofpopulations.Thisisofimportancebecausenotonlyitprovidesawaytocharacterizethepersistenceofpopula-nons,butalsothereareonlythresholdsbetweenpersistenceinthemeanandtheextinctionofpopulationsforgeneralnonautomonouspopulationmodels.In[2]thethresholdwasestablishedforone-dimensionalnonaut…     

Erratum to: Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure

正[1, Theorem 4.4] states that every infinite dimensional Banach space admits a homogenous measure of noncompactness not equivalent to the Hausdorff measure. Howevere, there is a gap in the proof. In fact,we found that [1, Lemma 4.3] is not true. In this erratum, we give a corrected proof of [1, Theorem 4.4].     

||A~(-1)||_∞ AND EQUIDIAGONAL-DOMINANCE

1.IntroductionInpracticeitisoftennecessarytoestimatethenormilA--'llooofamatrixA.In[1]and[2]anestimateisgiven,undertheconditionwherenistheorderofthemainsA~(ail).Thecondition(2)indicatesthatAisastrictlydiagonallydominantmatrix.In[31wegeneralize(1)toTheleftinequalityholds,whenMisanL-matrix,lmiil>,F.Imijlforevery1andN=(nil)20.Theestimate(1)is,infact,anestimateofIIi(A)--'lloo,wherem(A)isthecomparativemainsofA[4].LetD=diagA,B=D--A.Thenm(A)=IDI--IBIandwhen(2)holds.Ingeneral,wetaketheuppe…     

THE MULTI-PARAMETERS OVERRELAXATION METHOD

1.IntroductionRecently,manymathematicalliteratureshaveprovidedsomenewiterativemeth-odsforsolvingthelinearsystem.Kuang[2]presentedatwo-parameteriterativemethodcalledTORmethod,whichiseffectivetogivethenumericalsolutionofpartialdif-ferentialequations.Wang[,']extendedtheTORmethodtotheGTORmethedandimprovessomeresultsof[3,11,12].In[5],LialsodiscussedtheGTORmethod,andextendedthecorrespondingresultsof[10,11].Recently3SongandDai[9]presentedthemulti-parametersoverrelaxation(MPOR)method,whosespe…     

PSEUDO ALMOST PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

51.IntroductionDifferentialequationswithpiecewiseconstantarguments(DEPCA)candescribehybriddynandcalsystemsandthereforecombinepropertiesofbothdtherentialequationsanddifferenceeqllations.Theyhaveapplicationsincertainbiomedicalmodels[1].In[2,3]andthereferencesthereintherehavebeenalotofresultsconcerningDEPCA.Nevertheless,allofthemdealtwiththestabilityperiodicity,andoscillationetc-ofsolutionsofDEPCA.Re-cently,[4]disscusedtheetistenceofalInostperiodicsolutionsofDEPCA.Inthispaper,wedefineps…     

Carmichael Numbers of Order 3

In 2002, Agrawal, Kayal and Saxena presented a polynomial time primality testing algorithm(the AKS algorithm) in [1], which can determine whether an input number is prime or composite.Papers [2] and [3] play an important role in their primality testing algorithm. In [3], the authors     

Nonoverlapping Domain Decomposition Method with Mixed Element for Elliptic Problems

1.IntroductionDomaindecompositionasanewmethodofcomputationalmathematics,waJsdevel-opedsincethedevelopmentofparallelcomputersandmultiprocessorsupercomputers-Usingdomaindecompositionwecandecreasethescaleoftheproblemandimplementthesub-problemsonparallelcomputer.Fromatechnicalpointofviewmostofdo-maindecompositionmethodsconsideredsofarhavebeendealingwithfiniteelementmethods.In[1,2]ZhangandHuanghavegivenakindofnonoverlappingdomaindecompositionprocedurewithpiecewiselinearfiniteelementapproximation.…     

MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW (Ⅰ)

51.IntroductionThespectralfiowforaoneparameterfamilyoflinearselfadjointFredholmoperatorsisintroducedbyAtiyah-Patodi-Singerl2]intheirstudyofindextheoryonmanifoldswithboundary.Sincethenothersignificantapplicationshavebeenfound.In[17],J.RobbinandD.SalamonstudiedindetailthespectralflowforthecurvesoflinearselfadjointFredhomoperatorswithinvertibleoperatorsattheendpointsandprovedanindextheorem.In[7]and[8]thenotionofthespectralflowwasgeneralizedtothehigherdimensionalcasebyX.DaiandW.Zhang.Inthisp…     

A MULTI-PARAMETER SPLITTING EXTRAPOLATION AND A PARALLEL ALGORITHM FOR ELLIPTIC EIGENVALUE PROBLEM

1.IntroductionTheextrapolationmethodhasbecomeanimportanttechniquetoobtainmoreaccuratenumericalsolutionssinceitwasfirstestablishedbyruchardsonin1926.Theapplicationsofextrapolationmethodinthefinitdifferencecanbefoundin[14].In1983,Q.Lin,T.LhandS.Shen[8]intro…     

ON THE BOUNDARY ESTIMATION OF THE SOLUTION OF STRONG QUASI-LINEAR ELLIPTIC EQUATIONS

In [1] we investigated the problems of calculus of variations with strong non-linearity. In[2] we already indecated its Euler equation is evidently the following elliptic type equation of divergent form with strongly increasing coefficient     

The Gradient Theory of the Phase Transitions with Dirichlet Boundary Condition

§ 1.Introduction　 In this paper,we study the asymptotic behavior of minimizers{ uε} ε>0 (ε→ 0 ) of thevariational probleminf∫Ω[εp- 1 | Du| p + 1εW(x,u) ] dx:u∈ W1 ,p(Ω ) ,u =g,x∈ Ω (Pε)where p>1 ,N≥ 2 ,andΩ RN is a bounded open domain with Ω∈C2 .　 This kind of problems comes from the theory of phase transitions and are widelystudied in recent years.In [1 ]— [1 4] ,the authors investigated these problems underthe integral constraint∫Ωudx =constant,In [1 5]— [1 6] ,…     

Carleson Measure and Multipliers on Bergman Space

1. Introduction.In 1962, Carleson [2] proved the well known Carleson measure theorem for Hardy space. In 1975. Hastings [5] obtained an analogous theorem for Bergman space. In this paper we prove a Carleson type theorem for the quasi-normal weighted Bergman space using a way other than Hastings'.As an application we obtain a theorem on multiplier theory. This generalizes     

Rings with Maximal Finite Subrings

In[1 ] and[2 ] ,itwas proved thata ring with a finite maximal subring mustbe finite.Special cases of this result had been shown for commutative ring(see[3 ] ) and for PI-rings (see [4 ] ) . Lanski[5] extends the result to the ring with a finite maximal invariantsubring with respect to certain automorphism.In this paper,we shall consider ringswith maximal finite subrings. Such a ring,of course,is not necessarily finite. Becauseevery finite ring has maximal finite subrings,we shall be interest…