A NOTE OF CONVERGENCE RATES FOR SUMS OF ρ-MIXING SEQUENCES

1.IntroductionandMainResultSincethedefinitiononthecompleteconvergencewasintroducedbyHsuandRobbins[1],therehavebeenmanyauthorswhodevotethemselvestothestudyonthisconvergenceofiidrandomvariables,seeGut[2,3],BaiandSu[4]andLin[5].Meanwhile,somescholarshav...     

THE RATES OF CONVERGENCE OF M-ESTIMATORS FOR PARTLY LINEAR MODELS IN DEPENDENT CASES

51.IntroductionAnembeddingofacoveringmaporaprincipalG-bundleT:E- Xintoavectorbundlep:V→XisamapH:E-VwhichmapsEhomeomorphicallyontoitsimageH(E)inVsuchthatpoH=7.In[6l,HansenprovedthatanyfinitecoveringmapoveraCW-complexcanbeembeddedintothetrivialrealm-planebundleifdimX5m 1.Embeddingfinite..covringmapsintoarbitraryvectorbundleswasconsideredbyDuval1andHuschl3].Suchanembeddingproblemwasalsodiscussedin[4,5,6,7,8,11,12]and[13].Inthisnote,thefirstpoilltistostudyingreaterdepththeembeddingproble…     

EIGENVECTORS OF SYSTEM OF HAMMERSTEIN INTEGRAL EQUATIONS IN BANACH SPACES ANDAPPLICATIONS

1IntroductionLetEbeaBanachspaceandI=[O,l].ConsiderthesystemofHammersteinintegralequationsinE:wherekiEC[IxI,R'](i=1,2)arenonnegative,fieC[IxExE,E](i=1,2)andyt,YEC[I,E].Inthispaper,weinvestigatetheexistenceofeigenvectorsofsystem(l)bymeansoffixedpointindextheory.WealsogivesomeapplicationstoasystelllofSturm-Liouvilleproblemsofordinarydtherentialequations.Iuwl1atfollows,PdenotesthenormalconeofEwithanormalconstantN(see[1,2l):95u5vimplieslluII5N11vIl,whereoisthezeroelementofE.ExEisaBana…     

SMOOTHNESS OF INERTIAL MANIFOLD UNDER TIME DISCRETIZATION

0IntroductionInertialmanifolds(IM)arenewobjectsthathavebeenintroducedinrelationwiththestudyoflargetimebehaviorofnonlineardissipativePDE,see[1].In[2],theyareextendedtodiscretizeddynamicsstemmingfromdissipativePDE.Frommathematicalpointofview,thesearesmootllfiniteLipschitzmanifoldsthatareinviantbytheflowofassociatedsolutions,andattractallthetrajectorieswithexponentialspeed,see[1].Fromphysicalpointofview,IMmodeltheinteractionlawsbetweensmallandlargestructureofaturbulentflow,andrepresentsitspe…     

LEFT INVERSES AND RIGHT INVERSES OF A STRONG ENDOMORPHISM OF A GRAPH

1IntroductionConsiderableattelltionhasbeendevotedtotilesemigroupoftheelldomorphislllsofagraph,inparticular,thesemigroupofthestrongendomorpllisnasofagraph,seesurvey[1].Themainpurposeoftheseresearchesliesintheapplicatiollsofthealgebraictheoryofsendgroupstothetheoryofgraphs.ItiswellknowllthatoneofthemostimportantconceptsillselltigrouptheoryisGreen'srelations.In[2],thecharacterizatiollofGreen'srelationsonsEnd(G),themolloidofthestrongendomorphisnisofagrapllG.isgiven.LetSbeasemigroup.Thenotation…     

THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

1.IntroductionandDefinitionsTheinducedrepresentationofgroupC*-algebrasfirstwasalgebraicallyintroducedbyfueffelin[3].P.Greenin[6]similiaxlyintroducedtheoneforcovariantdynamicsystem.TheinducedrepresentationofcrossedproductsbycoactionswasintroducedbyK.Mansfieldin[9].Using[8]wecanobtaintheinducedrepresentationofgrollpoidC*-algebrasin[1Ol.TherichapplicationofthesecanbefoundamongmanypapersrelativetotheC*-analysisofgroupoidandgroup.TheC*-groupoiddynamicsystemanditsreducedcrossedprod-uctwereintro…     

THE BLOCH CONSTANT OF LOCALLY BIHOLOMORPHIC MAPPINGS ON BOUNDED SYMMETRIC DOMAINS

51.IntroductionIn[11,westudiedtheboundsofBlochconstantofholomorphicmappingsonirreducibleboundedsymmetricdomains.ThispaperisasuccessivepaPerof[1].WestudytheboundsoftheBlochconstantoflocallybiholomorphicmappingsonirreducibleboundedsymmetricdomains.AllthenotationsofthispaPerarethesameasthoseweusedin[1].LetDbeadomain,whichcontainstheorigin.AholomorphicmappingonDisdefinedasaBlochmappingifthefamilyofmappingsFj={g:g(z)=f(rk(z))-j(gh(o)),forallrkEAut(D)},isanormalfamily.TheBlochnormofaBlochmapp…     

REGULARIZATION METHOD FOR IMPROVING OPTIMAL CONVERGENCE RATE OF THE REGULARIZED SOLUTION OF ILL-POSED PROBLEMS

1IntroductionThestudyoflllallymathematicalphysicsproblemsleadstosolvingoperatorequatiollsofthefirstkind,andtheoperatorequatiollsofthefirstkindaretypicallyill--posedprobellis[1,2,3,4].Themethodsforsolvillgill-posedproblellishavebeenstudiedbyagreatnumberofresearchers.WementionTikhonovandArsellill[2],Morozov[3]IGroetscll[4],Engll51,HouandLi['],ChenandHouI7]alldoillerscholars.Illtheirresearches,they11avediscussedtheproblemoffindingstableapproxilllatesolutiollsand11aveillvestigatedtileconverge…     

Φ-INEQUALITIES AND LAWS OF LARGE NUMBERS OF HARDY MARTINGALETRANSFORMS

In[101,GarlinghasintroducedtheAUMDpropertyofComplexBanachspaceusinginequalityofmartingaletransforms,somefactsshowwhichdiffersfromUMDpropertyofrealBanachspaceintroducedbyBurkholder[6].GarlingalsoprovedthatAUMDpropertyimpliessuperreflexivityandARNP.In[13],XuprovedHMT.isequivalenttoAMT.thatistheBanachspacesforwhicllHardymartingalesconvergeunconditiollallyarethoseforwhichanalyticmartingalesconvergeunconditionally.Hardymartingalesandanalyticmartingalesformaspecialclassofmartingalesforwh…     

QUALITATIVE ANALYSIS OF A DICRETE POPULATION MODEL

1IntroductionandPreliminariesInthispapertweconsiderthenonlinearbackwarddifferenceequationwhereafb,candkareconstantsandsatisfyEq.(1.l)maybeviewedasadiscreteanalogueofthemodelofsinglespeciespopulatiollwithaquadraticper-capitagrowthratewhicllwasstudiedbyGopalsalllyandLadasin[2].Therefore,wesaythatEq.(1.1)isadiscretepopulationmodel.Inarecelltpaper[5],Rodriguesstudiedanotherdiscreteanologueof(1.3),.namely,thefollowingforwarddifferenceequationalldobtailledsomeresultsfortilequalitativebehaviorsofso…     

一类特殊分布纪录值之和的中心极限定理

摘要：设{X，Xn,n≥1)为独立同分布的服从某连续分布F的随机变量序列，X^(1)=X1，X^(2),X^(3),…为其纪录值序列．令ψ(u)=F^-1(1-e^-u)．其中F^-1是F的反函数．本文研究当ψ(u)=log^pu时Tn=∑k=1^nX^(k)=^dn∑k=1^nψ(Sn)的极限性质．解决了户为所有正整数时Tn的中心极限定理．     

ADDITIVE FAMILIES OF INVARIANTS OF FORMS OF DEGREE d

Abstract

Let d be a positive integer, and F be a field of characteristic zero. Suppose that for each positive integer n, I _n, is a GL _n,(F)- invariant of forms of degree d in x₁, …, x _n, over F. We call {I _n} an additive family of invariants if I _p+q (f ⊥ g) = I _p(f).I _q(g) whenever f; g are forms of degree d over F in x _l, …, x _p; …, x _q respectively, and where (f ⊥ g)(x _l, …, x _p+q) = f(x ₁, …, x _p,) + g (x _p+1, …, x _p+q). It is well-known that the family of discriminants of the quadratic forms is additive. We prove that in odd degree d each invariant in an additive family must be a constant. We also give an example in each even degree d of a nontrivial family of invariants of the forms of degree d. The proofs depend on the symbolic method for representing invariants of a form, which we review.     

COMPARISON OF PRODUCTS OF THE VARIETIES OF LIE ALGEBRAS

Abstract

In Fortes (2001), we introduced a notion of order for associative pairs and we obtained a Goldie-like characterization of left orders in a semiprime pair coinciding with its socle. In this paper, we take up again that notion of order to establish a Faith-Utumi theorem, which studies left orders in a prime pair coinciding with its socle.     

一类微分方程组的非允许解

利用亚纯函数Nevanlinna的值分布理论，我们研究了一类代数微分方程组非允许解的存在性问题。并通过亏量δ(a，w)改进了非允许解的估计．     

函数集的完全性

1.:敲g(x)篇〔一二,二]上之非降的有界缝差两数,业具有性鬓(K)s‘二一0,一。(:);f--:.,。g。尹(:)!d:一郁匕,(‘一”,”;dg)篇在〔一二,司上定羲业且满足修件:,一{户,(柳dg(·)}青<一,>l的可测蝮值函数族{f(幻}.封龄一徊乙“(一二,侧d刃中之子族凌B(幻},若由f(劣)(乙,(一二,二:dg),夕>1生+上夕q=1,及f--:ha”“’“““’一0纷{B(x)}之任何B(哟成立必滇致f(幻在〔一二,司上规乎虚虚等焚零则释{B(x)}在乙“(一二,侧dg)中完全. 函数族的完全性是舆函数横造的一些简题很有阴保的.徙【l]我们知道{e‘”}豁。是在乙,(一二,州dg),,>1,中完全的,…     

小康判别函数的建立与分析

近几年，国内在研究小康水平的定量指标分析中，应用较多的有综合评分法、层次分析法和模糊识别法。这几种方法比单项指标更全面、灵活，但在权数的确定上都难以克服人为因素的影响。当指标之间存在两个或两个以上的高度相关时，对问题的研究总存在一定的局限性。为了科学地研究小康问题，本文基于判别分析，建立城市小康的判别系数，来综合评价出我国城市小康水平的定量标准。     

两类方程亚纯解(n,1)级的上界估计

本文给出Riccati方程及另外一类具有代表性微分方程的亚纯解（n,1)级的上界估计，在一定条件下确立了文[2]中的猜测的正确性。     

对称矩阵部分特征值之和的非光滑分析

本文研究n阶实对称矩阵A的前m项最大特征值之和fm（A）的非光滑分析问题．利用Ky－Fan的关于特征值之和的变分原理以及凸分析理论，得到了fm（A）的次梯度和方向导数的显式表达式．     

一类pnm阶群的构造

本文研究了一类特殊的pnm阶有限群的构造.利用求解数论同余方程的方法和群的扩张理论,得到了具有m阶循环正规子群,其补子群为循环群的Pnm阶有限群的构造及相关的计数定理.