THE SOLUTION TO THE SK-MODEL

IIntroductlonAs one ofwell－kn。mean ield models for spin glasses,the SK(Sherrin红on－Kirkpatri山)model has been studied by many authors恤叫2]nd[81,andthe references therein)．Particu－larl儿丁劝a以andls]repm眈* some quite lmerestingresults on It in his one－hour Invited talk tthe International Congress ofMathem航icians held t Berlin in August,ig98．In mathematical terms;the SK－Model Is the study of a cert。n random measure on Z。:＝{一1;1}”for a natural。mber N．Z。Is called configu…     

THE FINITE INVARIANT MEASURES AND THE REVERSIBLE MEASURES OF THE DIFFUSIONS WITH THE VENTZEL''''S BOUNDARY CONDITIONS IN THE CIRCULAR DISC

For a given rotation-invariant operator Ω in the unit disc, the necessary condition for thef xistence of finite invariant measures of the strong Markov transition functions determined by Ω with the Ventzel's boundary conditions of finite rank is established If only rotation-invariant transition functions are considered, then the necessary and sufficient conditions for a given measure to be invariant and to be reversible, and all the cor6esponding boundary conditions for posseusiug these properties have been found explicitly in this paper.     

THE WEAK CONCENTRATION OF THE SK-MODEL

1. Main ResultThe SK-model is one of the welLknown mean field models for spin glasses and Talagrandlllreported some advances of this model. Concretely, the SK-model can be described as follows.SK-model (without external field). For a natural nUInber N, letWhere (gij)1相似文献   

THE HAUSDORFF MEASURE FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

91.IntroductionTheso-calledWestwaterprocessisthecoordinateprocessunderthepolymermeasureu(g)in3-dimensionsconstructedbyWestwater(see[7,8]),andthepolymermeasurev(g)onCo([O,1]-R')isformallydefinedbywhereC,isthenormalization,gE[o,oo)isacouplingconstant,pistheWienermeasureonCo([o,11-R').Inarecentpaper(see[9]),weprovedthattheHausdorffdimensionofthesamplepathoftheWestwaterprocess{X,,t6[O,1]}isalsotwowithprobability1tou(g).Actually,weprovedin[9]thatgh(ImX)5C,y(g)-a.e.(1.1)m(ImX)5C,y(g)-a.e.(1.…     

ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS

This paper considers the Calerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble （RFB） functions. The stability features of the residual-free bubble functions for the linearized Navier-Stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements.     

THE TRANSFINITE BASIS OF THE BIDUAL SPACE OF THE LONG JAMES SPACE

A transfinite basis of the bidual space of the long James space is presented in this paper. Moreover, we prove that the space J(w+r) has the approximation property, where J (ω) is the James space, r is any finite integer.     

THE ASYMPTOTIC FORMULA OF THE ORTHOGONAL RATIONAL FUNCTION ON THE UNIT CIRCLE

In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circlewith respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.     

THE ENERGY CONSERVATION OF THE LANDAU-LIFSHITZ-BLOCH EQUATION

In this paper,we consider the three-dimensional Landau-Lifshitz-Bloch equation in the whole space,which can describe the micromagnetic dynamic behavior of material at all temperatures,especially near the Curie temperature.We establish a sufficient condition of energy conservation for when weak solutions of the Landau-Lifshitz-Bloch equation with the temperature higher than the Curie temperature and its gradient belong to the Besov space■ for some α∈(1/2,1) and p=9/3α+1.Moreover,we also use the d...     

ON THE SENSITIVITY OF THE LDU FACTORIZATION

1　IntroductionG.W.Stewart,X.-W.Chang and A.Barralund etc.have done lot of perturbationanalyses on LU,QR and Cholesky factorizations( see[5] ,[6] ,[1 ] ,[2 ] ,[4 ] ,[3 ] ) .We givesensitivity analysisfor LDU factorization in this paper.The LDU factorization ( or LDMT) is an important method in numerical linear algebra( see [7] ) ,and can be viewed as the general form for LDLT factorization. The differencebetween LDU and LU factorizations in upper triangular matrix U,i.e. U is uni…     

THE SERIES SOLUTION OF THE GEL'FAND-LEVITAN-MARCHENKO EQUATION

The convergence of the Neumann series solution of the Gel'fand-Levitan-Marchenko equation in L~∞[0, ∞), L~1[0, ∞) and L~2[0, ∞) is proved and the explicit expression of the series solution is given.     

ON THE REGULARITY OF THE MINIMUM SOLUTION OF THE RESTRAINED VARIATIONAL PROBLEMS

This paper is concerned with the regularity of minimum solution u of the following functional on the restraint Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Hlder continuous.     

THE GRADED MODULES FOR THE POISSON ALGEBRAS

§0.ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｗｅｋｎｏｗ,ｔｈｅｎｏｎｃｌａｓｓｉｃａｌ(ｇｒａｄｅｄ)ｓｉｍｐｌｅｍｏｄｕｌａｒＬｉｅａｌｇｅｂｒａｓｗｈｅｎｔｈｅｂａｃｋｇｒｏｕｎｄｆｉｅｌｄｉｓｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｐ>5ｈａｖｅｆｏｕｒｔｙｐｅｓ:Ｗ(ｎ,ｍ),Ｓ(ｎ,ｍ),Ｈ(ｎ,ｍ)ａｎｄＫ(ｎ,ｍ).Ｆｏｒｔｈｅｇｒａｄｅｄｍｏｄｕｌｅｓｏｆｔｈｅｆｉｒｓｔｔｈｒｅｅｔｙｐｅｓ,Ｓｈｅｎｇａｖｅａｃｏｍｐｌｅｔｅｄｅｓｃｒｉｐｔｉｏｎｂａｓｅｄｏｎｈｉｓｍｉｘｅｄｐｒｏｄｕｃｔｒｅａｌｉｚａｔｉｏｎｓｉｎ…     

ON THE SPACES OF THE MAXIMAL POINTS

For a continuous domain D, some characterization that the convex powerdomain CD is a domain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it is proved that the set of the maximal points Max(CD) of CD with the relative Scott topology is homeomorphic to the set of all Scott compact subsets of Max(.D) with the topology induced by the Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable.     

ON THE CONVERGENCE OF THE PADE TABLE

This paper offers a general result on the problem whether there exists an infinitesubsequence of [L/M](z) approximants from the (M+1)-th row of the pade tableconverging to f(z). According to this result one cam get the optimum conclusion (mentionedin the last paragraph).     

ON THE EQUIVALENCE OF THE ABEL EQUATION

This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.     

THE SOLUBILITY OF THE MULTIDIMENSIONAL TLS PROBLEM

A necessary and sufficient condition of the solubility far the multidimensional TLS problem is presented.     

ON THE CONTINUABILITY OF SOLUTIONS IN THE FUTURE FOR THE LIENARD SYSTEM

ＯＮＴＨＥＣＯＮＴＩＮＵＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＳＩＮＴＨＥＦＵＴＵＲＥＦＯＲＴＨＥＬＩＥＮＡＲＤＳＹＳＴＥＭＨｕａｎｇＬｉｈｏｎｇ（黄立宏）（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，湖南大学，邮编：４１００８２）Ａｂｓｔｒａｃｔ：Ｔｈｅｍａｉｎｐ...     

THE INVOLUTIVE REPRESENTATION OF THE SOLUTION FOR THE COUPLED BURGER－MKDV EQUATION

ＴＨＥＩＮＶＯＬＵＴＩＶＥＲＥＰＲＥＳＥＮＴＡＴＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮ　ＦＯＲＴＨＥＣＯＵＰＬＥＤＢＵＲＧＥＲ－ＭＫＤＶＥＱＵＡＴＩＯＮ￥ＺｈａｎｇＢａｏｃａｉ（张保才）＆ＧｕＺｈｕｑｕａｎ（顾祝全）（ＳｈｉｊｉａｚｈｕａｎｇＲａｉｌｗａｙ...     

THE RELATIVISTIC EQUAL TIME EQUATION AND THE POTENTIAL MODEL OF THE MESONS SPECTRUM

A new relativistic equal time equation is applied to study the structure of mesons. We get a kind of equal time wave functions of natural J~(PC) mesons and a Schrdinger-like type relativistic equation. It is shown that all the meson's spectrum can be described by this equation using phenomenological potential.     

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

nAbstract Let p 0 and μ be a normal function on [0, 1), ν(r) =(1-r~2)~(1+(n/p)) μ(r) for r ∈ [0, 1). In this article, the bounded or compact weighted composition operator T_φ,ψfrom the μ-Bergman space A~p(μ) to the normal weight Bloch type space β_ν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator C_φis compact from A~p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that C_φis compact on β_μ for a 1.