THE GLOBAL THEOREM OF A.N.BERLINSKII

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SUPERCONVERGENCE OF THE FULL-DISCRETE F.E.M. FOR COMPRESSIBLE MISCIBLE DISPLACEMENT: THE FULL TENSOR CASE

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THE PROOF OF A.M. FINK′S CONJECTURE

ＴＨＥＰＲＯＯＦＯＦＡ．Ｍ．ＦＩＮＫ′ＳＣＯＮＪＥＣＴＵＲＥ￥ＺｅｎｇＷｅｉｙａｏ（曾唯尧）（ＨｕｎａｎＬｉｇｈｔＩｎｄｕｓｔｒｉａｌＣｏｌｌｅｇｅ）Ａｂｓｔｒａｃｔ：ＩｎｔｈｉｓｐａｐｅｒｗｅｗｉｌｌｓｈｏｗＡ．Ｍ．Ｆｉｎｋ′ｓｃｏｎｊｅｃｔｕｒｅ...     

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.     

A NOTE ON THE C.NEUMANN PROBLEM

We prove that the C. Neumann problem in the case where the potential matrix A hasmultiple eigenvalues is completely integrable by means of the moment map and the confocalquadric.     

ON CONDITIONS FOR THE NON LOCALLY CONVEX LINEAR TOPOLOGICAL SPACE TO HAVE THE H.-B. EXTENSION PROPERTY

In this paper, the conditions for the non lcally convex topological vector space to have the H,-B. extension property is discussed, and the following three results are proved; (1)A closed subspace E0 of a linear topological space E to have the H.-B. property if and only if for every closed hyperplane of E0 is weakly closed, (2) A locally bounded linear topological space (E,τo)to have the H.-B extension property if and only if for every closed subspace E0 of E, the weak topology σ(E0,E^*0)属于τ1|E0, where τ1 is the finest locally convex topology on E which is coarser then τ0. (3)Let E be separated and let E be the completion of E. If every closed subspace E0 of E is the complete hull of E0∩E,then E has H.-B. extension property if and only if E has H.-B. extension property.     

ON THE CONJECTURE OF A.LINS, W.DE MELO AND C.C.PUGH

We have proved that Lienard equation with F(x) = -F(-x) has at most n limit cycles. Under the condition, an affirmative answer to A.Lins, W.de Melo and C.C.Pugh's conjecture is given.     

FINDING PROJECTIONS ONTO THE INTERSECTION OF CONVEX SETS IN HILBERT SPACES. II.

We present a parallel iterative algorithm to find the shortest distance projection of a given point onto the intersection of a finite number of closed convex sets in a real Hilbert space ; the number of sets used at each iteration stept corresponding to the number of available processors, may be smaller than the total number of sets. The relaxation coefficient at each iteration step is determined by a geometrical condition in an associated Hilbert space, while for the weights mild conditions are given to assure norm convergence of the resulting sequence. These mild conditions leave enough flexibility to determine the weights more specifically in order to improve the speed of convergence.     

THE EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR EVOLUTION EQUATIONS AND APPLICATIONS TO P. D. E.

The main purpose of this paper is to discuss the existence and asymptotic behavior of solutions forand for which the sufficient conditions of asymptotic behavior are obtained and the restriction for the existence is reduced.     

ON THE FINITE GROUP WITH A T.L SYLOW P-SUBGROUP

This paper studies the relations between T.I.conditions and cyclic conditions on theSylow p-subgroups of a finite group G.As examples,the following two results are proved.1.Let G be a finite group with a T.I.Sylow p-subgroup P.If p=3 or 5,wesuppose G contains no composition factors isomorphic to the simple group L_2(2~3)or Ss(2~5)respectively.If G has a normal subgroup W such that p|(|W|,|G/W|),then G isp-solvable.2.Let G be a finite group with a T.I.Sylow p-subgroup P.Suppose p>11 and P isnot normal in G.Then P is cyclic if and only if G has no composition factors L_2(p~n)(n>1)and U_3(p~m)(m≥1).     

SOME BOUNDARY PROBLEMS OF THE SPIN SYSTEMS AND THE SYSTEMS OF FERRO-MAGNETIC CHAIN Ⅰ. NONLINEAR BOUNDARY PROBLEMS

§1. Introduction The nonlinear system of partial differential equations and the corresponding system with diffusion term are interesting and meaningful both in physical and mathematical point of view, where z= (u, v, w) and f(x, t, z) are two three-dimensional vector functions and"× "denotes the cross product operator of two three-dimensional vectors. The system (1) contains the so-called Landau- Lifschitz equation of isotropic Heigenberg ferro-magnetio chain as the     

RATES OF A.S.CONVERGENCE OF THE ESTIMATION OF ERROR VARIANCE IN LINEAR MODELS

Under appropriate conditions we obtain the best rates of a.s.convergence of estimates5_n~2 of error variance σ~2 and establish the law of iterated logarithm     

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…     

SOME BOUNDARY PROBLEMS OF THE SPIN SYSTEMS AND THE SYSTEMS OF FERRO-MAGNETIC CHAIN Ⅱ. Mixed Problems and Others

In the present paper the authors considered the mixed problem with nonlinear boundary conditions and the initial condition for the spin system and the system of ferro-magnetic chain in the rectangular domain Q_t.     

ON THE EXPECTATION AND VARIANCE OF HAMMING DISTANCE BETWEEN TWO I.I.D RANDOM VECTORS

1.IntroductionLetFZn={0,1}"beann-dimensionalvectorspaceoverthebinaryfieldFZ={0,1}.TheHammingdistancebetweentwovectorsx=(xl,'tx.)andy=(yi,'ty.)isthenumberofcoordinateswheretheydiffer,andisdenotedbydH(x,y),dH(X,y)=ZIXi~ail.i=1TheHammingweightofxisthenumberofnon-zerocoordinates,andisdenotedbyWH(x).ObviouslyAH(x)=dH(x,0),where0isthezerovector.Thescalarproductofxandyis(x,y)=xlyl ' xestinF2.ForasetAgFZn,IAIdenotesthecardinalityofA.TheaveragedistanceinAisdefinedby*Thisresearchissupp…     

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.