泛代数的二次扩张

在本文中引入了泛代数的二次扩张的概念，解决了ＴＵ－ＥＣ（Ａ）和ＵＴ－ＥＣ（Ａ）的存在、真类和基数问题，范畴ＴＵ－ＥＣ（Ａ）（及ＵＴ－ＥＣ（Ａ）），并得到了有关二次扩张的几个同构定理，还对一点二次扩张作了讨论。     

A LIOUVILLE THEOREM FOR STATIONARY INCOMPRESSIBLE FLUIDS OF VON MISES TYPE

We consider entire solutions u of the equations describing the stationary flow of a generalized Newtonian fluid in 2 D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness of u implies its constancy. A positive answer is true for p-fluids in the case p 1(including the classical Navier-Stokes system for the choice p = 2), and recently we established this Liouville property for the Prandtl-Eyring fluid model,for which the dissipative potential has nearly linear growth. Here we finally discuss the case of perfectly plastic fluids whose flow is governed by a von Mises-type stress-strain relation formally corresponding to the case p = 1. It turns out that, for dissipative potentials of linear growth, the condition of μ-ellipticity with exponent μ 2 is sufficient for proving the Liouville theorem.     

Brown运动在Hlder范数下的拟必然Strassen重对数律的收敛速率

本文研究了Brown运动的泛函极限问题.利用Brown运动在Hlder范数下关于容度的大偏差与小偏差,获得了Brown运动在Hlder范数下的Strassen型重对数律的拟必然收敛速率,推广了文[2]中的结果.     

关于万有Teichmüller空间T1的分支

对数导数或pre-Schwarz导数组成的万有Teichmuller空间模型T1由无限个分支所组成.本文得到了分支Lθ的中心点到有界分支L的距离,同时也对分支Lθ与L的距离及L的中心点到Lθ的距离进行了估计.     

THE DISTANCE BETWEEN DIFFERENT COMPONENTS OF THE UNIVERSAL TEICHMULLER SPACE

The model of the universal Teichmuller space by the derivatives of logarithm is the union of infinite disconnected components. In this paper, it is proved that the distance between different components is 0, and the distance from the center of a component to every other component is 2.     

关于万有Teichmüller空间T_1的分支

对数导数或pre-SchwaLrz导数组成的万有Teichmtiller空间模型T_1由无限个分支所组成。本文得到了分支L_θ的中心点到有界分支L的距离,同时也对分支L_θ与L的距离及L的中心点到L_θ的距离进行了估计。     

THE UNIVERSAL UNITARY MATRIX AND UNIVERSAL HERMITE MATRIX

Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal(oblique)Hermite matrix are studied further,and thismust be useful for matrix theory and applications(like optimization theory,symplecticgeometry and physics etc).In the paper,C~(m×n)shows m×n compound matrix set,C_n~(m×n)shows n step compound invertible matrix set,A~* shows conjugate transpose matrix of A,     

A REMARK ON THE ATTRACTORS OF NON－NEWTONIAN FLUIDS

This paper corrects some mistakes in the proof of absorbing sets theorem of attractors of non-Newtonian fluids, and establishes again the existence of bounded absorbing sets.     

THE UNIVERSAL DUAL COMODULE OF MODULE IN HOPF ALGEBRAS

The purpose of this paper is to present some dual properties of dual comodule.It turns out that dual comodule has universal property (cf.Theorem 2). Since (()~*, ()~O) isan adjoint pair (cf.Theorem 3), some nice properties of functor()~O are obtained. FinallyTheoram 4 provides that the cotensor product is the dual of the tensor product by (M_A     

ON THE LOCAL WELL-POSEDNESS FOR THE DUMBBELL MODEL OF POLYMERIC FLUIDS

In this paper, we consider the local well-posedness of smooth solutions to a coupled microscopic-macroscopic model for polymeric fluid in general space dimension and with general initial data in Holder space.     

SOME PATH PROPERTIES OF BROWNIAN MOTION AND SUPER-BROWNIAN MOTION ON THE SIERPINSKI GASKET

1SomeNotationsLetB(t)betheBrownianmotionontheSierpinskigasket.ThisprocesswasfirstconstructedbyM.T.BallotandE.A.Perkins[2],sowewillsdoptthenotationstherein.Forpurposeofsyste~izationsomeboortantnotationswillbereviewedbriefly.LetaO=(0,0),al=(1,0)andaZ==(i,4),letFO={ac,al,a2}bethevenicesOfanequilateraltriangleintheplaneofsideone.DefineinductivelyLetG6=U7=.Fi'GObeGStogetherwithitsreflectioninthey-axis.LetthenG=of(Goo),theclosureOfG.,isnamedtheSierpinskigasket.NowweintroduceG(u):LetG(o…     

SOME LIOUVILLE TYPE THEOREMS FOR THE P-SUB-LAPLACIAN ON THE GROUP OF HEISENBERG TYPE

In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.     

Sierpinski Gasket上布朗运动的维数性质

本文研究Sierpinski Gasket上的布朗运动X的象集、图集的Hausdorff维数性质,证明了存在零概率集Ⅳ,若ω∈Nc,则对任意紧集F(?)[0,∞),有(i)dimX(F+t)=min(α-1dimF,df),a.e.t>0,(ii)dimGrX|F+t=min(α-1dimF,(1-α)df+dimF),a.e.t>0,其中ds=log3/log2,α=log2/log5.     

SELF-INTERSECTIONS OF BROWNIAN MOTIONON THE SIERPRISKI GASKET

1IntroductionIn[1],BarlowandPerkinsconstructeda"Brownianmotion"takingvaluesintheSierpinskigasket,afractalsubsetofR',thisisapointrecurrentsymmetric'diffosionprocesscharacterizedbylocalisotropyandhomogeneityproperties.Inthispaper,wediscussforwhichE,X(E)4{X(t),tEE}hask-multiplepoints,thatisdoesthereexistxsuchthatX(tl)=X(tz)=''=X(tk)=xforatleastkdifferenttieE?Thestructureofthispaperisasfollows.InSection2,somedefinitionsarerecalled.InSection3,wediscusstheealstenceofk-lllultiplepoints.Throu…     

矩阵的泛正定与广义逆偏序

引言出现在二次型和 Hermite 型研究中的正定矩阵不仅理论结果非常丰富,而且在几乎所有的数值分析以及应用数学和力学各分支中有着广泛的应用.我们用 P_n 表示所有 n 阶实正定阵的集合