LOWER BOUNDS FOR SUP＋INF AND SUP＊INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3

We give two results about Harnack type inequalities. First, on Riemannian surfaces, we have an estimate of type sup ＋ inf. The second result concern the solutions of prescribed scalar curvature equation on the unit ball of Rn with Dirichlet condition. Next, we give an inequality of type （supK ^u）^2s-1 × infπu ≤ c for positive solutions of △u = V u^5 on Ω belong toR^3, where K is a compact set of Ω and V is s-Holderian, s ∈] - 1/2, 1]. For the case s = 1/2 and Ω = S3, we prove that, if minΩ u 〉 m 〉 0 （for some particular constant m 〉 0）, and the H¨olderian constant A of V tends to 0 （in certain meaning）, we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of Ω.     

ANALYTIC AND HARMONIC CONTINUATIONS AND DISTRIBUTIONS

The present paper gives several theorems concerning analytic and harmonic continuations described by distributional limits. For distributions on spheres, comparatively complete results are given. Generalizing the Direchlet and Neumann problem so that the boundary values are distributions, we obtain the results on existence and uniqueness. For one complex variable, a generalized Riemann's mapping theorem is obtained.     

OSCILLATION AND VARIATION OF THE LAGUERRE HEAT AND POISSON SEMIGROUPS AND RIESZ TRANSFORMS＊

In this article,we study Lp-boundedness properties of the oscillation and variation operators for the heat and Poissson semigroup and Riesz transforms in the Laguerre settings.Also,we characterize Hard...     

ATTRACTORS AND QUASI-ATTRACTORS

In this paper, some properties of attractor and quasi-attractor are given. Some of them generalize Conley's results in [1,2].     

MULTIRESOLUTIONS AND PRIMITIVES

In wavelet theory smootheness is one of the main interests. By the Mallat-Meyer construction (see [He] or [Ne]) the problem of finding smooth wavelets is reduces to finding smooth scaling functions of multiresolu-tims. From a given scaling function g a smoother one can be made by taking convolution with e. g. the characteristic function of [0,1]. In this article a characterisation of the multiresolution generated by that convolution-will be given by means of primitives of functions in the multiresolution generated by g. From this , the spline muhtresolutiom follow as a special case.     

ON THE DIFFERENTIAL AND DIFFERENCE INDEPENDENCE OFΓANDζ

In this paper,we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function.It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations.     

BIFURCATION PROBLEMS OF MULTIPARAMETER AND MULTIBRANCH AND THEIR APPLICATIONS

This paper deals with the bifurcation problems of multiparameter and multibranch and their approximations. It derives general approximation results of solution branches in the neighbourhood of a singular (limit, turning or multibranch) point, and shows that turning and multibranch points are bifurcation points. The abstract theories are applied to a mixed finite element approximation of stationary Navier-Stokes equation.     

α-TRANSIENCE AND α-RECURRENCE FOR RANDOM WALKS AND LEVY PROCESSES

The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove that the process X is quasi-symmetric if and only if X is not α-recurrent for all α< 0 which gives a probabilistic explanation of quasi-symmetry, a concept originated from C. J. Stone.     

FEATURES AND APPLICATIONS OF BERTALANFFY-RICHARDS‘ AND SCHNUTE'S GROWTH EQUATIONS

ABSTRACT. Based on various ranges of the parameter m (or b), the paper analyzes the features and the integral forms of the Schnute and the Bertalanffy-Richards growth equations as well as the two aspects of their special cases (such as Gompertz, logistic and monomolecular models). It is a first attempt to investigate all the corresponding relationships among parameters of the models derived from the Schnute and the Bertalanffy-Richards growth equations. All the models from the two are empirically fitted by different data sets for eucalypt plantations. Unlike earlier papers, the results of this paper show that either of the two growth equations can be considered as a model for estimating forest growth given a parameter range, and both can produce similar growth performances. Some other aspects of the two growth equations are discussed so that the two can be used correctly.     

POTENTIALITY AND REVERSIBILITY FOR THE N-SPIN-FLIP PROCESSES AND THE N-GENERALIZED SPIN-FLIP-PROCESSES

The Markov processes with infinite particle system are one of the new branches in probability, recently it is developed rapidly. It relates not only to the statistical physics of balanced state, but also to the statistical physics of the unbalanced state and other subjectst In this paper, two kinds of Markov processes with infinite     

EXPONENTIAL TRICHOTOMY AND ROUGHNESS

ConsiderthesystemwhereAfR-R"x"isacontinuousnxnmatrixandxCR".LetX(l)bethefundamentalmatrixof(l)withX(0)=I.Definition1Thesystem(1)issaidtohaveanexponentialtricholoTll.yif.thereexistlinearprojectionsPandQsuchthatandconstantsKZ1,or>0,fi21suchthatanda.aarecall…     

STABILITY AND TOPOLOGICAL EQUIVALENCE

ＳＴＡＢＩＬＩＴＹＡＮＤＴＯＰＯＬＯＧＩＣＡＬＥＱＵＩＶＡＬＥＮＣＥＷａｎｇＸｕｅｘｉｎ(汪学鑫)（ＺｈｅｊｉａｎｇＡｇｒｉｃｕｌｔｕｒａｌＵｎｉｖｅｒｓｉｔｙ,浙江学业大学,邮编:３１００２９）ＪｉａｎｇＹａｎｗｅｉ(姜学伟)（ＫｅｓａｎＴｅａｃｈｅｒｓ?..     

MULTIFUNCTION AND ITS APPLICATION

§ 1. Introduction The study of multifunction has been developed extensively with application to mathematics in economics, optimal control, game theory, mathematical programming and decision prooess, etc. Especially, it has been widely used in mathematical economics. Debreu's work Theory of Value is closely related to the method of multifunction which economists called correspondence. Economic equilibrium theory has long been treated by calculus since Walras. Von Neumann's work in 1943 on economic theory has been an initiative to form a'new kind of mathematical method to economic theory and reduced the dependence on calculus. The early development of mathematical economics including the 19th century and even up to the World War Ⅱ was largely in terms of calculus; it was doubtless that th(?)     

POTENTIALITY AND REVERSIBILITY FOR THE N-SPIN-FLIP PROCESSES AND THE N-GENERALIZED SPIN-FLIP-PROCESSES

§1 Introduction The Markov processes with infinite particle system are one of the new branches in probability, recently it is developed rapidly. It relates not only to the statistical physics of balanced state, but also to the statistical physics of the unbalanced state and other subjects.     

UHF-ALGEBRAS AND *-ISOMORPHISMS

The following problem is discussed: If μ is an AF-algebra, A and B are two C-algebras, x(A) and x(B) are the unit balls of μ A and μ B respectively, and there is an affine isomorphism from X(A) onto x(B), when are A and B isomorphic? This problem was inspired by K-theory of C*-algebras. If μ is a UHP-algebra of type {m~p}, an orientation on x(A) and x(B), i. e., an action of the special group of μ, is introduced. Then it is obtained that if the affine isomorphism commutes with the group action then A and B are isomorphic.     

HERMITE EXPANSIONS AND FRACTALMEASURES

1IntroductionLetB.(x)denotetileballofradiusrcenteredatalapositivemeasureponR"iscalledlocallyuniformlyor-dinlellsiollal,0Sa5ncifIL(B.(x))5cabforallxER"alld7'51.ThisclassofmeasureswasilltroducedbyStrichartz.Theycontainanimportantclassofl'1'actalmeasureswhiclliscalledself-silltilal'llleasure(see[1]and[2]).Strichartzhavedevelopedatheoryoffi.actalspectralasylnptotics.Herevealtheirfi.actalnatureintheasymptoticbehavioroftheFouriertransforlllatiollalldwaveletexpansionsin[2]and[3].UsingthemeanThv…     

STABILITY AND SUPERSTABILITY OF JORDAN HOMOMORPHISMS AND JORDAN DERIVATIONS ON BANACH ALGEBRAS AND C~＊-ALGEBRAS： A FIXED POINT APPROACH

Using fixed point methods, we prove the Hyers-Ulam-Rassias stability and superstability of Jordan homomorphisms (Jordan *-homomorphisms), and Jordan derivations (Jordan *-derivations) on Banach algebras (C*-algebras) for the generalized Jensen-type functional equationwhere r is a fixed positive real number in (1, ∞).     

The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES

ＴｈｅＨＡＵＳＤＯＲＦＦＤＩＭＥＮＳＩＯＮＡＮＤＭＥＡＳＵＲＥＯＦＴＨＥＧＥＮＥＲＡＬＩＺＥＤＭＯＲＡＮＦＲＡＣＴＡＬＳＡＮＤＦＯＵＲＩＥＲＳＥＲＩＥＳ￥ＲＥＮＦＵＴｈＯ；ＬＩＡＮＧＪＩＮＲＯＮＧＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｓｔｕｄｉｅｓｔｈ...