15 September 1996, Volume 39 Issue 5

    

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  On Super-Isometric Dilation of Operator

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0096

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  In this paper,we investigated the conditions of operators'dilated spuer-isometric.It is shown that the super-isometrically dilatable operator has a nontrivial invariant sub space, and it is proved,in addition,that for is unitarily equivalent to Mf if const.provided some abate condition is satisfied.
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  Pointwise Quasi-Uniformities and Pseudo-Quasi-Metrics on Completely Distributive Lattices

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0093

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  In this paper j a new theory on poilitwise quasi-uniformity is based on completelydistributive lattices.Properties of closure,locally basis, continuity etc.are discussed in inducedtopological molecular lattices. EaCh tOPological molecular lattice can be induced by a pot￣isequasi-whfondty.Moreover,an equldsnt definition and a characterization of pseudDequasimetric in [8]are given.P seudth quas i- metrization theorem is obt anied.
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  On the Existence of Meromorphic Solutions of One Class of Ordinary Differential Equations

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0091

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  In this paper,we apply the value distribution theory of Nevanlinna to solve the tence and possible number of meromorphic solutions of the differential equations with a domainative coefficient Pn or P0. At the same time,we give some examples to show that our results are sharp.
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  Admissibility of Quadrstic Estimator of Error Variance in Normal Linear Model

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0092

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  Suppose Y is distributed N(Xβ,σ2I) and rank (X)
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  The Structure Theorem of Hopf Algebras and the Order of Antipode

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0090

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  Let nH be the order of a Hopf algebra H's antipode.By means of a Hopf algebra structure theorem under Hopf algebra isomorphism,we prove nHg=nH for irreducible component Ho of H.For Hopf algebra extension L,we show that nL may be arbitrary even order,where nH| nL'
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  Completely Characterize the Exponent Set for the Class of Non-symmetric Primitive Matrices with Nonzero Symmetry Elements

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0094

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  In this paper we completely determine the index set for the class of n×n (n>5)non-symmetric primitive matrices with at least one pair of nonzero symmetry entries. The main results are the following:(1)trace is nonzero,regardless of n(>5) is odd or even,we always have (2)trace is zero,(i)if n(>5) is odd,then (ii) if n(>5) is even) then
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  Existence of Almost Periodic Solutions of Neutral Functional Differential Equationswith Infinite Delay

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0095

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  This paper presents some existence theorems for almost periodic solutions to neutral functional differential equations with infinite delay by means of Liapunov functionals.
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  Two Properties of the Monoids Presented by Special Thue Systems

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0089

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  Two sufficient and necessary conditions are given for the monoids presented by finitespecial Church-Rosser Thue systems to be groups and regular ones respectively.And thus an algorithm is derived to decide whether such a monoid is a group or a regular monoid.
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  The Bifurcation and Stability of Time-periodic Solutions for the Evolution Equation with One Parameter

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0083

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  In this paper we discuss the bifurcation and stability of take-periodic solutions for the evolution equation =F(t,μ,u) by using methods of asymptotic expansion and spectral analysis,and the results of existence and stability criterion were obtained.
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  Multi-Row Quasi-Cogrendience Classification of Matrices and It's Application

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0079

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  Generalizing the notion of quasi-cogredience of square matrices, this paper advances the notion of multi-row quasi-cogredience of rectangular matrices with all entries in a field F and a square number as it's number of columns,and gives out the result of the 2-row quasicogredience classification of M2,4(Fp)──the simplest case.One of it's applications appears in the isomorphism classification of finite rings.
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  Tangent Properties of Inclusions for Nonconvex Set-Valued Maps and Applications

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0081

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  In this paper,we investigate the tangent properties of inclusion for the set-valued map F defined on K which is a closed subset of a Banach space X with nonempty and nonconvex values in X.Our results extend the results of [1,p.161] and [9, p.125].As the examples of application, two viability problems for nonconvex differential inclusions and nonconvex control systems in infinite dimensional spaces are considered.A convenient tangential condition which is equivalent to the tangential condition of[8]is also given.
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  The Positive Solutoins of Abstract Semilinear Evolution Equations and Their Applicatious

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0082

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  In this paper, the characteristics of positive operators semigroups in ordered Banach spaces are discussed.The supersolution and subsolution method for the study of ordinary differential equations and partial differential equations is applied to semilinear evolution equations in ordered Banach spaces.The results on the existence of the global solutions and positive solutions are obtained.
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  On the Generalized Numerical with the Completely Symmetric Function

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0080

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  A necessary and sufficieat condition for the m-numerical range of a matrix A with the completely symmetric symmetric function Ck to be a line segment in the complex plane is given in this note.
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  Dimension of the Global Attractor for the Damped Sine-Gordon Equation

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0078

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  An estimate of dimension of the global attractor for the damped Sine-Gordon equation with homogeneous Dirichlet boundary condition is obtained by introducing a new norm.This estimate shows that the Hausdorff dimension of the global attractor decreases when both the "damping" and the "diffusing" increase or the coefficient of the Sine term decreases.In particular, under certain conditions,the dimension is zero.
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  The State Characters of the Occupation Times for a Class of Super-processes in a Movable Medium

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0086

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  This article concerns the particle systems in a movable medium,which aunder Dawson's hypothesis lead to a class of measure-valued branching processes (Super-processes).The Super-processes describe a variety of phenomena on propagating of particles,and they have many distinctive properties.We here mainly approach their integral-processes i.e. occupation time processes and for which two important characters: the existence of density fields and the convergence for large time behavior,will be demonstrated.
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  On the Functions Denoting the Number of Prime Factors of a Natural Number

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0084

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  Let g(n) be an arbitrary arithmetical function for which g(0)=0.Define j(n)=for n> 1 and f(1)=0,where is the standard factorisation of n.In thisi=1paper,the asymptotic formula for the sum given, where Ω(n) denotes the number oftotal prime factors of n.
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  Convergence of (0, 1, 3) Interpolation on the Unit Circle

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0085

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  In this paper, we study the property of uniform convergence for(0,1,3)interpolation on the set obtained by projecting vertically the zeros of Legendre polynomial onto the unit circle.
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  On the Stability of a Homoclinic Cycle and a Heterocliulc Cycle in Space

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0088

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  After defining the concept of stability of a homoclinic cycle or a heteroclinic cycle in their part neighborhood for space systems,this paper gives a criterion for determining the stability of a homoclinic cycle or a heteroclinic cycle in space for the fast time.The results given in this paper include and extend the results already obtained by the authors of [1]-[3] which are used to determine the stability of a homoclinic cycle or a heteroclinic cycle on a plane in a sense.Lastly the stability of the homoclinic cycle in Lorenz system and the stability of the heteroclinic cycle in a ecological model with 3-species by Lotka-Volterra equation are discussed.The result obtained coinsides with the conclusion of.[9]-[11].
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  The Lipschitz Functions and Littlewood-Paley g-Function on Spaces of Homogeneous Type

  Acta Mathematica Sinica, Chinese Series. 1996, 39(5): . https://doi.org/10.12386/A1996sxxb0087

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  On normal spaces of homogeneous type with orderθ,if the sequence of operators is an approximation to the identity, Dk = Sk- Sk-1, in this paper a sufficient and'necessary condition by {Dk}k∈Z for f∈Lipα(the Lipschitz function class,0<α<θ) is given.As a corollary of this result,it is obtained that the Littlewood-Paley g-function of f∈ Lip α,g(f)(x) is either infinit everywhere or bounded on Lipα.