15 July 1995, Volume 38 Issue 3

    

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  Stnbility of Nonlinear Analytic Difference Systems

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0050

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  The stability problem of solutions of nonlinear analvtic difference svstems is studied byintroducing the concept of k-stability.Some new simple criteria for stability are given.Examples are employed to illustrate the theory.
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  Singular Integral Along Lower-Dimensional Set

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0051

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  In this paper,the authors discuss the L￣p-boundedness of singular integral alonglower-dimensional sets and its“local”version. For certain“collvex”surface,the authors provethat they are bounded on L￣P(R￣n),p>1. The results extend the corresponding ones of E.M.Stein￣[1].
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  On Maximal Essential Right Ideals of Rings

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0049

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  Let R be a ring. We consider the following two conditions:(*)Every maximal essential right ideal of R is either a GP-injective right R-module or aright anuihilator. (*) Every maximal essential right ideal of R is a YJ-injective right R-module.The aim of this paper is to investigate rings satisfying(*)or(*).Several new characteristicpropertles of strongly regular rings and division rings are also given.
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  Constrtiction of Two-type Stiperprocesses

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0052

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  Using the ideal of Dynkin’s branching particle systems for reference,We constructa widespread class of two-type superprocesses by taking limit to the renormalized two-typebranching particle systems,and study the properties of the additive functional of the two-typesuperprocesses.
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  Convergence and Cauchy Structures on Locales

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0043

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  In this paper,we have introduced covergence and Cauchy structures on focales,andgiven a characterization of compact locale using the convergence structure. Also,to ensure theuniqueness of limit,a satisfied Hausdorff property in locale is presented.Moreover,we have alsoconsiderded completeness of uniformity locale and proved that compat property is equivalent tocomplete and total bounded properties for general local.
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  Stability for Nonlinear Differential Systems with Infinite Delay

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0045

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  The main purpose of this paper is as follows:(1)to establish some nonlinear integro-differential inequalities with infinite delay and theinverse inequalities under the local conditions;(2)to study the stability of the nonlinear differen-tial systems with infinite delay by using the method of variation of constants, Liapunov function(need not find P-function)and the inequalities established;(3)to give some examples to showthe application and advantage of the theorems in the paper.
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  Harmonic Analysis on Compact Homogeneous Spaces (Ⅳ)──The Riesz and Bessel Transformations

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0046

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  The Riesz and Bessel potential operators and Riesz and Bessel transformations oncompact homogeneous spaces are discussed in this paper. Furthermore,we construct concretekernel functions for these operators and we prove the H￣p(M)boundedness for these operatorsfor p>0. Especially, we proved that the Riesz and Bessel transformations, as singular integrals,are H￣p bounded for p>0.
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  Oscillation Criteria for Difference Eqtiations with Continuous Arguments

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0044

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  In this paper, we establish oscillation criteria for difference equations with continuousarguments by teachnique of dispersing arguments.Some examples are given to illustrate thetheory.
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  On Whitney’s and Tutte’s Conjecture

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0048

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  To look into the method of theoretial proof of the four colour problem Whitney andTutte studied the four colour problem by transforming the four colour problem into a problem on4-colourings of circuits.Furthermore,they proposed a conjecture which implies the four colourconjecture. In this paper the combinatorial invariance of Kempe sets is studied and it is provedthat Whitney’s and Tutte’s conjecture is not true.
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  Comment of the Paper“Structure of an Idempotent Element in of Zhao Junxi

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0047

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  In this note we prove that the idenipotent element Q in the paper“Structnre of anidempotent element in ”is not an operator in the nest algebra algN,and hence is not anelement of as claimed by the author of that paper.
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  Some Norm Closed Ideals in Nest Algebras

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0041

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  Let R_N be the Jacobson radical of the nest algebra algN, we write for the normclosed two- sided ideal generated by the set R￣n ={T_1T_2…T_n.J . R. Ringrose[1, Theorem 5. 4 ] obtained the character of the Jacobson radical R_N . In this paper,we give an “if and only if ”that has the generalized Ringrose character.
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  A Theorem on the Dimensions of Self-Similar Sets

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0038

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  In this paper , we propose a“resoluable condition”that is weaker than“open setcondition”for (strict)self-similar set, and prove that under“resoluable condition”,the Hausdorffand Bonligand dimensionof a self-similar set is identical with its similar dimension,
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  Univalence Criteria of Holomorphic Mappings of Several Complex Variables

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0039

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  In the article we use subordination Chain's methods to obtain several univalence criteria for holomorphic mappings of several complex variables.
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  Perfect Splines Determined by Cyclic variation Diminishing Kernel and Uniquenessof Optimal Sampling Points

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0040

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  The uniqueness of perfect splines, determined by cyclic variation diminishing kernel(CVD kernel),with prescribed zeros is proved. The uniqueness of optimal sampling points for aconvOlution class with CVD kernel is also proved.
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  Hilbert Modular Forms and Special Values of Some Dirichlet Series

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0042

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  For any two cusp Hilbert modular forms f(z) and g(z) with weightsl and k respec-tively(k>l+4),a kind of Dirichlet series is defined.And we also investigate the special valuesof the Dirichlet series. Our results generalize the conclusions in [2].
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  A Combinatorial Problem on Finite Groups

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0057

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  et G be a finite group of order n(Written additively),p the least prime divisor ofn,and In this paper,we prove that if G is nilpotent or G is in another certainclass ofgroups,then is the least integer t with the property that every subset a_1,…,a_t oft nonzero elements in G so that every element g∈G can be written in the form g=a_(i1)+…+a_(il),with all i_j distincted
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  Some Problems On a Class of Nonlinear Eqliations in Banach Space

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0056

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  In the paper,the boundary conditions(Sω,A,a)and(LM,ω)are introduced,the resultson the extension and the computation of fixed point index for k-set-contraction locally properfield are established.Use them with the weak semidifferentiability, the problems concerningthe positive solution,the multiple positive solutions and the set of eigenvectors for a class ofnonlinear equations are studied.And as an application, a two point boundary value problem isstudied in this paper.
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  Exceptional Sets for Differential Polynomials

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0055

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  In this paper,we prove the following theorem,Let f be a transcendental entirefunction and be a differential polynomial in f such that.Givenε>0, there exists K=K(ε,γQ,q)>0 such that if(a_n)converges to infinity withfor all n≠n, while(ρ_n)satisfiesthen F-b must have infinitely many zeros outside the union of the discs B(a_n,ρ_n)={z:|z-a_n|<ρ_n)for any b∈C, b≠0.Where γQ is the degree of Q(f).
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  Finite Groups with Only Quasinormal and Selfnormal Subgroups

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0054

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  In this paper authors study such a finite group in which each subgroup is eitherquasinormal or selfuormal and characterize this kind of finite groups. The main result is Theorem Every subgroup of group G is either quasinormal or selfuormal if and only ifG is precisely one of the followingⅠ)G is a quasi-Hamilton group.Ⅱ)G=HP, where H is a normal abelian p'-Hall subgrou.P=〈x〉∈Syl_p(G),〈x￣p〉=O_p(G)=Z(G)and x induces a fixed-point-free power automorphisim of order p on H. p is thesmallest prime factor of |G|.The theorem in paper[1]can be obtained by the above theorem.
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  On Positively Curved Totally Complex Submanifolds in a Quaternion ProjectiveSpace

  Acta Mathematica Sinica, Chinese Series. 1995, 38(3): . https://doi.org/10.12386/A1995sxxb0053

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  This paper consider totally complex submanifolds of quaternionic projective space.We prove that a compact totally complex submanifold with positively sectional curvature inquaternion projective space is totally geodesic.