15 November 1996, Volume 39 Issue 6

    

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  On the Number of Solutions of Thue's Equation

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0097

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  Let m be a positive integer, and let f(X, Y) = aoXn + a1Xn(-1)Y + ... + anYn ∈z[X,Y] be an irreducible binary form of degree n witn n≥3.In this paper we prove that if gcd(m, a0)=1,n≥400 and m≥10(35),then the equation |f(x,y)|= m has at most 6nv(m)integer solutions(x, y) with gcd (x, y) =1,where v(m)is the number of solutions of the congruence F(z) = f(z, 1) ≡ 0(modm). Moreover, if gcd(m,DF) = 1, Where DF is the discriminant of F, then the equation has at most 6n(ω(m)+1) solutions(x,y), where ω(m)is the number of distinct prime factors of m.
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  The Drazin Inverses of Morphisms

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0098

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  In this paper we establish the concepts of index and Drazin inverse for morphisms in an abelian category, prove that the morphisms for which the Drazin inverse edests must have core-nilpotent decomposition and give an equivalence characterization of the Drazin inverse.
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  A Criterion for Primitive Polynomials over Galois Rings

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0099

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  In this paper,we present a link between the representation of a root of a basic irreducible polynomial f(x)over Galois ring and its order,and derive two algebraic discriminants respectively for primitive polynomials and subprimitive polynomials.The main parts in the discriminants are determined respectively by the coefficients of f(x) mod p and f(x) mod p2.
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  On the Semisimple Structure of l-groups

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0100

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  Let Gbe an l-group,one convex l-subgroup A of G is said to be superfluous, if A∨V W = G for an arbitary convex l-subgroup W of G, then W = G. Again let R(G) be the convex l-subgroup which is generated by the union of all superfluous convex subgroups of G. We prove that R(G) is one kind of radical of l-group G in Amitsur-Kurosh sence. Furthermore, we obtain the semisimple structure theorem for finite-valued l-groups,i.e. R(G) = 0 iff G is l-isomorphic to a subdirect product of simple l-groups with semisimplicity. Moreover, we also obtain some important corollaries.
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  Invariance Flow of Nonlinear Semigroups of Contraction

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0104

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  In this paper, we give the necessary and sufficient condition that the nonlinear sendgroup of contraction has invariant now in a Banach space.We also characterize the positive nonlinear of contraction in a C*-algebra and a Hilbert space.
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  On a Diophantine Inequality Involving Prime Numbers

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0101

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  Let 1
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  On the Asymptotic Behavior of Almost-orbits of Asymptotically Nonexpansive Semigroups in Uniformly Convex Banach Spaces

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0102

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  Let X be a uniformly convex Banach space with a Fr chet differentiable norm, C be a bounded closed convex subset of X, and S = {T(t): t≥0} be an aspoptoticajly nonexpansive semigroup on C. If u(·): [0, ∞) → C is an almost-orbit of S which is uniformly continuous in t ∈[0, ∞) then {u(t): t≥0} almost converges weakly to the unique point of the set,.
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  On Hyperreflexivity of Non-CSL Algebras

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0103

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  In this papert the hyperreflealvity of some non-CSL algebras on a Hilbert space is discussed.Using Arveson's characterization of hyperreflekivity,we give an exact estimation of hyperreflexive constant for a certain non-CSL algebras,and by which, we prove that the algebra determined by any realization of the pentagon is not hroerreflekive. As a corollary,we obtain the main result in[11].In addition, we also give a result concerned with the relation between hyperreflexivity and 2-decomposability for operator algebras.
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  Small Sample Comparison of Two Usual Variance Estimators of the Ratio Estimator

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0111

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  This paper gives small sample comparison of two usual variance estimators of the ratio estimator by using the criterion of Feng and Zou(1994)or Sundberg(1994),which is the open problem put by Cochran(1977).We solve this problem in a sense.
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  Solutions of Superlinear Hammerstein Integral Equations in Banach Spaces and Applications

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0114

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  In this paper we study the existence of positive and nontrivial solutions for superlinear Hammerstein integral equations in Banach spaces by means of the fixed point index theory.The results are applied to Sturm-Liouville problems of superlinear ODEs in Banach spaces.Finally,an example for infinite system of nonlinear ODE is given.
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  Some Sufficient Conditions for a Finite Group to be Soluble

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0112

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  In this paper,we investigate, using the concept of semi-normal subgroup,the solvability of finite groups on the basis of [1].We obtain a series of sufficient conditions for a finite group to be solvable.
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  Local Index Theorem for de RHam-Hodge-Signature Operator

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0113

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  There holds the global Atiyah-Singer Index Theorem for general elliptical differential operators. But for local index theorem,people can only give a proof for concrete operator and the teclnique used in the proof varies from one to another.We present here the suitable definition of de Rham-Hodge-Signature operator D and the proof of its locaf index theorem.From[6],we conclude that the local index for D is neither of type α nor type β. This is dtherent from the case of classical elliptic differential operators.
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  Reflection of Singularities for Boundary Value Problem of Operators with Involutive Characteristics of Variable Multiplicity

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0115

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  Let Ω, the boundary on be locally {t = o} near x0∈ Ω,andΩ is non characteristics for m-order partial differential operator P(x, t, Dx, Dt).Suppose that there are m real roots (containing multiple roots)λj(x, t,ξ), (j =1,..., m) of the equation σ(P)(x, t, ξ,) = 0in and the involutive condition is satisfied. Then under the Levi condition we get that the C∞ singularity of solutions u of the Dirichlet boundary value problem for P is invaxiable in reflection conic class of the boundary.
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  Quasitriangular Hopf Algebras and Biproducts

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0116

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  In this paper we showed first that(H,R)is a quasitriangular Hopf algebra if and only if H is a coalgebra in HM and H is left Yetter-Drinfeld module by considering H as a left H-module via multiplication of H and as a left H-comodule via(TR)(1 h), where is twist map. We generalized then a result of Hopf algebra with a projection. Final,we study the relationship between Double Smash product,quasitriangular Hopf algebra,and biproduct.
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  Limit Behaviors of Convolution Sequences of Probability Measures on Compact Topological Semigroups

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0108

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  In this paper we discuss some important limit behaviors of convolution sequences of probability measures on compact semigroups.In Theorem 1,we use the algebra structure of the support of probability measures to give a limit theorem for composition convergent sequence.In Theorem 2, we discuss the i.i.d random variable convolution power sequences and a result of Kawada-It type is set up on some compact semigroups.Some results on compact groups,compact commutative semigroups,compact L-X semigroups are extended.
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  Biordered Sets of P-regular Semigroups

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0109

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  The necessary and sufficient condition for a biordered set to be that of the idempotents of a P-regular semigroup is characterized in this paper.The theorem obtained here not only is a generalization of the theorem, given by D.Easdown,for biordered sets of bands,but also gives a characterization of biordered sets of idempotents of regular *-semigroups.Further,some special cases and a generalization to non-regular ones of P-regular semigroups are discussed.
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  The Finite Groups Which Are Rarely Automorphism Groups

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0110

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  In this paper,we will show that the Abelian p-groups of order less than p9 cannot occurs as the full automorphisms groups of a finite group. This result also extends MacHale's result in 1983.
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  Characterize rings with character modules

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0106

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  Let R be a ring,M a left R-module,M* = Homz(M, Q/Z), the character module of M.Colby,R.R.and Chetham,T.J.obtained some characterizations of iF rings,coherent rings, Noetherian rings, Artinian rings with "character modules", respectively.In this paper, using the notion of"character"modules,we obtain a number of more significant characterizations of some rings.
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  The Dynamical System of Polynomials when Orbits of Some Finite Critical Points Converge to Infinity

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0107

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  In this paper, the following results are proved.Let p(z)be a polynomial of degree d and J be the Julia set.Suppose the orbits of m (1≤m≤d-1)finite critical points of p(z)coverge to infinity.Then p|J is topologically semiconjugate to the one-sided shift on m + 1 symbols. In particular, when m = d-1, p|J is topologically conjugate to one-sided shift on d symbols.
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  Positive Periodic Solution for Neutral Delay Model

  Acta Mathematica Sinica, Chinese Series. 1996, 39(6): . https://doi.org/10.12386/A1996sxxb0105

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  In this paper,we employ some new technics to study the existence of a positive periodic solution of the neutral delay modelN'(t)=N(t)[a(t)-β(t)N(t)-b(t)N(t-T(t))-c(t)N'(t-T(t))].Our results in this paper answer an open question in [1] and correct the mistakes in [2].