数学季刊

The Problem on Class Numbers of Quadratic Number Fields

陆洪文

1996, 11(3): 1-7.

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It is a survey of the problem on class numbers of quadratic number fields.

Higher Singular Integral and Its Application

殷承元

1996, 11(3): 8-12.

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In this paper,the definition of higher Hadamard integral on complex ball is given,and some results are obtained.

Solvability of Boundary Value Problems for Some Functional Differential Equations

胡适耕, 洪世煌

1996, 11(3): 13-18.

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This paper considers the following boundary value problems for functional differential equations: x' (t) = f(t, x_t) (0<t<b) ,x₀ = x_1, and x"(t) = f(t,x_t, x' (t)) (0<t<b) , x(b) = B. By using certain fixed point theorem based on degree theory,some sufficient conditions for solvability of the above problems are given.

The Complete Chromatic Number of Maximal Outerplane Graphs

王维凡

1996, 11(3): 19-23.

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Let G be a maximal outerplane graph and X0(G) the complete chromatic number of G. This paper determines exactly X₀(G) for △(G)≠5 and proves 6≤X₀.(G)≤7 for △(G) = 5, where △(G) is the maximum degree of vertices of G.

Some Properties of Two Subclasses of Analytic Functions

刘金林

1996, 11(3): 24-28.

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This paper discusses some properties of two classes V_k[α,β] and R_k[α,β ]. Sharp distortion theorem and radius of convexity and starlikeness are obtained. Hadamard product of functions in the classes are also studied.

A Characterization of Quasitriangular Hopf Algebras

郝志峰

1996, 11(3): 29-32.

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In this paper,we show that if H is a finite dimensional Hopf algebra then H is quasitri-angular if and only if H is coquasi-triangular. As a consequentility ,we obtain a generalized result of Sauchenburg.

An Exact Solltary Wave Solutions for a New Derivative Nonlinear Schrodinger Equation

陈守信, 吴瑞杰

1996, 11(3): 33-35.

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In this letter, an exact one-soliton solution for a new derivative nonlinear Schrodinger equation is obtained.

On Infinite Disjoint Congruence Covering Systems

陈永高

1996, 11(3): 36-39.

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In this paper we show that for any α∈(0,l] there exists an infinite disjoint covering system ... .

Explicit Expression of Hermite Interpolation Basis Functions under the Ball Basis

王建根, 尚有林, 丁建立

1996, 11(3): 40-43.

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In paper [1],it was shown that an explicit expression of the cardinal basis functions for two-point Hermite interpolation. This paper will show the explicit expression of Hermite interpolation under the Ball basis.

C_p-Groups and Some Results on the p-nilpotency

赵耀庆, 韦革, 李世余

1996, 11(3): 44-49.

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Let P∈SylpG,ch(P) be any characteristic subgroup of P. A group C is called a C_p-group if G satisfies the condition "NG(ch(P)) is p-nilpotent implies that G is p-nilpotent". In this paper some properties on G_p-groups and some suffcient conditions for a group to be p-nilpotent are obtained.

Fractal Dimension of Graph of Weierstrass Function and Its Derivative of the Fractional Order

邓冠铁

1996, 11(3): 50-54.

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In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative.

Some Results on B_r-Spaces

朱同林, 王戍堂

1996, 11(3): 55-58.

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In this paper,the following results are obtained: (1) The Sorgenfrey Line is a non-B_r- space; (2) We introduce Well-distributed complete spaces and locally Cech complete spaces and prove both the two classes of spacs are Br-spaces. The first result shows that there is the non-B_r- space which is paracompact, Lindelof and complete quasi-metric. The second result generalizes the Byczowski &. Pol theorem(i. e. Cech-complete spaces are Br-spaces) in two aspect...

Two Kinds of Solvable Complete Lie Algebras

朱林生

1996, 11(3): 59-66.

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In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nilpotent Lie algebras.

The Stable Limit Cycles of a Generalized Lienard Equation

刘舒强

1996, 11(3): 67-71.

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In this paper we give a series of sufficient conditions for the existence of autonomous systems with three singular points.

LF λ-subgroup Generated by LF Subset

姜保庆, 程庆, 任学军

1996, 11(3): 72-73.

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On Projective Modules with Constant Ranks

陈焕艮

1996, 11(3): 74-78.

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On Projective Modules with Constant RanksIn this paper,we investigate module structures of rings over which every finitely generated projective module with constant rank is stably free. As applications,we give characterizations of some related rings.

K-very Smooth Banach Spaces

刘证

1996, 11(3): 79-86.

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We introduce the notion of K-very smoothness which is a generalization of very smoothness in Banach spaces. A necessary and sufficient condition for a Banach space to be K-very smooth is obtained. We also consider some relations between K-very smoothness and other geometrical notions.

On Dual Cosine Operator Function

丁天彪, 田利钦

1996, 11(3): 87-90.

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Some basic properties of daul cosine operator function are given. The concept and characterization of θ-reflexivity with respect to cosine operator function are first studied.

A Note on Orthogonal Multiplication

田立根

1996, 11(3): 91-93.

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Hurewicz-Radon theorem [1] gives a sufficient and necessary condition about the existence of an orthogonal multiplication f:R^k×Rⁿ→Rⁿ. In this paper,we shall discuss two extensions of the theorem.that is,the sufficient and necessary conditions about the existence of an orthogonal multiplication f:R^k×Rⁿ→Rⁿ⁺¹or f:R^k×Rⁿ→Rⁿ⁺²

Continuous Order Homomorphism and bi-continuous Mapping

刘忠志, 王建平, 刘文钦

1996, 11(3): 94-96.

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The relation of LF topology on set X to the classical topology is always important for us to understand LF topology. In this paper, we construct a bitopological space from a LF topologial space,and we show that for a continuous order homomorphism between two LF topological spaces there is a correspondent bicontinuous mapping between the constructed bitopological spaces.Let X be a set,L be a fuzzy lattice,use Lx denote all the fuzzy subsets of X use πx denote set X×{L\{ O, 1} }, P（πx） is power set of πx. Now we first define mapping, a of πx into itself as following.

Suboptimal Control of Time-Varying Neutral Control Systems

肖会敏

1996, 11(3): 97-102.

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In this paper,the optimal control of time-varying neutral control systems is investigated by means of the Maxmium Principle of time-delay systems.optimal control law is given. Then sub-optimal control of time-varying neutral control systems is studied by using sensitivity approach. Algorithm for suboptimal control is given.

The Explicit Expressions of Level-k Circulant Matrices of Type（n₁,n₂.…,n_k） and Their Some Properties

江兆林, 郭运瑞

1996, 11(3): 103-110.

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In this paper, we give the explicit expressions of level-k circulant matrices of type (n₁,n₂,…n_k) and of order n₁n₂…n_k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.

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