数学季刊

The Generalized KKM Map and Its Applications to Variational Inequalities

李耀堂

1993, 8(3): 1-6.

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In this paper,applying the concept of generalized KKM map,we study problems ofvariational inequalities.We weaken convexity(concavity)conditions for a functional of two variables■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree method of acute angle principle about monotone operator as an application of these results.

On the Consistency of ZFⁿ in ZFⁿ⁺³

李旭华

1993, 8(3): 7-12.

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By restricting the common replacement axiom schema of ZF to ∑M-formulae,Professor Zhang Jinwen constructed a series of subsystems of Zennelo-Frankel set theory ZF and he called themZFM. Zhao Xi shun show that the consistency of ZFM can be deducted from ZF. Professor ZhangJinwen raised the question whether the consistency of ZFM can be deducted from ZF^M+m（M） for somem（n）≥1. In this paper,we get a positive solution to Professor Zhang's problem.Moreover,weshow that the consistency of ZFM can be deducted from ZF^M+3.

Holder Continuity for Solutions of Degenerate Parabolic Equation with Two Degenerate Points

刘建中, 李育生, 崔国忠

1993, 8(3): 13-23.

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In this paper we discuss the quasilinear parabolic equationU■=▽(uu（1-u）β.Vu)+■（x,t.u）▽u+C（x,t,u）which is degenerate at u =0 and u=1.Let u（x,t）be a weak solution of the equation satisfying0<u（x,t）<1.Under some assumptions we establish H■lder continuity of u（x,t）.

Generalized Szász-Mirakjan Operator Approximation

程海来

1993, 8(3): 24-29.

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In this paper we shall defin a kind of generahzed Szász-Mirakjan operator and discussits convergence and degree of approximation,extend some results got by J.Grof and Z.Ditzian.

A Remark on Contact Hypersurfaces of a Complex Hyperbolic Space

许志才

1993, 8(3): 30-34.

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A differentiable manifold is said to be contact if it admits a linear functional f on the tangent bundle satisfying f ∧（df）M-1≠0.This remark obtain the following the classification: LetM be a complete connected contact hyper-surface of CH²（-4）,then M is congruent to one of the following:（i）A tube of radius r>0 around a totally geodesic,totally real hyperbolic space form H²（-1）;（ii）A tube of radius r>0 around a totally geodesic complex hyperbolic space form CH¹（-4）;（iii）A geodesic hypersphere of radius r>0,or（iv）A horosphere.

Generalization of Weighted Weak Type Hardy Inequalities

李黎, 李登峰

1993, 8(3): 35-38.

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A Class of the Quasilinear Hyperbolic Equations with the Inhomogenous Terms

杨乔, 刘法贵

1993, 8(3): 39-44.

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In this paper,we discuss a class of the quasillinear hyperbolic equations with theinhomogeneous terms:u■+σ（v）+2α（t）u=0.v■-u-0Under the certain of hypothesis.we prove the globally existence theorems of the smooth solutionsfor its Cauchy problem.

Distance-Stability of Nonlinear Discrete Systems

曹守明, 肖会敏

1993, 8(3): 45-49.

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In this paper,the distance-sability of nonlinear discrete system is investigated by meansof the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.

A Equivalent Definition of Radical Property

田震

1993, 8(3): 50-51.

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This paper study the radical propertys in the sence of Amitsut and Kurosh from reference [1].

Strong Consistency for the Kernal Estimates of the Random Window Width of the Density Function and its Derivatives Under Φ-Mixing Samples

樊家琨

1993, 8(3): 52-56.

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In the paper,we study the strong uniform consistency for the kernal estimates of randomwindow wIth of density function and its derivatives under the condition that the sequence {X_n}of the are the identically Φ-mixing random variabks.

Coefficient Conditions of Locally Topological Structure for Nonlinear Homogeneous System in Third Critical Case

李学敏

1993, 8(3): 57-62.

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On a Result of Pointed Representations of finite Dimensional Simple Lie Algebras

徐祥

1993, 8(3): 63-65.

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There have been a great many of studies on the pointed representations of finite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of animpottant Lemma,and from this we derive our main result:Irreducible pointed modules of finite-dimesional simple Lie algebras are all Harish-Chandra modules.

On the Geometrical Meaning of the Dynamic Equations in Analytical Mechanics

刘书振, 陈书勤, 王惠民

1993, 8(3): 66-70.

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In this paper,the modern geometrical structure of analytical mechanics,the exterior differential forms and the geometrical meaning of dynamic equations are briefly discussed.

On The Order of Weyl-Heisenburg Wavelet Approximation

蒋迅, 王子玉

1993, 8(3): 71-75.

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The order of a concrete Weyl-Heisenburing wavelet approximation is given.This order isshown to be optimal.

The Hypoellipticity for a Class of Nonhomogeneous Convolution Operator on the Nilpotent Lie Group H_n×R^k

郑驻军

1993, 8(3): 76-81.

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In this paper,we use the method of representation of Lie group to study a class of nonhomoge-neous convolution operator on the nilpotent Lie group HM×Rk,and give a criteerion of their hypoellipticity.

The Level Structures of the Kernel and Hull on Lattice—Valued Funcetions and Induced Spaces

李永明

1993, 8(3): 82-87.

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It is studied systematically for the level strcture of the kernel and hull on continuous-lattice-calued function.In terms of these results,the level characterixations of induced space are obtained.

On Meromorphic Starlike Multivalent Functions

杨定恭

1993, 8(3): 88-93.

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In this paper we introduce and study some new subclasses of meromorphic starlike multivalentfunctions.Inclusion relations are established,Integral transforms of functions in these classes are alsoconsidered.In particular,our results include or improve several results due to Mogra et al.[2],Mogra [3],Goel and Sohe [4] and Bajpai [5].

A Note on Equation Xⁿ+Yⁿ=Zⁿ

候绍胜

1993, 8(3): 94-94.

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Random Symmetrical Sampling

李新, 杨金钟

1993, 8(3): 95-96.

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On a Matrix Equation AX+XB=C over a Skew Field

王卿文, 秦建国

1993, 8(3): 97-102.

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In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skewfield,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).Aconvenient,simple and practical method of solving(I)is also given.As a particular case,we alsogive a simple method of finding a system of fundamental solutions of a homogeneous system of rightlinear equations over a skew field.

2-Harmonic Curves Isometrially Immersed in a Surface

格桑尼玛

1993, 8(3): 103-107.

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In this paper,the author proves the necessary and sufficient condition for the existenceof 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface NIE3.

Another Extension of the Mitrinovic-Djokovic Inequality

王振, 陈计

1993, 8(3): 108-110.

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Another generalization ofthe Mitrinovic-Djokovic inequality is proved by elenientary means.

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