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Table of Content
30 September 1993, Volume 8 Issue 3
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The Generalized KKM Map and Its Applications to Variational Inequalities
Li Yaotang
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 ZF
n
in ZF
n+3
Li Xuhua
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
Liu Jian zhong, Li Yusheng, Cui Guozhong
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
Cheng Hailai
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
Xu Zhicai
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 CH
2
（-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 H
2
（-1）;（ii）A tube of radius r>0 around a totally geodesic complex hyperbolic space form CH
1
（-4）;（iii）A geodesic hypersphere of radius r>0,or（iv）A horosphere.
Generalization of Weighted Weak Type Hardy Inequalities
Li Li, Li Dengfeng
1993, 8(3): 35-38.
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A Class of the Quasilinear Hyperbolic Equations with the Inhomogenous Terms
Yang Qiao, Liu Fagui
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
Cao Shouming, Xiao Huimin
1993, 8(3): 45-49.
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In this paper,the distance-sability of nonlinear dscrete system is investigated by neans of the Gauss-Seidel iteraton method.Some algebric critera of the distance-stability are obtained.Construction of Lyapunov function is avoided.
A Equivalent Definition of Radical Property
Tian Zhen
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
Fan Jiakun
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
Li Xuemin
1993, 8(3): 57-62.
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On a Result of Pointed Representations of finite Dimensional Simple Lie Algebras
Xu Xiang
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
Liu Shuzhen, Chen Shuqin, Wang Huimin
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
Jiang Xun, Wang Ziyu
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
Zheng Zhujun
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
Li Yongming
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
Yang Dinggong
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 X
n
+Y
n
=Z
n
Hou Shaosheng
1993, 8(3): 94-94.
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Random Symmetrical Sampling
Li Xin, Yang Jinzhong
1993, 8(3): 95-96.
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On a Matrix Equation AX+XB=C over a Skew Field
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
Gesang Nima
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
Wang Zhen, Chen Ji
1993, 8(3): 108-110.
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Another generalization ofthe Mitrinovic-Djokovic inequality is proved by elenientary means.
