Chinese Quarterly Journal of Mathematics

Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences

Xue Liugen, Li Xuechen, Ma Quanfu

1999, 14(2): 1-10.

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In the paper,we study the strong convergence rates of double kernel estimates of conditional density under stationary sequences.

The Qualitative Analysis of a Class Autocatalytic Reactions Model

Shen Boqian, Zhang Cheng

1999, 14(2): 11-20.

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The Formula of General Term of the Sum of Equal Powers of Natural Numbers

Gao Yingmin, Yang Zhizhong

1999, 14(2): 21-27.

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The formula of general term of the sum of equal powers of natural numbers.

A Note on the First Eigenvalue of Hypersurfaces

Zhou Zhenrong

1999, 14(2): 28-32.

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In this paper,we discuss the lower bound of the first eigenvalue of a closed convex or a minimal hypersurface in a closed Riemann manifold with Ricci curvature bounded below by a positive number.

Bordism Classes of Involutions on RP(2n)、CP(2n) and HP(2n)

Meng Zhaojing, Wang Yanying

1999, 14(2): 33-37.

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In this paper we discuss all possible bordism classes of involutions on RP（2n），CP（2n） and H P（2n）．

On the Inequalities for Traces and Singular Values of the Quaternion Matrices

Lu Yunxia, Zhang Shuqing, Wang Qingwen

1999, 14(2): 38-41.

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In this paper we derive some inequalities for traces and singular values of the quaternion matrices，extend and improve some of the corresponding results appeared in other papers we know ．

Iterative Approximation of Fixed Points for Uniformly Continuous and Strongly Pseudocontractive Mappings in Smooth Banach Spaces

Zhou Haiyun

1999, 14(2): 42-46.

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With an inequality and some analysis techniques，iterative approximation of fixed points for uniformly continuous and strongly pseudocontractive mappings in smooth Banach spaces is studied，and the recent corresponding results of Chidume are improved．

A Note on the Difference of Gaussian Measure of Two Balls in Hilbert Spaces

Guo Xinwei

1999, 14(2): 47-51.

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Let H be a separable Hilbert space, μ be a symmetric Gaussian measure on H. Applying the meathod of sum of independent random variables. A finer estimate of the difference of Gaussian measure of two balls is obtained.

On the Ascending Subgraph Decomposition Problem

Zhao Guangfeng, Dong Huiying, Wang Zhaoxia, Xu Fuxia

1999, 14(2): 52-58.

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Alavi and his fellows defined the concept of ascending subgraph decomposition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition in paper [1]. Paper [2] proved that K_n-R_n-1 has a star ascending subgraph decomposition,here K_n is the complete graph with order n and R_n-1 is a subgraph of K n with size at most n-1. In paper [3],Ma Kejie and Chen Huaitang proved that K_n-R_n has an ascending subgraph decomposition when the size of R n is not greater than n. In this paper we will prove K_n-R has an ascending subgraph decomposition when the size of R is less than 3n/2. This paper will also give the concept of comet and prove that K_n-R_n-1 has a comet ascending subgraph decomposition.

A Restriction Theorem on the Reduced Product Heisenberg Group

He Jianxun

1999, 14(2): 59-62.

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In this paper，we give the Plancherel formula on the reduced product Heisenberg group，
and obtain a restriction theorem on this group．

Interval Algorithm for a Kind of Nonsmooth Global Optimization

Shen Peiping

1999, 14(2): 63-68.

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Based on the interval analysis，a practical interval algorithm is developed for finding all global minimizers of a nonsmooth function on a closed domain X ⊂Rⁿ，which is given by defining a special derivative to the function and using the interval inclusion of derivative．Both theoretical analysis and numerical results show that this method is practical and effective．

The Properties of Finitely Generated Shift-invariant Subspace in L_2π²

Xue Mingzhi, Zhu Xiuge, Tian Jishan

1999, 14(2): 69-75.

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In this paper，some properties of shift-invariant subspace in Periodic wavelets theory are discussed．

On the Minimum Spanning Tree Determined by n Points in the Unit Square

Ye Jichang, Xu Yinfeng, Xu Chengxian

1999, 14(2): 76-82.

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Abstrac Let P_n be a set of n points in the unit square S，l（ P_n） denoe the length of the minimum spanning tree of P_n，and ... In this paper，the exact value of C_nfor n＝2，3，4 and the corresponding configurations are given．Additionally，thecoonjectures of the configuration for n＝5，6，7，8，9are proposed．

Stability Analysis of Optimal Control Systems via Liapunov Method

Liu Xianxing, Wen Chenglin

1999, 14(2): 83-87.

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The controlled objects are uncertain stable，but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable．T his paper analyses stability of optimal control systems which have quadric performance index via Liapunov method．

On the Cluster Set C [S_n/(2nφ（n）)^1/2] in 2-type Banach Space

Wang Xinquan, Tian Chang’an, Yang Changsen

1999, 14(2): 88-93.

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Suppose ｛X ，X n，n≥1｝are the i．i．d．random variables with values in 2-type Banach space B，... is a increasing function on ［0，＋∞），φ（ x ） →＋∞，and φ（ x ）/x is noincreasing； then we point out that the cluster set ... is ρK ，where ... and ...＜＋∞．

Boundary Extension of μ(z)-homeomorphism

Zheng Xueliang

1999, 14(2): 94-96.

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In this paper，we give a sufficient condition such that a μ（ z）-homeomorphism in Jordan
domain can topologically extend to the bound．

On the Decay of Solution of Some Nonlinear Hyperbolic Equation

Liang Baosong, Ye Yaojun

1999, 14(2): 97-101.

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In this paper we shall show the decay of solution to some nonlinear hyperbolic equation using a difference inequality．

Critical Fujita Exponents for Localized Reaction Diffusion Systems

Zhao Yun, Wang Shu, Zhang Jianping

1999, 14(2): 102-107.

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In this paper，we prove the existence of cirtical Fujita exponents for a class of localized reaction diffusion systems．

Boundedness of the Maximal Operator on Lip_α（Rⁿ）（0<α<1）

Yue Youlan, Wang Yueshan

1999, 14(2): 108-110.

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It provides the boundary proof of the maximal operator on Lipschitz space．i．e．，if f ∈Lip_α（Rⁿ）（0<α<1） and

inf_x∈RnM （ f ）（ x ）＜∞，then almost every x ∈Rⁿhas M （ f ）（ x ）＜∞ and exists a constant C independent of f and x ，such that M （ f ）α≤C＜α．

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