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K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2.1. department of mathematics,Inner Mongolia Normal {2., Huhhot 01002., china 2. department of mathematics, Harbin Institute of Technology, Harbin 150006, china department of mathematics Inner Mongolia Normal University Huhhot China department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

BAHADUR'S REPRESENTATION FOR NEAREST NEIGHBOR MEDIAN ESTIMATES: THE FIXED DESIGN CASE

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Systems Science and Mathematical Sciences 1999年第2期12卷 133-144页

作者： YANG Ying(department of Probability and Statistics, Peking university, Beijing 100871, {2.)WANG Bingzhang(department of mathematics and Information Science, yantai university, yantai 2.4005, {2.) 北京大学概率统计系北京烟台大学数学系山东烟台

Consider the nonparametric regression model Yi=g(xi) +ei, i=1, 2....,where g is an unknown function defined on the interval [0, 1], the fixed design points xi(i≥1) are known and ei’s are i.i.d. random variables with median zero. The regressor is assumed to take values in [0, 1]∈ R and the regressand to be real valued. This paper stu-dies the behavior of the nearest neighbor median estimate gnh(x)=m(Yn1(x), Yn2.x),...,Ynh(x)), where h is the number of the nearest neighbor. Under suitable conditions, Bahadur’s representation for the above-mentioned the nonparametric regression function g is obtained. Law of iterated logarithm and asymptotic normality are also established.

关键词： Nearest neighbor median estimates Bahadur’s representation asymptotic normality law of iterated logarithm.

Hamiltonian type Lie bialgebras

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Science china mathematics 2007年第9期50卷 1267-1279页

作者： Bin XIN~(1+) Guang-ai SONG~2.Yu-cai SU~3 1 department of mathematics,Shanghai Jiao Tong {2.,Shanghai 2.02.0,china 2.College of mathematics and Information Science,Shandong Institute of Business and Technology,yantai 2.4005,china 3 department of mathematics,{2. of Science and Technology of china,Hefei 2.002.,china department of mathematics Shanghai Jiao Tong University Shanghai 200240 China College of mathematics Information Science Shandong Institute of Business Technology Yantai 264005 China department of mathematics University of Science Technology of china Hefei 230026 China

We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H^1(H,H(?)H) is *** then show that all Lie bialgebra structures on H are triangular.

关键词： Lie bialgebra Yang-Baxter equation Hamiltonian Lie algebra 17B62 17B05 17B37 17B66

CMC surfaces in the hyperbolic 3-space

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Chinese Science Bulletin 1998年第7期43卷 547-550页

作者： YU Zuhuan 1, 2.and LI Zhenqi 1, 3 1. Institute of mathematics, Fudan university, Shanghai 2.0433, {2. 2. department of mathematics,Sichuan Union university, Chengdu 610064, {2. 3. department of mathematics, Nanchang university, Nanchang 33 nstitute of Mathemalics Fudan University Shanghai China department of mathematics Sichuan Union University Chengdu China department of mathematics Nanchang University Nanchang China

CMC-H surfaces satisfying H≥1 are studied. It is proved that these surfaces possess a natural representation which is a generalization of the Bryant’s result.

关键词： hyperbolic space CMC surface Weierstrass representation.

PACKING A TREE OF ORDER p WITH A (p,p+1)-GRAPH

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Journal of Systems Science & Complexity 2003年第1期16卷 122-132页

作者： WANGMin LIGuojun departmentofmathematics YantaiUniversityYantai264005China departmentofmathematics ShandongUniversityJinan250100China

Let G1 and G2.be two graphs of the same order,If G1 is isomorphic to a spanning subgraph of the complement of G2.then we say that G1 and G2.are packable.A graph G is called a (p,m)-graph if G has p vertices and m *** main purpose of this paper is to present a necessary and sufficient condition for a tree of order p and a (p,p+1)-graph to be packable.

关键词： Packing tree (p p+ 1)-graph.

Minimal symmetric submanifolds in compact Riemannian symmetric spaces

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Chinese Science Bulletin 1998年第21期43卷 1786-1789页

作者： LIANG Ke 1 and JIN Quanqin 1,2.1. department of mathematics, Nankai {2., Tianjin 300071, china 2. department of mathematics, Hebei {2., Baoding 071002. china department of mathematics Nankai University Tianjin China department of mathematics Hebei University Baoding China

A necessary and sufficient condition for a symmetric submanifold to be minimal in its ambient compact Riemannian symmetric space is given. By this condition a complete classification of non- minimal symmetric submanif... 详细信息

关键词： symmetric space symmetric submanifold mean curvature vector.

Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1 and YANG Zhongqiang 2.1. department of mathematics, Sichuan {2., Chengdu 610064, china 2. department of mathematics, Shaanxi Normal {2., Xi’an 710062. china department of mathematics Sichuan University Chengdu China department of mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.

The Initial Boundary Value Problem for a Class ofGeneralized Nonlinear Schrodinger Equations

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Systems Science and Systems Engineering 1998年第4期8卷 488-491页

作者： YAN Guiqing(department of mathematics and Information Science, {2., yantai 2.4005)

We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the g... 详细信息

关键词： Nonlinear Schrodinger equation group of unitary operators prior estimate

Characteristic modules of quasi-hereditary algebras with three samples

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Chinese Science Bulletin 1997年第6期42卷 450-454页

作者： ZHANG Pu and LIN Yanan1. department of mathematics, {2. of Science and Technology of china, Hefei 2.002., china 2. department of mathematics, Xiamen {2., Xiamen 361005, china department of mathematics University of Science and Technology of China Hefei China department of mathematics Xiamen University Xiamen China

CLINE et al. have introduced the concept of quasi-hereditary algebra, which provided a

关键词： tilting module characteristic module quasi-hereditary algebra.