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Partitioning series-parallel multigraphs into υ*-excluding edge covers

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Science china mathematics 2006年第8期49卷 1082-1093页

作者： LIU Guizhen, DENG Xiaotie & XU Changqing School of mathematics and System Science, Shandong university, Jinan 250100, china department of Computer Science, City university of Hong Kong, Kowloon, Hong Kong, china department of applied mathematics, hebei university of technology, tianjin 300130, china School of mathematics and System Science Shandong University Jinan 250100 China department of Computer Science City University of Hong Kong Kowloon Hong Kong Hong Kong department of applied mathematics Hebei University of Technology Tianjin 300130 China

We prove that, for any given vertex υ* in a series-parallel graph G, its edge set can be partitioned into k = min{κ'(G) + 1,δ(G)} subsets such that each subset covers all the vertices of G possibly except for υ*, where δ(G) is the minimum degree of G and κ'(G) is the edge-connectivity of G. In addition, we show that the results in this paper are best possible and a polynomial time algorithm can be obtained for actually finding such a partition by our proof.

关键词： series-parallel graph, edge-connectivity, edge cover coloring, min-max theorem.

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连续型随机变量序列出现频率的强偏差定理

天津商学院学报 2001年第5期21卷 61-64页

作者：王玉津刘文天津商学院基础部天津300134 河北工业大学应用数理系天津300130

利用刘文教授提出的研究随机变量序列强极限定理的分析方法 ,引入似然比作为随机变量序列之间的偏差的一种度量 ,通过限制此偏差 ,确定了概率空间的某子集。

关键词：强偏差定理似然比上鞅连续型随机变量序列

ON THE CONDITIONAL VERSION OFKOLMOGOROV'S THREE-SERIES THEOREM

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Acta Mathematica Scientia 1999年第3期19卷 300-306页

作者：刘国欣 department of mathematics Hebei University of Technology Tianjin 300130 China

This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained.

关键词： Three-series theorem dependent r.v. ’s predictable local absolute continuity martingale

The genus of a type of graph

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Science china mathematics 2010年第9期53卷 457-464页

作者： SHAO ZeLing 1 & LIU YanPei 21 department of mathematics, hebei university of technology, tianjin 300401, china 2 department of mathematics, Beijing Jiaotong university, Beijing 100044, china department of mathematics Hebei University of Technology Tianjin China department of mathematics Beijing Jiaotong University Beijing China

Based on the joint tree model introduced by Liu, the genera of further types of graphs not necessary to have certain symmetry can be obtained. In this paper, we obtain the genus of a new type of graph with weak symmetry. As a corollary, the genus of complete tripartite graph K n,n,l (l≥n≥2) is also derived. The method used here is more direct than those methods, such as current graph, used to calculate the genus of a graph and can be realized in polynomial time.

关键词： surface joint tree embedding genus

A note on noncommutative moment problems

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Science china mathematics 2005年第8期48卷 1144-1151页

作者： MA Xiujuan School of Sciences, hebei university of technology, tianjin 300130, china mathematics Institute, Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, china School of Sciences Hebei University of Technology Tianjin China mathematics Institute Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Noncommutative moment problems for C*-algebras are studied. We generalize a result of Hadwin on tracial states to nontracial case. Our results are applied to obtain simple solutions to moment problems on the square and the circle as well as extend the positive unital functionals from a (discrete) complex group algebra to states on the group C*-algebra.

关键词： moment, free product, state, group C*-algebra.

On the composition operators on the Bloch space of several complex variables

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Science china mathematics 2005年第Z1期48卷 392-399页

作者： ZHOU Zehua & CHE Renyu department of mathematics, tianjin university, tianjin 300072, china LiuHui Center for applied mathematics, Nankai university & tianjin university,tianjin 300072, china department of mathematics Tianjin University Tianjin China LiuHui Center for applied mathematics Nankai University & Tianjin University Tianjin China

In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the compositio... 详细信息

关键词： Bloch space, bounded symmetric domains, composition operator, bergman metric.

Boundary Value Problems for Singular Second-Order Functional Differential Equations

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Acta Mathematicae Applicatae Sinica 2002年第2期18卷 249-254页

作者： Hui-zhao Liu, Da-qing Jiang, Yan Wangdepartment of applied mathematics, hebei university of technology, tianjin 300130, chinadepartment of mathematics, Northeast Normal university, Changchun 130024, china department of applied mathematics Hebei University of Technology Tianjin China department of mathematics Northeast Normal University Changchun China

Positive solutions to the boundary value problem,are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function denned on [0,1] and f(x,y) is a function defined on (0,1)×(0,∞), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong.

关键词： Singular boundary value problem existence Schauder fixed point theorem

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Science china mathematics 2004年第2期47卷 297-310页

作者： JIANG Chunlan & HE Huadepartment of mathematics, hebei university of technology, tianjin 300130, china department of mathematics, Universtiy of Pueto Rico, Rio Piedras San Juan, PR 00931, USA department of mathematics, hebei Normal university, Shijiazhuang 050016, china department of mathematics Hebei University of Technology Tianjin China department of mathematics Universtiy of Pueto Rico Rio Piedras San Juan USA department of mathematics Hebei Normal University Shijiazhuang China

This paper shows that every operator which is quasisimilar to strongly irreducible Cowen-Douglas operators is still strongly irreducible. This result answers a question posted by Davidson and Herrero (ref. [1]).

关键词： quasisimilar, strongly irreducible, Cowen-Douglas operators.

The closures of (U+K)-orbits of essentially normal triangular operator models

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Science china mathematics 2010年第11期53卷 1045-1066页

作者： ZHAI FaHui 1,& GUO XianZhou 2 1 department of mathematics,Qingdao university of Science and technology,Qingdao 266061,china 2 School of Sciences,hebei university of technology,tianjin 300401,china department of mathematics Qingdao University of Science and Technology Qingdao China School of Sciences Hebei University of Technology Tianjin China

The (U + K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as (U + K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the (U + K)-orbit of an essentially normal triangular operator T satisfying H={ker(T-λI):λ∈ρ F (T)} and σ p (T*)=ф.After that,we establish certain essentially normal triangular operator models with the form of the direct sums of triangular operators,adjoint of triangular operators and normal operators,show that such operator models generate the same closed (U + K)-orbit if they have the same spectral picture,and describe the closures of the (U + K)-orbits of these operator *** generalize some known results on the closures of (U + K)-orbits of essentially normal operators,and provide more positive cases to an open conjecture raised by Marcoux as Question 2 in his article "A survey of (U + K)-orbits".

关键词： (U+K)-orbit essentially normal operator triangular operator