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A Note on Abelian Extensions

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wuhan university Journal of Natural Sciences 2008年第1期13卷 6-8页

作者： YU Chuxiong1,2, FAN Yun3.1. school of mathematics and statistics, {3. university, {3. 43.072, hubei, china 2. school of mathematics and Computer Science, Jianghan university, {3. 43.056, hubei, china 3. school of mathematics and statistics, huazhong normal university, wuhan 430079, hubei, china school of mathematics and statistics Wuhan University Wuhan 430072 Hubei China

Let K/Q be any abelian extension where Q is the field of rational numbers. By Galois theory and the Frobenius formula for induced characters, we prove that there exists a metabelian group G and an irreducible characte... 详细信息

关键词： abelian extensions metabelian groups induced characters Galois groups

Criteria for Regularity of Elliptic Diffusion Processes and It’s Application

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wuhan university Journal of Natural Sciences 2005年第2期10卷 347-350页

作者： LI Bo 1,2 , ZHANG Xiao-min 3.1.school of mathematics and statistics,{3. normal university,wuhan 430079,hubei,china 2.school of mathematics and statistics, wuhan university, wuhan 43.072, hubei, china 3.Faculty of Science,Ningbo university,Ningbo 3.5211,Zhejiang, china huazhong normal university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.411407.7) (ISNI:***) wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Ningbo university Faculty of Science Ningbo Zhejiang China (GRID:grid.203507.3) (ISNI:***)

The cone condition for x to be tegular for B under the elliptic diffusionprocess was proved. We also gave a necessary and sufficient condition for 0 to be regular for thornunder the elliptic diffusion process.

关键词： regular capacity thorn diffusion process

A theorem of Fong's type for graded algebras

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Science china mathematics 2005年第5期48卷 577-582页

作者： FAN Yun & ZHU Ping school of mathematics and statistics, Central{3. normal university, wuhan 430079,{3. school of Mathematical Science, Nankai university, Tianjin 3.0071,{3. 1. school of mathematics and statistics Central China Normal University 430079 Wuhan China 2. school of Mathematical Science Nankai University 300071 Tianjin China

Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalgebra graded by a Hall p′-subgroup. A necessary and sufficient condition for the indecomposability of an induced module from a Hall p′-subgroup is obtained.

关键词： group graded algebra indecomposable induced module primitive idempotent.

On the Cayley-Bacharach property and the construction of vector bundles

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Science china mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2 1 Department of mathematics and statistics,huazhong {3. university,wuhan 430079,china 2 Department of mathematics,East china {3. university,Shanghai 200241,china 1. Department of mathematics and statistics Huazhong Normal University Wuhan 430079 China2. Department of Mathematics East China Normal University Shanghai 200241 China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES

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Acta Mathematica Scientia 2011年第1期31卷 353-360页

作者：邓勤涛 Department of mathematics Sun Yat-Sen University Laboratory of Nonlinear Analysis and School of Mathematics and StatisticsHuazhong Normal University

In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 663. （H2 114785 respectively） must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4（-1）（resp. H5（-1）） with constant mean curvature H satisfying H2 6643.（resp. H2 114785 ） must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].

关键词： k-weighted bi-Ricci curvature finite index constant mean curvature

normal scalar curvature and a pinching theorem in S^m×R and H^m×R

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Science china mathematics 2011年第9期54卷 1977-1984页

作者： CHEN Qun 1,2 & CUI Qing 3.1,1 school of mathematics and statistics,{3. university,{3. 430079,china 2 International Center for Theoretical Physics,Trieste 3.100,Italy 3.school of mathematics,Southwest Jiaotong university,Chengdu 61003.,china school of mathematics and statistics Wuhan University Wuhan China International Center for Theoretical Physics Trieste Italy school of mathematics Southwest Jiaotong University Chengdu China

We obtain an inequality in Sm×R and Hm×R which is similar to DDVV *** an application,we show that a minimal submanifold in H m×R with nonnegative scalar curvature must be a surface of the type γ×R,where γ is a g... 详细信息

关键词： product spaces DDVV conjecture pinching theorem

An efficient algorithm for finding the largest chain graph according to a given chain graph

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Science china mathematics 2005年第11期48卷 1517-1530页

作者： LIU Baijun,ZHENG Zhongguo & ZHAO Hui school of Mathematical Sciences, Peking university, Beijing 100871, china Department of {3., Central china normal university, wuhan 430079, china 1. school of Mathematical Sciences Peking University 100871 Beijing China 2. Department of statistics Central China Normal University 430079 Wuhan China

Chain graph (CG) is a general model of graphical Markov models. Some different chain graphs may describe the same conditional independence structure, then we say that these CGs are Markov equivalent. In 1990 Frydenberg showed that every class of Markov equivalent CGs has a CG which is called the largest chain graph with the greatest number of lines. This paper presents an efficient algorithm for finding the largest chain graph of the corresponding Markov equivalent class of a given CG. The computational complexity of the algorithm is O(n3.. It is more efficient than the complexity O(n!) of the present algorithms. Also a more intuitive graphical characterization of the largest chain graph is provided based on the algorithm in this paper.

关键词： graphical Markov model,chain graph,largest chain graph,protected arrows,efficient algorithm

On the Markov equivalence of maximal ancestral graphs

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Science china mathematics 2005年第4期48卷 548-562页

作者： ZHAO Hui, ZHENG Zhongguo & LIU Baijun school of Mathematical Sciences, Peking university, Beijing 100871, china Department of {3., Central china normal university, wuhan 430079, china 1. school of Mathematical Sciences Peking University 100871 Beijing China

Necessary and sufficient conditions for a maximal ancestral graph (MAnG)to be Markov equivalent to another MAnG and to a DAG are provided respectively. Also a polynomial-time algorithm for converting a MAnG into its e... 详细信息

关键词： maximal ancestral graph, Markov equivalence, minimal collider path, m-separation.

A Graph Theoretic Method to Handle Deadlocks in Flexible Manufacturing Cells

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武汉理工大学学报 2006年第S3期28卷 1117-1120页

作者： WANG Chunxiang~(1,2) LIU Donglin~3.(1.school of mathematics and statistics,{3. university,{3. 43.072,china, 2.school of mathematics and statistics,Central china normal university,{3. 430079,china 3.school of Electronic and Mechanical Engineering,{3. university of Technology,{3. 43.070,china) school of mathematics and statistics Wuhan UniversityWuhan 430072China school of mathematics and statistics Central China Normal UniversityWuhan 430079China school of Electronic and Mechanical Engineering Wuhan University of TechnologyWuhan 430070China

The deadlock-handling scheme is based on a bipartite graph model of the part-machine relationship in the manufac- turing cell.A distinction is made between permanent deadlock and transient *** deadlock depicts a manufactur- ing system state where parts are irrevocably blocked and where external intervention is required to resolve the deadlock,whereas a transient deadlock indicates that there is a positive probability that the deadlock will resolve itself over *** recover from dead- locks,one control policy is studied:resolve deadlocks in the manufacturing *** the policy,it is shown that it is sufficient to resolve any cycle in the set of deadlocked parts to resolve the ***,we estimate the deadlocks in flexible manufactur- ing cells.

关键词： permanent deadlock transient deadlock deadlock detection deadlock resolution graph