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A Note on Submodularity Preserved Involving the rank functions

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Journal of the Operations Research Society of China 2019年第3期7卷 399-407页

作者： Min Li Dong-Lei Du Da-Chuan Xu Zhen-Ning Zhang School of Mathematics and Statistics Shandong Normal UniversityJinan 250358China Faculty of Business Administration University of New BrunswickFrederictonCanada College of Applied Sciences Beijing University of TechnologyBeijing 100124China

In many kinds of games with economic significance,it is very important to study the submodularity of *** this paper,wemainly study the problem of maximizing a concave function over an intersection of two *** obtain that the submod-ularity may not be preserved,but it involves one maximal submodular problem(or minimal supermodular problem)with some ***,we also present examples showing that these conditions can be satisfied.

关键词： Matroid Submodular function rank function Convexclosure Game

Global rank Axioms for Poset Matroids

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Acta Mathematica Sinica,English Series 2004年第3期20卷 507-514页

作者： ShuChaoLI YanQinFENG DepartmentofMathematics CentralChinaNormalUniversityWuhan430079P.R.China DepartmentofMathematics NanjingUniversityNanjing210093P.R.China

An excellent introduction to the topic of poset matroids is due to Barnabei, Nicoletti and Pezzoli. In this paper, we investigate the rank axioms for poset matroids; thereby we can characterize poset matroids in a “global” version and a “pseudo-global” version. Some corresponding properties of combinatorial schemes are also obtained.

关键词： Poset matroids rank function Combinatorial scheme Distributive lattice

New Results on Global rank Axioms of Poset Matroids

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Acta Mathematica Sinica,English Series 2005年第1期21卷 143-154页

作者： ShuChaoLI YanQinFENG LaboratoryofNonlinearAnalysis DepartmentofMathematicsCentralChinaNormalUniversityWuhan430079P.R.China//DepartmentofControlScienceandEngineeringHuazhongUniversityofScienceandTechnologyWuhan430074P.R.China DepartmentofMathematics NanjingUniversityNanjing210093P.R.China

An excellent introduction to the topic of poset matroids is due to ***, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rankaxioms for poset matroids. In this paper, we study the special integral function f and obtain a newclass of poset matroids from the old ones, and then we generalize this result according to theproperties of f. Almost all of these results can be regarded as the application of global rankaxioms for poset matroids. The main results in our paper have, indeed, investigated the restrictionof the basis of the poset matroid, and we give them the corresponding geometric interpretation.

关键词： Poset matroids rank function Derivative function Combinatorial schemes

K-THEORETICALLY COMPLETE VON NEUMANN REGULAR RINGS

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Acta Mathematica Scientia 2004年第4期24卷 655-662页

作者：卢丹诚佟文廷 Department of Mathematics Suzhou University Suzhou 215006 China Department of Mathematics Nanjing University Nanjing 210093 Chinahe authors introduce the concept of Ko-complete ring and study the properties of Ko-complete unit-regular rings.

The authors introduce the concept of Ko-complete ring and study the properties of Ko-complete unit-regular rings.

关键词： Ko-complete rank function partially ordered Abelian group regular rings exchange rings