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Normal projection： deterministic and probabilistic algorithms

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Frontiers of Mathematics in China 2014年第1期9卷 93-99页

作者： Dongmei LI Jinwang liu weijun liu Department of Mathematics and Computing Sciences Hunan University of Scienceand Technology Xiangtan 411201 China Department of Mathematics and Statistics Central South University Changsha 410083 China

We consider the following problem： for a collection of points in an n-dimensional space, find a linear projection mapping the points to the ground field such that different points are mapped to different values. Such projections are called normal and are useful for making algebraic varieties into normal positions. The points may be given explicitly or implicitly and the coefficients of the projection come from a subset S of the ground field. If the subset S is small, this problem may be hard. This paper deals with relatively large S, a deterministic algorithm is given when the points are given explicitly, and a lower bound for success probability is given for a probabilistic algorithm from in the literature.

关键词： Normal projection primary decomposition of ideal deterministic algorithm

GVW ALGORITHM OVER PRINCIPAL IDEAL DOMAINS

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Journal of Systems Science & Complexity 2013年第4期26卷 619-633页

作者： LI Dongmei liu Jinwang liu weijun ZHENG Licui Department of Mathematics and Computing Sciences Hunan University of Science and Technology Xiangtan 411201 China Department of Mathematical and Statistical Central South University Changsha 410083 China. Department of Mathematics and Computing Sciences Hunan University of Science and Technology Xiangtan 411201 China. School of Mathematical and Statistical Central South University Changsha 410083 China.

GVW algorithm was given by Gao, Wang, and Volny in computing a Grobuer bases for ideal in a polynomial ring, which is much faster and more simple than F5. In this paper, the authors generalize GVW algorithm and presen... 详细信息

关键词： Buchberger's algorithm F5 algorithm Grobner basis GVW algorithm principal ideal domain.

The Comaximal Graphs of Noncommutative Rings

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Algebra Colloquium 2023年第3期30卷 439-448页

作者： Shouqiang Shen weijun liu Lihua Feng School of Applied Science Beijing Information Science and Technology University Beijing100192China School of Mathematics and Statistics HNP-LAMA Central South UniversityChangsha 410083China

For a ring R(not necessarily commutative)with identity,the comaximal graph of R,denoted byΩ(R),is a graph whose vertices are all the nonunit elements of R,and two distinct vertices a and b are adjacent if and only if Ra+Rb=*** this paper we consider a subgraphΩ_(1)(R)ofΩ(R)induced by R\Uℓ(R),where Uℓ(R)is the set of all left-invertible elements of *** characterize those rings R for whichΩ_(1)(R)\J(R)is a complete graph or a star graph,where J(R)is the Jacobson radical of *** investigate the clique number and the chromatic number of the graphΩ_(1)(R)\J(R),and we prove that if every left ideal of R is symmetric,then this graph is connected and its diameter is at most ***,we completely characterize the diameter ofΩ_(1)(R)\J(R).We also investigate the properties of R whenΩ_(1)(R)is a split graph.

关键词： comaximal graph noncommutative ring left invertible element split graph

Signed Zero-Divisor Graphs Over Commutative Rings

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Communications in Mathematics and Statistics 2024年第3期12卷 463-477页

作者： Lu Lu Lihua Feng weijun liu School of Mathematics and Statistics HNP-LAMACentral South UniversityChangsha 410083HunanPeople’s Republic of China

In this paper,we define signed zero-divisor graphs over commutative rings and investigate the interplay between the algebraic properties of the rings and the combinatorial properties of their corresponding signed zero-divisor *** investigate the structure of signed zero-divisor graphs,the relation between ideals and signed zero-divisor graphs,and the adjacency matrices and the spectra of signed zero-divisor graphs.

关键词： Ring Ideal Signed graph Adjacency matrix

Some Simple Groups Which are Determined by Their Orders and Degree-Patterns

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Algebra Colloquium 2024年第2期31卷 341-346页

作者： Qinghong Guo weijun liu Genghua Fan School of Mathematics and Statistics HNP-LAMACentral South University Changsha 410083China College of General Education Guangdong University of Science and Technology DongguanGuangdong 523083China 不详

Let G be a finite group and Irr(G)the set of all irreducible complex characters of *** cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of *** character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of *** show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.

关键词： irreducible complex character character-prime graph finite nonabelian simple group

GENERATION METHOD FOR FIVE-AXIS NC SPIRAL TOOL PATH BASED ON PARAMETRIC SURFACE MAPPING

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Journal of Systems Science & Complexity 2013年第5期26卷 676-694页

作者： ZHOU Bo ZHAO Jibin liu weijun LI Lun Graduate University of the Chinese Academy of Sciences Shenyang Institute of Automation Shenyang Institute of Automation

A new spiral tool path generation algorithm for 5-axis high speed machining is proposed in this ***,the voltage contours are calculated to satisfy the machining parameters in the mapping parametric domain by means of the electrostatic field model of partial differential ***,the mapping rules are constructed and the machining trajectory is planned out in the standard parametric domain in order to map and generate the spiral trajectory in the corresponding parametric ***,this trajectory is mapped onto the parametric surface for the obtainment of the spiral tool *** spiral tool path can realize the machining of complicated parametric surface and trimmed surface without tool *** above-mentioned algorithm has been implemented in several simulations and validated successfully through the actual machining of a complicated *** results indicate that this method is superior to the existing machining methods to realize the high speed machining of the complicate-shaped cavity based on parametric surface and trimmed surface.

关键词： 5-axis NC machining mapping rule partial differential equations spiral tool path.

On Block-transitive 6-（v, k, λ）-Designs with k at Most 10000

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Algebra Colloquium 2014年第2期21卷 231-234页

作者： Qionghua Tan weijun liu Jing Chen School of Mathematics Central South University Changsha Hunan 410075 China School of Mathematics and Physics Nanhua University Hengyang Hunan 421001 China

In recent years, there has been a great deal of research concerning the flag- transitive t-designs, however, few about the block-transitive t-designs with t large （t 〉 4）. In 1993, Cameron and Praeger conjectured that there are no non-trivial block-transitive 6-designs. In this paper, we prove that the conjecture is true when k ≤ 10000 and G ≤ Aut（D） is almost simple.

关键词： block-transitive 6-designs 3-homogeneous automorphism groups

Nickel Phosphide Nanorod Arrays Vertically Grown on Ni Foam as High-Efficiency Electrocatalyst for the Hydrogen Evolution Reaction

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Chinese Journal of Chemistry 2017年第4期35卷 405-409页

作者： Xiandong Dou weijun liu Qing liu Zhiqiang Niu School of Chemical and Environmental Engineering Shanghai Institute of Technology Shanghai 201418 China

An electrocatalyst of nickel phosphide （Ni2P） nanorod arrays vertically grown on Ni foam composite （NNFC） was prepared successfully using NaHzPO2 as phosphorus source by means of a facile method of in situ phospho- rization of Ni foam. The as-prepared NNFC exhibits excellent HER performance with an onset overpotential of 100 mV, a small Tafel slope of only 55 mV/dec, and a low overpotential involving 200 mV at a current density of 10 mA·cm^-2. Furthermore, the electrocatalyst was also demonstrated to possess high stability with a neglectable de- crease in activity even after durability test for 25 h.

关键词： electrocatalyst hydrogen evolution reaction Ni foam nickel phosphide

TWO-OPERATION HOMOMORPHIC PERFECT SHARING SCHEMES OVER RINGS

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Applied Mathematics(A Journal of Chinese Universities) 1999年第2期14卷 233-238页

作者： Ma Chuangui\ liu weijun Dept. of Appl. Math. Information Engineering Institute Zhengzhou

Two operation homomorphic sharing schemes were introduced by Frankel and Desmedt. They have proved that if the set of keys is a Boolean algebra or a finite field, then there does not exist a two operation homomorphic sharing scheme. In this paper it is proved that there do not exist perfect two operation homomorphic sharing schemes over finite rings with identities. A necessary condition for the existence of perfect two operation sharing schemes over finite rings without identities is given.

关键词： 1991 MR Subject Classification 94A60