Based on the concepts of set value map and power group,the definitions of comove relation,coset group and comove group were given,their properties were discussed and meaningful results were obtained.
<正> This article considers the coset structure of spin group via analyzing the expression of its representation.One example is also given to take a closer look at what the coset and the subgroup are.
Two new notions for the coset partition of dyadic additive groups are proposed,andtheir sufficient and necessary conditions are also given.On the basis of these works,the feasibilityproblem of implementing minority-lo...Two new notions for the coset partition of dyadic additive groups are proposed,andtheir sufficient and necessary conditions are also given.On the basis of these works,the feasibilityproblem of implementing minority-logic decoding algorithm for RM codes is solved.展开更多
We investigate action of a subgroup G1 of the Picard group on finite sets using coset diagrams. We show that its actions on the sets of 3, 4, 5, 6, 8, and 12 elements yield building blocks of Coset diagrams and that t...We investigate action of a subgroup G1 of the Picard group on finite sets using coset diagrams. We show that its actions on the sets of 3, 4, 5, 6, 8, and 12 elements yield building blocks of Coset diagrams and that these blocks can be connected together so that a diagram of n vertices can be obtained. We show that various combinations of these blocks represent alternating and symmetric groups of various degrees. We show also that the action of G1 on a set of n vertices is transitive.展开更多
In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differ...In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differentialrepresentations in both the group parameter space and its coset spaces.They are the generalization of the differentialrepresentations of the SO(3) rotation group in the Euler angles.These representations may find their applications in thestudy of the physical systems with SO(4) dynamical symmetry.展开更多
Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphis...Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △（3, 3, k） = （u, v： u^3 = v^3 = （uv）^k = 1〉on PL（Fq）, where q ≡ ±1（modk）. Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △（3, 3, k） on PL（Fq）. The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by （u^-v^-）^k. In this way, they get △（3, 3, k） as permutation groups on PL（Fq）.展开更多
文摘Based on the concepts of set value map and power group,the definitions of comove relation,coset group and comove group were given,their properties were discussed and meaningful results were obtained.
基金The project supported by National Key Basic Research Project of China under Grant No. 2004CB318000 and National Natural Science Foundation of China under Grant Nos. 10375038 and 90403018. The authors would like to express their thanks to Moningside Center, The Chinese Academy of Sciences. Part of the work was done when we were joining the Workshop on Mathematical Physics there.Acknowledgments We are deeply grateful to Profs. Qi-Keng Lu, Han-Ying Guo, and Shi-Kun Wang for their valuable discussions, which essentially stimulate us to write down this work.
文摘<正> This article considers the coset structure of spin group via analyzing the expression of its representation.One example is also given to take a closer look at what the coset and the subgroup are.
文摘Two new notions for the coset partition of dyadic additive groups are proposed,andtheir sufficient and necessary conditions are also given.On the basis of these works,the feasibilityproblem of implementing minority-logic decoding algorithm for RM codes is solved.
文摘We investigate action of a subgroup G1 of the Picard group on finite sets using coset diagrams. We show that its actions on the sets of 3, 4, 5, 6, 8, and 12 elements yield building blocks of Coset diagrams and that these blocks can be connected together so that a diagram of n vertices can be obtained. We show that various combinations of these blocks represent alternating and symmetric groups of various degrees. We show also that the action of G1 on a set of n vertices is transitive.
基金National Natural Science Foundation of China under Grant Nos.10205007,10226033,10375039,and 90503008the Nuclear Theory Research Program for NCET and Fund of HIRFL of China
文摘In this paper we present systematic differential representations for the dynamical group SO(4).Theserepresentations include the left and the right differential representations and the left and the right adjoint differentialrepresentations in both the group parameter space and its coset spaces.They are the generalization of the differentialrepresentations of the SO(3) rotation group in the Euler angles.These representations may find their applications in thestudy of the physical systems with SO(4) dynamical symmetry.
文摘Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △（3, 3, k） = （u, v： u^3 = v^3 = （uv）^k = 1〉on PL（Fq）, where q ≡ ±1（modk）. Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △（3, 3, k） on PL（Fq）. The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by （u^-v^-）^k. In this way, they get △（3, 3, k） as permutation groups on PL（Fq）.
