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Connectivities of Minimal Cayley Coset Digraphs 被引量:2
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作者 MENG JIXIANG 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第4期497-500,共4页
we prove that the Connectivities of Minimal Cayley Coset Digraphs are their regular degrees. Connectivity of transitive digraphs and a combinatorial propertyof finite groups Ann., Discrete Math., 8 1980 61--64 ... we prove that the Connectivities of Minimal Cayley Coset Digraphs are their regular degrees. Connectivity of transitive digraphs and a combinatorial propertyof finite groups Ann., Discrete Math., 8 1980 61--64 Meng Jixiang and Huang Qiongxiang On the connectivity of Cayley digraphs, to appear Sabidussi, G. Vertex transitive graphs Monatsh. Math., 68 1969 426--438 Watkins, M. E. Connectivity of transitive graphs J. Combin. Theory, 8 1970 23--29 Zemor, G. On positive and negative atoms of Cayley digraphs Discrete Applied Math., 23 1989 193--195 Department of Mathematics,Xinjiang University,Urumpi 830046.APPLIED MATHEMATICS 3. Statement of Inexact Method Here we assume F to be continuousely differentiable. Inexact Newton method was first studied in the solution of smooth equations (see ). Now, such a technique has been widely used in optimizations, nonlinear complementarity problems and nonsmooth equations (see, and , etc.) In order to establish the related inexact methods,we introduce a nonlinear operator T(x): R n R n . Its components are defined as follows: (T(x)p) i=[HL(2:1,Z;2,Z] (x k+p k) i, if i∈(x k), H i(x k)+ min {(p k) i,F i(x k) Tp k}, if i∈(x k), F i(x k)+F i(x k) Tp k, i∈(x k).(3.1) Then, it is clear that the subproblem (2.5) turns to T(x k)p k=0.(3.2) In inexact algorithm, we determine p k in the followinginexact way ( see ). ‖T(x k)p k‖ υ k‖H(x k)‖,(3.3) where υ k is a given positive sequence. It is then obviously that (3.2),or equivalently (2.5), is a special case of (3.3) corresponding to υ k=0 . In particular, (3.3) can be used as a termination rule of the iterative process for solving (2.5). The following proposition shows the existence of λ k satisfying (2.4). Proposition 3.1. Let F be continuously differe ntiable. υ k is chosen so that υ k for some constant ∈(0,1). Then p k generated by (3.3) is a descent direction of θ at x k, and for some constant σ∈(0, min (1/2,1- holds θ(x k)-θ(x k+λ kp k) 2σλ kθ(x k)(3.4) for all sufficiently small λ k>0. Proof For simplification, we omit the lower subscripts k and denote (x k) i , H i(x k) , (BH(x k)p k) i , etc.by x i , H i , (BHp) i , etc. respectively. To estimate the directional derivative of θ at x k along p k , we divide it into three parts: D p k θ(x k)=H T(x k)BH(x k)p k=T 1+T 2+T 3,(3.5) where T 1=Σ i∈α k H i(BHp) i , T 2=Σ i∈β k H i(BHp) i , T 3=Σ i∈γ k H i(BHp) i . Consider i∈α k= k∪α -(x k) . In this case, we always have H i(BH(x)p) i=H i 2+H i(x i+p i) . If i∈ k , then H i(BHp) i -H i 2+|H i‖(T(x)p) i|. If i∈α -(x k) , then x i<0 . We have either x i+p i 0 , or x i+p i<0 . When x i+p i 0 , we get H i(BH(x)p) i -H i 2 .In the later case, x i+p i<0 , so H i(BH(x)p) i=-H i 2+|H i‖x i+p i|. Then, by elementary computation, we deduce that T 1 -Σi∈α kH i 2+Σ i∈α k|H i‖(T(x)p) i|.(3.6) Received March 1, 1995. 1991 MR Subject Classification: 05C25 展开更多
关键词 Connectivity Cayley coset digraph
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Iterative Decoding of Parallel Concatenated Block Codes and Coset Based MAP Decoding Algorithm for F24 Code 被引量:1
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作者 LI Ming, CAO Jia lin, DENG Jia mei School of Electromechanical Engineering and Automation, Shanghai University, Shanghai 200072, China 《Journal of Shanghai University(English Edition)》 CAS 2001年第2期116-122,共7页
A multi dimensional concatenation scheme for block codes is introduced, in which information symbols are interleaved and re encoded for more than once. It provides a convenient platform to design high performance co... A multi dimensional concatenation scheme for block codes is introduced, in which information symbols are interleaved and re encoded for more than once. It provides a convenient platform to design high performance codes with flexible interleaver size. Coset based MAP soft in/soft out decoding algorithms are presented for the F24 code. Simulation results show that the proposed coding scheme can achieve high coding gain with flexible interleaver length and very low decoding complexity. 展开更多
关键词 iterative decoding parallel concatenated codes MAP(maximum a posterior) decoding coset principle
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Coset Structure of Spin Group 被引量:1
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作者 WANG Na WU Ke 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第6期987-994,共8页
This article considers One example is also given to take a the coset structure closer look at what of spin group via analyzing the expression of its representation. the coset and the subgroup are.
关键词 spin group group representation coset structure
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COSET DIAGRAMS FOR A HOMOMORPHIC IMAGE OFΔ(3,3,k)
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作者 M.Ashiq Q.Mushtaq 《Acta Mathematica Scientia》 SCIE CSCD 2008年第2期363-370,共8页
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
关键词 coset diagrams conjugacy classes nondegenerate homomorphism projec tire line and triangle groups
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COSET PARTITION OF ADDITIVE GROUPS AND MINORITY-LOGIC DECODING ALGORITHM FOR RM CODES
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作者 陆正福 胡正名 阮传慨 《Journal of Electronics(China)》 1993年第2期139-145,共7页
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
关键词 Coding DYADIC ADDITIVE group coset RM code
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Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target withℤ2n Grading
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作者 KE San-Min LI Xin-Ying +1 位作者 WANG Chun YUE Rui-Hong 《Chinese Physics Letters》 SCIE CAS CSCD 2011年第10期48-51,共4页
The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target withℤ2n grading is derived using a first−order Hamiltonian formulation and by adding to the Lax conn... The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target withℤ2n grading is derived using a first−order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints.This enables us to show that the conserved charges of the theory are in involution.When n=2,our results coincide with the results given by Magro for the pure spinor description of AdS5×S5 string theory(when the ghost terms are omitted). 展开更多
关键词 coset ALGEBRA Nonlinear
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The Coset Group and Com ove Group
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作者 林楠 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第1期94-97, ,共4页
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.
关键词 set value map power group coset group comove group
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Palm Vein Authentication Based on the Coset Decomposition Method
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作者 Mohamed Sayed 《Journal of Information Security》 2015年第3期197-205,共9页
The palm vein authentication technology is extremely safe, accurate and reliable as it uses the vascular patterns contained within the body to confirm personal identification. The pattern of veins in the palm is compl... The palm vein authentication technology is extremely safe, accurate and reliable as it uses the vascular patterns contained within the body to confirm personal identification. The pattern of veins in the palm is complex and unique to each individual. Its non-contact function gives it a healthful advantage over other biometric technologies. This paper presents an algebraic method for personal authentication and identification using internal contactless palm vein images. We use MATLAB image processing toolbox to enhance the palm vein images and employ coset decomposition concept to store and identify the encoded palm vein feature vectors. Experimental evidence shows the validation and influence of the proposed approach. 展开更多
关键词 BIOMETRICS coset Decomposition Method HAND VEINS PERSONAL AUTHENTICATION
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A general mirror equivalence theorem for coset vertex operator algebras
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作者 Robert McRae 《Science China Mathematics》 SCIE CSCD 2024年第10期2237-2282,共46页
We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules... We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA(U).Specifically,we assume that A≌■_(i∈I)U_(i)■V_(i) as a U■V-module,where the U-modules Uiare simple and distinct and are objects of a semisimple braided ribbon category of Umodules,and the V-modules Viare semisimple and contained in a(not necessarily rigid) braided tensor category of V-modules.We also assume U=ComA(V).Under these conditions,we construct a braid-reversed tensor equivalence τ:u_(A)→v_(A),where u_(A)is the semisimple category of U-modules with simple objects Ui,i∈I,and v_(A)is the category of V-modules whose objects are finite direct sums of Vi.In particular,the V-modules Viare simple and distinct,and v_(A)is a rigid tensor category.As an application,we find a rigid semisimple tensor subcategory of modules for the Virasoro algebra at central charge 13+6p+6p^(-1),p∈Z_(≥2), which is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional sl2-modules.Consequently,the Virasoro vertex operator algebra at central charge 13+6p+6p^(-1)is the PSL_(2)(C)-fixed-point subalgebra of a simple conformal vertex algebra w(-p),analogous to the realization of the Virasoro vertex operator algebra at central charge 13-6p-6p^(-1)as the PSL_(2)(C)-fixed-point subalgebra of the triplet algebra W(p). 展开更多
关键词 vertex operator algebras coset conformal eld theory braid-reversed tensor equivalence Virasoro algebra
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A result on certain coset subalgebras of the βγ-system 被引量:1
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作者 楚彦军 黄芳 郑驻军 《Chinese Physics C》 SCIE CAS CSCD 2011年第2期149-152,共4页
In this paper, for the highest weight module V4 of sl(2,C) with the highest weight 4, we describe subalgebras Sβ(V4)+ and Sγ(V4)+ of the βγ-system coset S(V4)+ by giving their generators. These eoset su... In this paper, for the highest weight module V4 of sl(2,C) with the highest weight 4, we describe subalgebras Sβ(V4)+ and Sγ(V4)+ of the βγ-system coset S(V4)+ by giving their generators. These eoset subalgebras are interesting, new examples of strongly finitely generated vertex algebra. 展开更多
关键词 vertex algebra coset βγ-system -ring Hilbert series
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Coset vertex operator algebras and W-algebras of A-type 被引量:1
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作者 Tomoyuki Arakawa Cuipo Jiang 《Science China Mathematics》 SCIE CSCD 2018年第2期191-206,共16页
We give an explicit description for a weight three generator of the coset vertex operator algebra C_L_(sln)(l,0)L_(sln)(1,0)(L_(sln)(l+1,0),for n≥2, l≥1. Furthermore, we prove that the nommutant C_L_(sl3)(l,0)L_(sl3... We give an explicit description for a weight three generator of the coset vertex operator algebra C_L_(sln)(l,0)L_(sln)(1,0)(L_(sln)(l+1,0),for n≥2, l≥1. Furthermore, we prove that the nommutant C_L_(sl3)(l,0)L_(sl3)(1,0)(L_(sl3)(l+1,0)) is isomorphic to the W-algebra W_(-3+(l+3)/(l+4))(sl_3), which confirms the conjecture for the sl_3 case that C_L_g(l,0)L_g(1,0)(L_g(l + 1,0)) is isomorphic to W_(-h+(l+h)/(l+h+1))(g) for simaly-laced Lie algebras g with its Coxeter number h for a positive integer l. 展开更多
关键词 W-algebra coset vertex operator algebra rationality
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Diference Systems of Sets Based on Cosets Partitions
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作者 Geng Sheng ZHANG Hong Rui WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第12期2261-2272,共12页
Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of th... Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs. 展开更多
关键词 Difference systems of sets code synchronization difference set coset OPTIMAL
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Coset Diagram for the Action of Picard Group on Q(i, √3)
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作者 Qaiser Mushtaq Saima Anis 《Algebra Colloquium》 SCIE CSCD 2016年第1期33-44,共12页
In this paper coset diagrams, propounded by Higman, are used to investigate the behavior of elements as words in orbits of the action of the Picard group F = PSL(2, Z[i]) on Q(i, √3). Graphical interpretation of ... In this paper coset diagrams, propounded by Higman, are used to investigate the behavior of elements as words in orbits of the action of the Picard group F = PSL(2, Z[i]) on Q(i, √3). Graphical interpretation of amalgamation of the components of F is also given. Some elements a+b√3/c of Q(i, √3) and their conjugates a-b√3/c a c over Q(i) have different signs in the orbits of the biquadratic field Q(i, √3) when acted upon by F. Such real quadratic irrational numbers are called ambiguous numbers. It is shown that ambiguous numbers in these coset diagrams form a unique pattern. It is proved that there are a finite number of ambiguous numbers in an orbit Fa, and they form a closed path which is the only closed path in the orbit Гa. We also devise a procedure to obtain ambiguous numbers of the form a-b√3/c, where b is a positive integer. 展开更多
关键词 Picard group biquadratic field coset diagrams and ambiguous numbers
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新纠缠辅助量子MDS码的构造
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作者 汪盼 王立启 朱士信 《电子学报》 EI CAS CSCD 北大核心 2024年第1期288-297,共10页
纠缠辅助量子纠错码是经典量子纠错码的推广,通过在接收者和发送者双方预先共享纠缠态的方式实现量子通信.由于预先共享纠缠态会造成额外的费用,如何构造具有较小预先共享纠缠态的纠缠辅助量子纠错码是一个有趣的问题.本文给出了有限域... 纠缠辅助量子纠错码是经典量子纠错码的推广,通过在接收者和发送者双方预先共享纠缠态的方式实现量子通信.由于预先共享纠缠态会造成额外的费用,如何构造具有较小预先共享纠缠态的纠缠辅助量子纠错码是一个有趣的问题.本文给出了有限域Fq2上一类负循环码是厄米特对偶包含码的充分条件,通过研究其分圆陪集的结构性质,确定了不同数目的预先共享纠缠态的存在条件,并结合纠缠辅助量子纠错码的构造方法,构造了一些新的具有较小预先共享纠缠态的纠缠辅助量子Maximum-Distance-Separable(MDS)码. 展开更多
关键词 分圆陪集 负循环码 纠缠辅助量子纠错码 MDS码
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几类量子BCH码的构造 被引量:1
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作者 蒲可莉 廖群英 《四川师范大学学报(自然科学版)》 CAS 2024年第5期689-695,共7页
量子纠错码可以有效地克服量子消相干,是实现量子计算的关键技术.量子纠错码可以利用满足特定关系的经典纠错码来进行构造.BCH码作为一类距离可设计的特殊循环码,具有很好的代数结构,所以可以用来构造量子BCH码.首先给出有限域F_(q)(q... 量子纠错码可以有效地克服量子消相干,是实现量子计算的关键技术.量子纠错码可以利用满足特定关系的经典纠错码来进行构造.BCH码作为一类距离可设计的特殊循环码,具有很好的代数结构,所以可以用来构造量子BCH码.首先给出有限域F_(q)(q为素数方幂)上模n分圆陪集是单元集的等价刻画和性质.然后利用CSS构造和Steane构造得到两类有限域F_(q)上的新的量子BCH码,最后将分圆陪集的相关结果推广到有限域F_(q^(2))上,并利用Hermitian构造得到一类量子BCH码. 展开更多
关键词 分圆陪集 CSS构造 Steane构造 Hermitian构造 量子BCH码
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基于常循环码的纠缠辅助量子Maximum-Distance-Separable码的构造
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作者 刘航宇 王立启 《大学数学》 2024年第4期7-16,共10页
纠缠辅助量子纠错码可以看作是经典量子纠错码的引申,其与经典量子纠错码的差别在于,如果发送者和接收者双方提前共享纠缠态,在不满足对偶包含的的情况下也可以由任意经典线性码构造出来.本文通过研究分圆陪集的结构性质,利用常循环码... 纠缠辅助量子纠错码可以看作是经典量子纠错码的引申,其与经典量子纠错码的差别在于,如果发送者和接收者双方提前共享纠缠态,在不满足对偶包含的的情况下也可以由任意经典线性码构造出来.本文通过研究分圆陪集的结构性质,利用常循环码构造出几类新的具有较小预先共享纠缠态的纠缠辅助量子Maximum-Distance-Separable(MDS)码. 展开更多
关键词 纠缠辅助量子纠错码 常循环码 分圆陪集 MDS码
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基于L_∞最小搜索和陪集码的高光谱图像无损及近无损压缩 被引量:12
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作者 宋娟 李云松 +1 位作者 吴成柯 王柯俨 《电子学报》 EI CAS CSCD 北大核心 2011年第7期1551-1555,共5页
分布式信源编码(DSC)由于其较低的编码复杂度及较高的抗误码性被应用于高光谱图像压缩.在典型的基于陪集码的分布式高光谱图像无损压缩算法s-DSC(scalar coset DSC)框架下,本文指出最优的预测准则应为无穷范数最小,提出了基于L∞最小搜... 分布式信源编码(DSC)由于其较低的编码复杂度及较高的抗误码性被应用于高光谱图像压缩.在典型的基于陪集码的分布式高光谱图像无损压缩算法s-DSC(scalar coset DSC)框架下,本文指出最优的预测准则应为无穷范数最小,提出了基于L∞最小搜索的预测方法来逼近最优准则,并将框架推广到近无损压缩.实验表明,和原有的s-DSC相比,本文算法无损压缩的平均码率降低了大约0.25bpp,近无损性能也明显优于JPEG-LS,本文算法具有较低的计算复杂度、较高的压缩性能,且具有一定的抗误码能力,适用于星上压缩. 展开更多
关键词 高光谱图像 无损及近无损压缩 分布式信源编码 陪集码 预测 无穷范数
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有限域上非本原BCH码的对偶包含判定 被引量:7
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作者 肖芳英 陈汉武 +2 位作者 刘志昊 李志强 刘文杰 《电子学报》 EI CAS CSCD 北大核心 2010年第8期1858-1861,共4页
循环陪集在经典和量子纠错编码理论中具有非常重要的作用.根据CSS编码定理知,利用经典BCH码构造量子BCH码时需要判断经典BCH码是否包含其对偶码.本文给出了循环陪集的若干重要性质,根据这些性质得到了判断有限域上非本原BCH码是否包含... 循环陪集在经典和量子纠错编码理论中具有非常重要的作用.根据CSS编码定理知,利用经典BCH码构造量子BCH码时需要判断经典BCH码是否包含其对偶码.本文给出了循环陪集的若干重要性质,根据这些性质得到了判断有限域上非本原BCH码是否包含其对偶码的准则.本文给出的判断准则时间复杂度为多项式的,并且该判断准则对本原BCH码也适用. 展开更多
关键词 量子纠错码 BCH码 对偶码 循环陪集
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基于分类和陪集码的高光谱图像无损压缩 被引量:11
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作者 宋娟 吴成柯 +1 位作者 张静 刘海英 《电子与信息学报》 EI CSCD 北大核心 2011年第1期231-234,共4页
在基于陪集码的高光谱图像压缩算法中,由于按照编码块的最大残差确定整块无损压缩所需的码率存在较大冗余,该文提出了基于分类和陪集码的高光谱图像压缩算法。首先利用前一波段对应位置的预测噪声对当前波段编码块的像素进行分类,将具... 在基于陪集码的高光谱图像压缩算法中,由于按照编码块的最大残差确定整块无损压缩所需的码率存在较大冗余,该文提出了基于分类和陪集码的高光谱图像压缩算法。首先利用前一波段对应位置的预测噪声对当前波段编码块的像素进行分类,将具有相似相关性的像素归于一类,然后对每一类像素分别进行陪集码编码。实验表明分类可以有效地降低码率。和基于陪集码的算法相比,该文算法无损压缩的平均码率降低了大约0.4 bpp。 展开更多
关键词 高光谱图像 无损压缩 分布式信源编码 陪集码 分类
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qp阶群陪集图的CI性 被引量:5
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作者 徐尚进 朱雁 邓芸萍 《广西大学学报(自然科学版)》 CAS CSCD 2007年第3期278-281,共4页
Sabidussi陪集图X:=Sab(G,H,D)当子群H=1时恰是Cayley图,故Sabidussi陪集图较Cayley图更具一般性,类似于Cayley图的CI性,我们同样可以研究Sabidussi陪集图的CI性.本文主要研究qp阶群陪集图的CI性(其中q与p是满足q<p的素数),并得到一... Sabidussi陪集图X:=Sab(G,H,D)当子群H=1时恰是Cayley图,故Sabidussi陪集图较Cayley图更具一般性,类似于Cayley图的CI性,我们同样可以研究Sabidussi陪集图的CI性.本文主要研究qp阶群陪集图的CI性(其中q与p是满足q<p的素数),并得到一些结果. 展开更多
关键词 有限群 陪集图 陪集图的CI性
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