A NEW ALGORITHM FOR COMPUTING THE INVERSE AND GENERALIZED INVERSE OF THE SCALED FACTOR CIRCULANT MATRIX

A new algorithm for finding the inverse of a nonsingular scaled factor circulant matrix is presented by the Euclid＇s algorithm. Extension is made to compute the group inverse and the Moore-Penrose inverse of the singular scaled factor circulant matrix. Numerical examples are presented to demonstrate the implementation of the proposed algorithm.     

Nowhere-zero 3-flows in Cayley graphs and Sylow 2-subgroups

Tutte’s 3-Flow Conjecture suggests that every bridgeless graph with no 3-edge-cut can have its edges directed and labelled by the numbers 1 or 2 in such a way that at each vertex the sum of incoming values equals the sum of outgoing values. In this paper we show that Tutte’s 3-Flow Conjecture is true for Cayley graphs of groups whose Sylow 2-subgroup is a direct factor of the group; in particular, it is true for Cayley graphs of nilpotent groups. This improves a recent result of Potočnik et al. (Discrete Math. 297:119–127, 2005) concerning nowhere-zero 3-flows in abelian Cayley graphs.     

Linear maps preserving group majorization

A necessary and sufficient condition for a linear map to preserve group majorizations is given. The condition is applied to prove some preservation results.     

Group methodology in production management: A solution based on a hierarchical classification method

We consider the problem submitted by Garcia and Proth and we propose for it a solution obtained by simply applying our very general method of hierarchical classification based on the likelihood of the links, in the case of an incidence table of data. This application is done on each of the two sides of the incidence data table. In our approach, the common number p of classes has not to be fixed arbitrarily, but is an observed possible result—provided by the notions of ‘significant’ levels and nodes of the classification tree—for the ‘natural’ association between two partitions. We compare our solution with the previous one.     

Binary group and Chinese postman polyhedra

A new proof of the characterization of the Chinese postman polyhedra is given. In developing this proof, a theorem of Gomory about homomorphic lifting of facets for group polyhedra is generalized to subproblems. Some results for the Chinese postman problem are generalized to binary group problems. In addition, a connection is made between Fulkerson's blocking polyhedra and a blocking pair of binary group problems. A connection is also developed between minors and lifting of facets for group problems.     

甲苯的激光拉曼光谱研究

采用激光拉曼光谱技术获得了甲苯的振动拉曼光谱,结合群论方法及退偏度测量,指认了其中16条振动谱线,为有机混合物中对甲苯的识别提供了依据．选择甲苯全对称环呼吸振动（1008.8cm－1）为检测谱线,对不同浓度的甲苯／四氯化碳样品进行了分析．研究结果表明：在200．1～2．61g／L浓度范围内,甲苯／四氯化碳振动拉曼光谱强度比与甲苯浓度呈良好的线性关系,线性相关系数为0.997．为甲苯的定量分析提供了一种有效的研究方法．     

超短脉冲在光子晶体中传播时的色散参量

利用最小二乘拟合法分析了光子晶体的能带结构,定量分析了二维光子晶体的色散参量.为了考虑脉冲各频率的作用,通过引入与频率分量相关的权重因子,从而解析了群速度和平均群速度色散,进而解析出脉冲波络渐变的理论结果.通过FDTD数值模拟后,发现数值模拟结果与理论解析结果完全相吻合.本文处理光子晶体的色散参量的方法,为制作光子晶体色散器件如光子晶体色散补偿器、脉冲展宽和压缩器有一定的借鉴作用.     

Twisted injectivity in projected entangled pair states and the classification of quantum phases

We introduce a class of projected entangled pair states (PEPS) which is based on a group symmetry twisted by a 3-cocycle of the group. This twisted symmetry is expressed as a matrix product operator (MPO) with bond dimension greater than 1 and acts on the virtual boundary of a PEPS tensor. We show that it gives rise to a new standard form for PEPS from which we construct a family of local Hamiltonians which are gapped, frustration-free and include fixed points of the renormalization group flow. Based on this insight, we advance the classification of 2D gapped quantum spin systems by showing how this new standard form for PEPS determines the emergent topological order of these local Hamiltonians. Specifically, we identify their universality class as Dijkgraaf–Witten topological quantum field theory (TQFT).     

Dispersion characteristics of complex refractive-index planar slab optical waveguide by using finite element method

In this paper, finite element method (FEM) mode analyses of planar slab optical waveguide having complicated refractive index profile are presented. We try to estimate the dispersion graph, mode cut-off condition, group delay and waveguide dispersion for the case of α-power and chirped-type refractive index profile. In order to obtain the more accurate result, we have derived the higher-order polynomial, which establishes the suitable relationship between b and V for different profile of optical waveguide. On the basis of the derived polynomials, the waveguide dispersion is analyzed for different type of refractive index profile waveguide. Our study shows that the waveguide dispersion can be substantially reduced when we deployed the optical waveguide having linearly chirped-type refractive index profile. Earlier too, the arbitrary refractive index profile has been analyzed but to the best of our knowledge chirped-type refractive index profile has not been analyzed till date for the case of planar slab optical waveguide.