Sum of Element Orders of Maximal Subgroups of the Symmetric Group

For a finite group G, let ψ(G) denote the sum of element orders of G. The aim of this article is to show that ψ(H) < ψ(A _n ) for every proper subgroup H of the symmetric group of degree n, which is different from the alternating group A _n .     

Second Maximum Sum of Element Orders of Finite Nilpotent Groups

In [1 Amiri , H. , Jafarian Amiri , S. M. , Isaacs , I. M. ( 2009 ). Sums of element orders in finite groups . Communications in Algebra 37 : 2978 – 2980 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]], the authors proved that the maximum sum of element orders on finite groups of the same order occurs in cyclic group. In this paper we obtain the structure of groups having maximum sum of element orders on noncyclic nilpotent group of the same order.     

Common Fixed Point and Invariant Approximation Results for Gregus Type I-Contractions

A fixed point theorem of Ciric, Diviccaro et al., Fisher and Sessa, Gregus, Jungck, and Mukherjee and Verma is generalized to weakly compatible maps. As applications, common fixed point and approximation results for Gregus type I-contractions are obtained. Our results unify and generalize various known results to the more general classes of noncommuting mappings.     

Quantum Secure Communication by Using GHZ State in High-Dimensional Hilbert Space

We propose a quantum superdense coding secure communication scheme by using GHZ state. This scheme combines the ideas of quantum superdense coding and sequence transmission. Its distinct advantage is high source capacity. In addition, in checking eavesdropping, we need not to destroy quantum entanglement.     

Mixed compatible element and mixed hybrid incompatible element variational methods in dynamics of viscous barotropic fluids

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Hessian orders and multinormal distributions

Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order, i.e., an integral stochastic order defined through a convex cone of Hessian matrices, and we prove that if two random vectors are ordered by the Hessian order, then their means are equal and the difference of their covariance matrices belongs to the dual of . Then we show that the same conditions are also sufficient for multinormal random vectors. We study several particular cases of this general result.     

V形切口应力强度因子的一种边界元分析方法

将V形切口结构分成围绕切口尖端的小扇形和剩余结构两部分. 尖端处扇形域应力场表示成关于尖端距离$\rho$的渐近级数展开式,从线弹性理论方程推导出了一组分析平面V形切口奇异性的常微分方程特征值问题,通过求解特征方程,得到前若干个奇性指数和相应的特征向量. 再将切口尖端的位移和应力表示为有限个奇性阶和特征向量的组合. 然后用边界元法分析挖去小扇形后的剩余结构. 将位移和应力的线性组合与边界积分方程联立,求解获得切口根部区域的应力场、应力幅值系数和整体结构的位移和应力. 从而准确计算出平面V形切口的奇异应力场和应力强度因子.