On the maximum cocliques of the rank 3 graph of 211 : M24

In this article, we consider the maximum cocliques of the 2¹¹: M₂₄ ‐graph Λ. We show that the maximum cocliques of size 24 of Λ can be obtained from two Hadamard matrices of size 24, and that there are exactly two maximum cocliques up to equivalence. We verify that the two nonisomorphic designs with parameters 5‐(24,9,6) can be constructed from the maximum cocliques of Λ, and that these designs are isomorphic to the support designs of minimum weights of the ternary extended quadratic residue and Pless symmetry [24,12,9] codes. Further, we give a new construction of Λ from these 5‐(24,9,6) designs. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 323–332, 2009     

The Spectral Theory of Amenable Actions and Invariants of Discrete Groups

Let G denote a semisimple group, a discrete subgroup, B=G/P the Poisson boundary. Regarding invariants of discrete subgroups we prove, in particular, the following:(1) For any -quasi-invariant measure on B, and any probablity measure on , the norm of the operator () on L ²(B,) is equal to (), where is the unitary representation in L ²(X,), and is the regular representation of .(2) In particular this estimate holds when is Lebesgue measure on B, a Patterson–Sullivan measure, or a -stationary measure, and implies explicit lower bounds for the displacement and Margulis number of (w.r.t. a finite generating set), the dimension of the conformal density, the -entropy of the measure, and Lyapunov exponents of .(3) In particular, when G=PSL₂() and is free, the new lower bound of the displacement is somewhat smaller than the Culler–Shalen bound (which requires an additional assumption) and is greater than the standard ball-packing bound.We also prove that ()=_G() for any amenable action of G and L ¹(G), and conversely, give a spectral criterion for amenability of an action of G under certain natural dynamical conditions. In addition, we establish a uniform lower bound for the -entropy of any measure quasi-invariant under the action of a group with property T, and use this fact to construct an interesting class of actions of such groups, related to 'virtual' maximal parabolic subgroups. Most of the results hold in fact in greater generality, and apply for instance when G is any semi-simple algebraic group, or when is any word-hyperbolic group, acting on their Poisson boundary, for example.     

Corrigendum: The cover time of the giant component of a random graph,Random Structures and Algorithms 32 (2008), 401–439

The above paper gives an asymptotically precise estimate of the cover time of the giant component of a sparse random graph. The proof as it stands is not tight enough, and in particular, Eq. (64) is not strong enough to prove (65). The o(1) term in (64) needs to be improved to o(1/(lnn)²) for (65) to follow. The following section, which replaces Section 3.6, amends this oversight. The notation and definitions are from the paper. A further correction is needed. Property P2 claims that the conductance of the giant is whp , Ω(1/lnn). The proof of P2 in the appendix of the paper is not quite complete. A complete proof of Property P2 can be found in 1 , 2 . © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

团队目标导向影响因素的探索性研究:基于扎根理论和概念格-加权群组DEMATEL方法

团队目标导向对团队目标的实现有重要的引导作用,研究团队目标导向的影响因素是从根本上加强团队目标导向引导作用的前提基础。本研究以人的认知为视角,首先通过扎根理论方法从质化研究角度选取团队目标导向的影响因素,其次运用概念格-加权群组DEMATEL方法进行影响因素重要度的识别,在此基础上以实例的形式分别运用传统DEMATEL方法和概念格-加权群组DEMATEL方法计算影响因素的重要程度,并对计算结果的差异进行比较分析,得出团队目标导向受个体层面和组织层面因素的影响更大,其中最重要的影响因素是组织承诺和组织公平感,并为企业管理者提出相应管理启示。     

Remarks on Nonassociative Structures in Quantum Projective Field Theory: the Central Extension jl(2,C) of the Double sl(2,C)+sl(2,C) of the Simple Lie Algebra sl(2,C) and Related Topics

This paper is a revised and expanded version of two notes devoted to nonassociative structures in quantum projective field theory.     

2‐(v,k,1) Designs Admitting a Primitive Rank 3 Automorphism Group of Affine Type: The Extraspecial and the Exceptional Classes

2‐(v,k,1) designs admitting a primitive rank 3 automorphism group , where G₀ belongs to the Extraspecial Class, or to the Exceptional Class of Liebeck's Theorem in [23], are classified.     

基于非局部弹性应力场理论的纳米尺度效应研究:纳米梁的平衡条件、控制方程以及静态挠度

该文成功地解答了3个关于非局部应力理论用于纳米梁的问题:(ⅰ) 在绝大多数研究中,非局部效应增加导致纳米结构体刚度下降,其现象表现为弯曲挠度增加,固有频率减少,屈曲载荷下降,但为什么Eringen 的非局部弹性理论给出了完全相反的结论;(ⅱ) 为什么在某些研究结果中,非局部效应消失或是对研究结果无影响,比如纳米悬臂梁在集中载荷作用下的弯曲挠度; (ⅲ) 在高阶控制方程中,为什么高阶边界条件不存在．通过应用非局部弹性理论和精确变分原理分析纳米梁的弯曲问题,推导出全新的平衡条件、控制方程、边界条件和静态响应．这些方程和条件包含了与之前的相关研究结果符号相反的高阶微分项,这一差别导致了纳米效应对结构体的影响结果完全相反． 还证明之前为大家所公认的纳米梁静态或动态平衡条件实际上没有达到平衡,只有用等效弯矩代替非局部弯矩时,才可达到平衡．这些结论通常是可以被其它方法,比如应变梯度理论、耦合应力模型以及相关实验所证明．