A result on combinatorial curvature for embedded graphs on a surface

Let G be an infinite graph embedded in a surface such that each open face of the embedding is homeomorphic to an open disk and is bounded by finite number of edges. For each vertex x of G, we define the combinatorial curvature

     

On the perturbations of spectra of upper triangular operator matrices

In this paper we investigate perturbations of the regular spectrum of an upper triangular operator matrix such as acting on a Hilbert space H⊕K.     

Regular matrices and their strong preservers over semirings

An m×n matrix A over a semiring is called regular if there is an n×m matrix G over such that AGA=A. We study the problem of characterizing those linear operators T on the matrices over a semiring such that T(X) is regular if and only if X is. Complete characterizations are obtained for many semirings including the Boolean algebra, the nonnegative reals, the nonnegative integers and the fuzzy scalars.     

Abel's method on summation by parts and theta hypergeometric series

Abel's lemma on summation by parts is reformulated to investigate systematically terminating theta hypergeometric series. Most of the known identities are reviewed and several new transformation and summation formulae are established. The authors are convinced by the exhibited examples that the iterating machinery based on the modified Abel lemma is powerful and a natural choice for dealing with terminating theta hypergeometric series.     

基于灰色关联分析和主成分分析组合权重的确定方法研究

为了提高综合评价模型中权重的准确性和客观性,以主成分分析法和灰色关联分析法为基础,建立了组合权重模型,从而修正了灰色关联分析法和主成分分析法在确定权重过程中的缺陷,为综合评价体系中权重的确定提出一种新的思路.     

A rational Arnoldi process with applications

The rational Arnoldi process is a popular method for the computation of a few eigenvalues of a large non‐Hermitian matrix and for the approximation of matrix functions. The method is particularly attractive when the rational functions that determine the process have only few distinct poles , because then few factorizations of matrices of the form A ? z_jI have to be computed. We discuss recursion relations for orthogonal bases of rational Krylov subspaces determined by rational functions with few distinct poles. These recursion formulas yield a new implementation of the rational Arnoldi process. Applications of the rational Arnoldi process to the approximation of matrix functions as well as to the computation of eigenvalues and pseudospectra of A are described. The new implementation is compared to several available implementations.     

理想反应器的时空特性和内在联系

以理想反应器时间和空间特性为出发点,探讨了间歇操作釜式反应器(BR)、平推流反应器(PFR)和全混流反应器(CSTR)等理想反应器之间的内在联系,推导了循环操作PFR反应器的停留时间分布函数,分析了多段串联全混流反应器和循环操作PFR反应器在各理想反应器之间的桥梁和纽带作用。在此基础上,简要归纳了各理想反应器之间的联系。     

聚合物流动方程教学剖析及其流变本构关系自然哲理探讨

阐述了流体流动过程中三大守恒方程的原理及其各项表达式的物理含义,分析了三大守恒方程联立流体流变本构方程的必要性并进行了数字求解;对材料流变本构关系原理从自然哲理角度进行了探讨,深化教学内容,启发学生思维,达到更好的教学效果。     

Bi53+‐Polykationen in geordneten und plastischen Kristallen von Bi5[AlI4]3 und Bi5[AlBr4]3

Bi₅³⁺ Polycations in Ordered and Plastic Crystals of Bi₅[AlI₄]₃ and Bi₅[AlBr₄]₃ Dark‐red air‐sensitive crystals of pentabismuth‐tris(tetrabromoaluminate) Bi₅[AlBr₄]₃ and black crystals of Bi₅[AlI₄]₃ have been crystallized from melts of Bi, BiX₃ and AlX₃ (X = Br, I). X‐ray diffraction on a single crystal of Bi₅[AlI₄]₃ (T = 293(2) K; space group Pnma; a = 2143.6(3) pm, b = 1889.1(1) pm, c = 811.74(5) pm) revealed an ordered packing of Bi₅³⁺ trigonal bipyramids and [AlI₄]^? tetrahedra that corresponds to the PuBr₃ structure type. Contrary to the so far known Bi₅³⁺ polycations with accurate D_3h symmetry, the bismuth cluster found in Bi₅[AlI₄]₃ holds only C_s symmetry. The room temperature structure of the tetrabromoaluminate Bi₅[AlBr₄]₃, which is related to the AuCu₃ type, shows a dynamic disorder of the Bi₅³⁺ polycations (T = 293(2) K; space group ; a = 1766.2(3) pm). Slight cooling induces the transition into an ordered rhombohedral phase isostructural to Bi₅[AlCl₄]₃ (T = 260(2) K; space group a = 1241.5(8) pm, c = 3041(2) pm).