Sign patterns that allow diagonalizability revisited

Characterization of sign patterns that allow diagonalizability has been a long-standing open problem. In this article, necessary and sufficient conditions for a sign pattern to allow diagonalizability are obtained, in terms of allowing related properties. Some properties of normal sign patterns are considered. In particular, it is shown that normal sign patterns of order up to 3 allow diagonalizability. Two combinatorial necessary conditions for a sign pattern to allow diagonalizability are also presented.     

Improved lower bounds on the total variation distance for the Poisson approximation

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen–Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.     

The MAP/PH/N retrial queue in a random environment

We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.     

Lexical Scope and Statistical Computing

Abstract

Programming environments such as S and Lisp-Stat have languages for performing computations, data storage mechanisms, and a graphical interface. These languages provide an interactive interface to data analysis that is invaluable. To take full advantage of these programming environments, statisticians must understand the differences between them. Ihaka and Gentleman introduced R, a version of S which uses a different scoping regimen. In some ways this makes R behave more like Lisp-Stat. This article discusses the concept of scoping rules and shows how lexical scope can enhance the functionality of a language.     

Computing the partial word avoidability indices of ternary patterns

We study pattern avoidance in the context of partial words. The problem of classifying the avoidable binary patterns has been solved, so we move on to ternary and more general patterns. Our results, which are based on morphisms (iterated or not), determine all the ternary patternsʼ avoidability indices or at least give bounds for them.     

On some colorings of a double graph

In this note, we present some results concerning the chromatic index, the total chromatic index, the adjacent vertex distinguishing chromatic index and the adjacent vertex distinguishing total chromatic index for double graphs. In particular, we study the double graphs of class 1 and of type 1.     

了解积分——求和

求一个函数的黎曼积分,实际上就是一个分割、近似代替、求和、取极限的过程.求和运算是整个积分计算的轴心.就积分四部曲中的求和问题,做一个一般性的讨论.文中使用的是分析和讨论的语言,不去追求数学语言本身的严格性.目的不仅是探讨求和这个步骤,在黎曼积分意义下具体实现的过程和隐含的内容,而且对一般的积分中的求和实现的可能性、应该满足的条件、实现的过程,以及应该注意那些基本问题,也做一点儿逻辑上的探讨.已达到以知识为媒介,提高认知能力的目的.     

Maximum Matchings in the n-Dimensional Cube

The problem of efficient computation of maximum matchings in the n-dimensional cube, which is applied in coding theory, is solved. For an odd n, such a matching can be found by the method given in our Theorem 2. This method is based on the explicit construction (Theorem 1) of the maps of the vertex set that induce largest matchings in any bipartite subgraph of the n-dimensional cube for any n.     

Parabolicity and Hyperbolicity Conditions for Boundary Elements of Surfaces

Mathematical Notes -