On the Monotonicity of Process Number

Graph searching games involve a team of searchers that aims at capturing a fugitive in a graph. These games have been widely studied for their relationships with tree-and path-decomposition of graphs. In order to define decompositions for directed graphs, similar games have been proposed in directed graphs. In this paper, we consider such a game that has been defined and studied in the context of routing reconfiguration problems in WDM networks. Namely, in the processing game, the fugitive is invisible, arbitrary fast, it moves in the opposite direction of the arcs of a digraph, but only as long as it has access to a strongly connected component free of searchers. We prove that the processing game is monotone which leads to its equivalence with a new digraph decomposition.     

Symmetric Schröder paths and restricted involutions

Let A_k be the set of permutations in the symmetric group S_k with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns A_k. We present a bijection between symmetric Schröder paths of length 2n and involutions of length n+1 avoiding A₄. Statistics such as the number of right-to-left maxima and fixed points of the involution correspond to the number of steps in the symmetric Schröder path of a particular type. For each k≥3 we determine the generating function for the number of involutions avoiding the subsequences in A_k, according to length, first entry and number of fixed points.     

新一代ARINC429总线监听模块设计技术

在飞行试验中,机载ARINC429总线往往包含重要的试飞数据,采集ARINC429总线是试飞测试系统中重要的一环。以往的ARINC429总线采集技术,一般采用分离元器件构成,造成电路体积大、功耗大,可靠性降低。在新一代网络化采集器创新性预研背景下,提出了一种基于DSP和FPGA架构的通用设计方案,FPGA进行总线协议解析,DSP进行数据的筛选,充分发挥出FPGA的并行优势和DSP的灵活特性。同时,设计了数据采样和传递机制,并在实际工程中得到应用。     

Directed acyclic subsequence graph—Overview

The subsequence matching problem is to decide, for given strings S and T, whether S is a subsequence of T. The string S is called the pattern and the string T the text. We consider the case of multiple texts and show how to solve the subsequence matching problem in time linear in the length of the pattern. For this purpose we build an automaton that accepts all subsequences of given texts. This automaton is called the Directed Acyclic Subsequence Graph (DASG). We prove an upper bound for its number of states. Furthermore, we consider a modification of the subsequence matching problem: given a string S and a finite language L, we are to decide whether S is a subsequence of any string in L. We suppose that a finite automaton accepting L is given and present an algorithm for building the DASG for language L. We also mention applications of the DASG to some problems related to subsequences.     

Analogues of some Tauberian theorems for bounded variation

In this paper definitions for “bounded variation”, “subsequences”, “Pringsheim limit points”, and “stretchings” of a double sequence are presented. Using these definitions and the notion of regularity for four dimensional matrices, the following two questions will be answered. First, if there exists a four dimensional regular matrix A such that Ay = Σ _k,l=1,1 ^∞∞ a _m,n,k,l y _k,l is of bounded variation (BV) for every subsequence y of x, does it necessarily follow that x ∈ BV? Second, if there exists a four dimensional regular matrix A such that Ay ∈ BV for all stretchings y of x, does it necessarily follow that x ∈ BV? Also some natural implications and variations of the two Tauberian questions above will be presented.     

Subnormality of Bergman-like weighted shifts

For a,b,c,d?0 with ad−bc>0, we consider the unilateral weighted shift S(a,b,c,d) with weights . Using Schur product techniques, we prove that S(a,b,c,d) is always subnormal; more generally, we establish that for every p?1, all p-subshifts of S(a,b,c,d) are subnormal. As a consequence, we show that all Bergman-like weighted shifts are subnormal.     

An adaptation of a root finding method to searching ordered disk files

Three methods for locating a record in an ordered file are considered. The keys in the files are chosen from three different statistical distributions and the methods, two of which are taken from the literature and an adapted root finding method, are compared by tabulating information relating to standard statistics for the number of probes.