In this paper we deal with two aspects of applied mathematics , one is digraph theory and the other is infinite - dimensional linear system theory 本文将研究两个方面的内容：有向图理论与无穷维线性系统。这两个方面是应用数学中的两个非常重要的研究领域。
Generalized primitive exponents of digraphs are generalizations of traditional primitive exponents of primitive digraphs , with applications in memoryless communication systems 有向图的广义本原指数是本原有向图传统本原指数的推广，应用在非记忆通讯系统中。
Let d be a digraph , c is the hamilton cycle of d , then the arcs in a ( d ) - a ( c ) are called the directed brigdes of d . the set of directed bridges of d is denoted by b ( d ) ( or b ) 设d是有向图， d中不在有向hamilton圈上的弧称为d的有向桥，用b ( d )或b表示d的有向桥的集合。
A uniquely pancyclic digraph is a digraph which has exactly one directed cycle of each length l , for 3 l v , where v is the number of vertices of the digraph 一个唯一泛圈有向图是一个定向图，且对3 l v的每个l ，它恰好有一个长为l的有向圈，这里的v表示有向图的顶点数。
The establishment of layered orientation graph model and its expressing method were studied in this paper and application verification was made by taking certain typed airplane wing box as an example 研究了分层有向图模型的建立和表示方法，并以某型机翼翼盒为实例予以应用验证。
By means of the associated digraph of matrices we obtain the necessary and sufficient conditions of whether irreducibly doubly diagonally dominant matrices belongs to non - singular m - matrices 借助于矩阵的伴随有向图得到了不可约双对角占优矩阵是否为非奇异m -矩阵的充分必要条件。
( 3 ) we give an upper bound for lewin index , which is related to generalized primitive exponents of primitive digraph of order n and girth 2 , determine the index set of this class digraph and discuss the extreme cases ( 3 )第4节分析了围长为2的n阶本原有向图的l ( g )的上界及相应的指数集，并讨论了极端情形。
The main results are : ( 1 ) we give an upper bound for kth generalized primitive exponents of primitive digraphs with order n and girth 2 , and determine the exponent set of this class digraphs in section 2 主要内容有三部分： ( 1 )第2节给出了围长为2的n阶本原有向图的第k个顶点指数( exp _ d ( k ) )的上界及相应的指数集。
A belief network is a probability model defined on an acyclic directed graph ; distributed means nodes can be on different hosts , and heterogeneous means allowing different conditional distributions 一个信念网络是定义在一个非循环有向图上的概率模型；分布性指节点可以在不同的主机上，异质性指可以允许不同的条件分布。
This paper presents a research on the representation method of assembly constraints in die & mold structure design , and discuss the solving approach of assembly constraints based on directed graph and variable expression 研究模具结构装配设计中装配约束的表示方法，并讨论基于有向图和变量表达式的装配约束的求解方法。
