和图、整和图及模和图的几个结果

Let N denote the set of positive integers.The sum graph G (S) of a finite subset S (C) N is the graph (S,E) with uv ∈ E if and only if u v ∈ S.A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S С N.By using the set Z of all integers instead of N,we obtain the definition of the integral sum graph.A graph G=(V,E) is a mod sum graph if there exists a positive integer z and a labelling,λ,of the vertices of G with distinct elements from {0,1,2,...,z-1} so that uv ∈ E if and only if the sum,modulo z,of the labels assigned to u and v is the label of a vertex of G.In this paper,we prove that flower tree is integral sum graph.We prove that Dutch m-wind-mill (Dm) is integral sum graph and mod sum graph,and give the sum number of Dm.     

和图、整和图与模和图的几个结果

Let N denote the set of positive integers. The sum graph G^＋（S） of a finite subset S belong to N is the graph （S, E） with uv ∈ E if and only if u ＋ v ∈ S. A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S belong to N. By using the set Z of all integers instead of N, we obtain the definition of the integral sum graph. A graph G = （V, E） is a mod sum graph if there exists a positive integer z and a labelling, λ, of the vertices of G with distinct elements from {0, 1, 2,..., z - 1} so that uv ∈ E if and only if the sum, modulo z, of the labels assigned to u and v is the label of a vertex of G. In this paper, we prove that flower tree is integral sum graph. We prove that Dutch m-wind-mill （Dm） is integral sum graph and mod sum graph, and give the sum number of Dm.     

Harary's conjectures on integral sum graphs

Let N denote the set of positive integers and Z denote all integers. The (integral) sum graph of a finite subset S N(Z) is the graph (S, E) with uv ε E if and only if u + v ε S. A graph G is said to be an (integral) sum graph if it is isomorphic to the (integral) sum graph of some S N(Z). The (integral) sum number of a given graph G is the smallest number of isolated nodes which when added to G result in an (integral) sum graph.

We show that the integral sum number of a complete graph with n 4 nodes equals 2n − 3, which proves a conjecture of Harary. And we disprove another conjecture of Harary by showing that there are infinitely many trees which are not caterpillars but are integral sum graphs.     

Sum and direct sum of frame sequences

Casazza, Han and Larson characterized various properties of the direct sum of two frame sequences. We add characterizations of other properties and study the relationship between the direct sum and the sum of frame sequences. In particular, we find a necessary and sufficient condition for the sum of two strongly disjoint (orthogonal) frame sequences (in the same Hilbert space) to be a frame sequence, and thereby show that the sum of two strongly disjoint frame sequences may not be a frame sequence. We also show that the closedness of the sum of the synthesis operators of two frame sequences and that of the sum of the frame operators of the same frame sequences are not related. Other observations are also included.     

一个关于非负矩阵的不等式

证明:若(xij)是一个元素不全为零的m×n非负矩阵,则当0相似文献   

An aggregate label setting policy for the multi-objective shortest path problem

We consider label setting algorithms for the multi-objective shortest path problem with any number of sum and bottleneck objectives. We propose a weighted sum aggregate ordering of the labels, specifically tailored to combine sum and bottleneck objectives. We show that the aggregate order leads to a consistent reduction of solution times (up to two-thirds) with respect to the classical lexicographic order.     

Metric Regularity of the Sum of Multifunctions and Applications

The metric regularity of multifunctions plays a crucial role in modern variational analysis and optimization. This property is a key to study the stability of solutions of generalized equations. Many practical problems lead to generalized equations associated to the sum of multifunctions. This paper is devoted to study the metric regularity of the sum of multifunctions. As the sum of closed multifunctions is not necessarily closed, almost all known results in the literature on the metric regularity for one multifunction (which is assumed usually to be closed) fail to imply regularity properties of the sum of multifunctions. To avoid this difficulty, we use an approach based on the metric regularity of so-called epigraphical multifunctions and the theory of error bounds to study the metric regularity of the sum of two multifunctions, as well as some related important properties of variational systems. Firstly, we establish the metric regularity of the sum of a regular multifunction and a pseudo-Lipschitz multifunction with a suitable Lipschitz modulus. These results subsume some recent results by Durea and Strugariu. Secondly, we derive coderivative characterizations of the metric regularity of epigraphical multifunctions associated with the sum of multifunctions. Applications to the study of the behavior of solutions of variational systems are reported.     

梯子细分图L_n~*的排斥(下整)和数

(下整)和标号与排斥(下整)和标号是图的一种压缩表示.一个图G称为下整和图,若它同构于某个SQ+的下整和图.图Pn×K2称为梯子.本文给出了梯子细分图Ln*的定义,并确定了梯子细分图Ln*的排斥(下整)和数.     

ψ-混合随机变量序列的重对数律

本文讨论了同分布的 -混合序列其共同分布属于稳定分布(非高斯情形)吸引场部分和的Chover型重对数律.特别地当分布函数属于稳分布的正则吸引场时,得到了部分和及后置和更精细的结果,即积分检验的结果,由此立即可推出相应的Chover型重对数律.     

ψ-混合随机变量序列的重对数律

本文讨论了同分布的 -混合序列其共同分布属于稳定分布(非高斯情形)吸引场部分和的Chover型重对数律.特别地当分布函数属于稳分布的正则吸引场时,得到了部分和及后置和更精细的结果,即积分检验的结果,由此立即可推出相应的Chover型重对数律.