随机四角链的Hosoya多项式

图的Hosoya多项式包含图的许多和距离有关的信息,由它可以得到很多拓扑不变量,如Wiener指标和hyper-Wiener指标.本文主要研究随机四角链的Hosoya多项式,不仅给出了它的数学期望显式表达式,而且得到了对应随机四角链的Wiener指标和hyper-Wiener指标数学期望的显式表达式。     

公式H_n=lnn+C+ε_n应用举例

<正> 如所周知.有著名公式式中C=0.57721…,称为Euler(欧拉)常数。ε_n→0(n→+∞)本文将通过几个实例,阐述公式(1)在极限、积分、级数等方面的应用。例1 对任意给定的k∈N,k≥2.     

伪单调数列与带误差的凸组合迭代的收敛性

一 伪单调数列 定义1 设非负数列{ε_n}具有如下性质:“满足 a_(n+1)≤a_n+ε_n,n=1,2,… (1)且有下界的任意数列{a_n}必收敛”,则称数列{ε_n}具有“性质M”。 定理1 非负数列{ε_n}具有性质M的充要条件是级数sum from n=1 to ∞(ε_n)收敛。证 必要性:设非负数列{ε_n}具有性质M,取数列{a_(1n)}为     

图的预解Estrada指标的界的估计（英文）

n阶图G的子图中心度,即后来著名的Estrada指标定义为EE（G）=∑_（i=1）~N e~（λ2）.其中λ_1,λ_2……λ_n为图G的特征值.作为复杂网络的一种中心性测度和一种分子结构描述符,Estrada指标在许多研究领域有着广泛的应用.最近,Estrada和High-ama引进了一种新的复杂网络中心度,即∑_（i=1）~n n-1n-1λ_i：他们称之为预解中心度,后来又被称为预解Estrada指标.本文主要利用图G的顶点数和边数给出了图G的预解Estrada指标的若干界.     

单圈图的hyper-Wiener指标

令u（n）表示具有n个顶点的单圈图.在一个圈C3的一个顶点上悬挂n-3个悬挂边的n个顶点的单圈图记为U~＊（n-3,0,0）.本文证明了在u（n）中具有最小hyper-Wiener指数的单圈图是U~＊（n-3,0,0）.     

Asymptotic uniformity of the quantization error for the Ahlfors-David probability measures

Let μ be an Ahlfors-David probability measure on R~q;therefore,there exist some constants s_0 0 and ε_0,C_1,C_2 0 such that C_1ε~(s_0)≤μ(B(x,ε))≤C_2ε~(s_0) for all ε∈(0,ε_0) and x ∈ supp(μ).For n≥ 1,let α_n be an n-optimal set for μ of order r;furthermore,let {P_a(α_n)}_(a∈α_n) be an arbitrary Voronoi partition with respect to α_n.The n-th quantization error e_(n,r)(μ) for μ of order r can be defined as e_(n,r)~r(μ):=∫ d(x,α_n)~r dμ(x).We define I_a(α_n,μ):=∫_(P_a(α_n)) d(x,α_n)~r dμ(x),a ∈α_n,and prove that,the three quantities ■ are of the same order as that of 1/ne_(n,r)~r(μ).Thus,our result exhibits that,a weak version of Gersho's conjecture holds true for the Ahlfors-David probability measures on R~q.     

再论线性模型中误差方差的二次型估计的可容许性

设有线性模型Y=(y_1,…,y_n)′=Xβ ε=X(β_1,…,β_p)′ (ε_1,…,ε_n)′,(1.1)这里 X 为已知的,n×p 矩阵,n≥p,ε_1,…,ε_n 相互独立,E(ε_i)=0,E(ε_i~2)=σ~2,E(ε_i~3)=0,E(ε_i~4)=3σ~4,i=1,…,n.β∈R~p,0<σ~2<∞均为未知参数.欲估计σ~2,     

关于线性型的一个转换定理

<正> 命θ_1,…,θ_n为一组实数,n≥2;1,θ_1,…,θ_n信在有理数域上线性无关.对实数x,命 ‖x‖=min(x-[x],[x]+1-x),x=max(1,|x|).ε表示任意给定的正数,c_1,c_2表示仅依赖于ε,n,θ_1,…,θ_n的正常数.     

多重线性回归中数据联合影响的分解及数据的交叉影响

一、引言考虑多重线性回归模型Y=Xβ ε,(1)其中,Y=(y_1,…y_n_)′为 n×p 观察矩阵,X=(x_1,…,x_n)′为 n×(k 1)列满秩设计矩阵,β=(β_0,β_1,…β_k)′为(k 1)×p 未知参数矩阵,ε=(ε_1,…ε_n)′为 n×p 随机误差矩阵,ε_1…,ε_n 相互独立.     

几类多圈图的拉普拉斯谱刻画

设图G是一个简单连通图.如果任何一个与图G同拉普拉斯谱的图都与图G同构,则称图G是由其拉普拉斯谱确定的.定义了双圈图θ_n(p_1,p_2,…,p_t)和m圈图H_n(m·C_3;p_1,p_2,…,p_t).证明了双圈图θ_n(p)和θ_n(p,q),三圈图H_n(3·C_3;p)和H_n(3·C_3;p,q)分别是由它们的拉普拉斯谱确定的.     

Scrambling index set of primitive digraphs

The scrambling index k(D)$k(D)$ of a primitive digraph D is the smallest positive integer k such that for every pair of vertices x and y, there exists a vertex v such that there exist directed walks of length k from x to v and from y to v. In this paper, we study the scrambling index set of primitive digraphs.     

k-分支星状树的第二几何算术指标

数学化学中,第二几何算术指标是新近提出的一个图的拓扑指标,它与Szeged指标和点PI指标具有紧密关系.如果树的一个顶点υ的度大于等于3,则称顶点υ是其一个分支点.通过树的第二几何算术指标的一个增加或减少的变换,刻画了k-分支星状树的第二几何算术指标的最值,同时确定了相应的极图.     

图的Hyper-Wiener指数的综述(英文)

设G是一个图.G的顶点u和v的距离是u和v之间最短路的长度.Wiener指数是G中所有无序顶点对之间距离之和,而Hyper-Wiener指数定义为WW(G)=?∑u,v∈V(G)d(u,v)+?∑u,v∈V(G)d2(u,v),式中的和取遍G的所有顶点对.本文总结了图的Hyper-Wiener指数的最近结论.     

Structural satisfaction in simple games

A fundamental maxim for any theory of social behavior is that knowledge of the theory should not cause behavior that contradicts the theory's assertions. Although this maxim consistently has been heeded in the theory of noncooperative games, it largely has been ignored in solution theory for cooperative games. Solution theory, the central concern of this paper, seeks to identify a subset of the feasible outcomes of a cooperative game that are ‘stable’ results of competition among participants, each of whom attempts to bring about an outcome he favors, rather than to prescribe ‘fair’ outcomes that accord with a standard of equity. We show that learning by participants about the solution theory can cause the outcomes identified as stable by certain solution concepts to become unstable, and discover that an important distinction in this regard is whether the solution concept requires each element of the solution set to defend itself against alternatives rather than relying on other elements for its defense. Finally, we develop a concept of ‘solid’ solutions which have a special claim for stability.The unifying theme of this paper concerns the sense in which certain outcomes of a cooperative game may be regarded as stable, and the extent to which this stability requires that the players are ignorant of the theory. Although the issues raised here have implications for the theory of cooperative games in general, Section 1 establishes the focus of the analysis on collective decision games. Section 2 develops some general perspectives on solution theory which are used in Sections 3 and 4 to evaluate the Condorcet solution, the core, the robust proposals set, von Neumann- Morgenstern solutions and competitive solutions. Section 5 presents the concept of a solid solution and relates this idea to the solution concepts reviewed earlier. We demonstrate that in general a solution concept has a strong claim to stability only if it is solid. Finally, Section 6 concludes by indicating that the basic argument also can be applied to Aumann and Maschler's bargaining sets and, more generally, to solution theory for any cooperative game.     

On the differences between Szeged and Wiener indices of graphs

Let G be a connected graph and η(G)=Sz(G)−W(G), where W(G) and Sz(G) are the Wiener and Szeged indices of G, respectively. A well-known result of Klav?ar, Rajapakse, and Gutman states that η(G)≥0, and by a result of Dobrynin and Gutman η(G)=0 if and only if each block of G is complete. In this paper, a path-edge matrix for the graph G is presented by which it is possible to classify the graphs in which η(G)=2. It is also proved that there is no graph G with the property that η(G)=1 or η(G)=3. Finally, it is proved that, for a given positive integer k,k≠1,3, there exists a graph G with η(G)=k.     

Calculating the edge Wiener and edge Szeged indices of graphs

The edge Szeged and edge Wiener indices of graphs are new topological indices presented very recently. It is not difficult to apply a modification of the well-known cut method to compute the edge Szeged and edge Wiener indices of hexagonal systems. The aim of this paper is to propose a method for computing these indices for general graphs under some additional assumptions.     

Hyper- and reverse-Wiener indices of F-sums of graphs

The Wiener index W(G)=∑_{u,v}⊂V(G)d(u,v), the hyper-Wiener index and the reverse-Wiener index , where d(u,v) is the distance of two vertices u,v in G, d²(u,v)=d(u,v)², n=|V(G)| and D is the diameter of G. In [M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math. 157 (2009) 794-803], Eliasi and Taeri introduced the F-sums of two connected graphs. In this paper, we determine the hyper- and reverse-Wiener indices of the F-sum graphs and, subject to some condition, we present some exact expressions of the reverse-Wiener indices of the F-sum graphs.