奇优美图的构造

图G的标号是指G的顶点集到一个整数集的映射f,且对e=uv∈E(G)由f(u)和f(v)诱导出边e的标号f(uv).本文给出了二分奇优美图的概念,证明了一个图是二分奇优美的当且仅当它是二分优美的,并给出了一些构造奇优美图的方法.     

图P^3n的奇优美标号算法

本文讨论了图P^3n的奇优美性,给出了图只奇优美标号算法．     

探索金鱼图的奇优美性

给出了奇优美图和二分奇优美图的概念,并定义了金鱼图,证明了在鱼头为不同图形的情况下,金鱼图仍然是奇优美的,且是二分奇优美的.还证明了:对一个奇优美图H和一棵二分奇优美树T,用一条边连接T的一个顶点和H的标号基点u_0后所得到的金鱼图仍是奇优美图.     

探讨斐波纳契对虾树的优美性

具有完美匹配M的n阶树T是强优美的,如果对任意uv∈M,存在树T的一个优美标号f,使得f(u)+f(u)=n-1.给出了二分奇优美树和强优美树的概念,证明了斐波纳契对虾树是二分奇优美和强优美树.     

(2m+1,1)-p-树的二分强优美性和二分强奇优美性

给出了二分优美树和强优美树、强奇优美树、边对称树以及对偶标号的概念,定义了一类(2m+1,1)-p-树.并证明了(2m+1,1)-p-树是二分强优美树和二分强奇优美树,并验证了(2m+1,1)-p-树的优美标号是对偶标号.最后证明了(2m+1,1)-p-树的边对称树仍然是二分驺优美树,并将上面的结论推广到一般情形.     

图(C)2n的奇优美及其奇强协调性

该文定义了图(C)2n,并研究了该图的奇优美和奇强协调性.利用构造法分别给出了图(C)2n在n=4k(k≥2)、n=4k+2时的奇优美算法,在n=4kk≥2)时,的奇强协调算法,进而证明了图(C)2n在n=2k(k≥3)时是奇优美图,在n=4k(k≥2)时是奇强协调图等结论,从而推动了对图的奇优美性和奇强协调性的研究.最后提出猜想:当n=4k+2时,图(C)2n不是奇强协调图.     

关于图P3n优美性的研究

在n个顶点的路Pn上,当且仅当两点的距离为3时增加一条边,所得的图称为P3n,本文给出了图P3n(n≥4)的优美标号,从而证明了P3n都是优美图.     

太阳图的奇优美性和奇强协调性

设k_1,k_2,…,k_n是非负整数,C_n=v_v_2…v_nv_1是有n个顶点n条边的圈,则称图C_n+{v_1v_(11),v_1v_(12),…,v_1v_1k_1,v_2v_(21),…,v_2k_2,…,v_nv_(n1),…,v_nk_n}为(k_1,k_2,…,k_n)轮环图,简记为C(k_1,k_1,…,k_n).研究了太阳图1C_n的奇优美性及其奇强协调性,得到了太阳图1C_n在n为偶数时的奇优美标号算法和奇强协调标号算法,从而证明了太阳图1C_n在n为偶数时是奇优美图和奇强协调图的结论.     

图_n~2的奇优美及其奇强协调性

该文定义了图_n~2,并研究了该图的奇优美和奇强协调性.利用构造法分别给出了图_n~2在n=4k(k≥2)、n=4k+2时的奇优美算法,在n=4k(k≥2)时,的奇强协调算法,进而证明了图_n~2在n=2k(k≥3)时是奇优美图,在n=4k(k≥2)时是奇强协调图等结论,从而推动了对图的奇优美性和奇强协调性的研究.最后提出猜想:当n=4k+2时,图_n~2不是奇强协调图.     

图Cn及其r-冠的新的优美标号

研究了关于图的r-冠的优美标号的一个问题,证明了：当n≡0,3（mod 4）时,图Cn及其r-冠是优美图,所给出的新的优美标号不同于现有文献中得到的结果.进而证明了当n≡0（mod 4）时,图Cn及其r-冠也是交错图.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

L－fuzzy集网的R－收敛性质

本文在ＬＦ拓扑空间中建立了Ｌ－ｆｕｚｚｙ集网的弱收敛（Ｒ－收敛）概念，应用文［４］中的Ｒ－闭包，系统讨论了它们的性质，证明了等式ＲｌｉｍＡ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ和ＲｌｉｍＡ＿ｎ＝Ａ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ并且给出了Ｌ－ｆｕｚｚｙ集网与其子网之间的关系。     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².