全有向图的幂敛指数

设D为有向图，T（D）为D的全有向图（Total-digraph),k(D)和p(D)分别为D的幂敛指数（Index of convergence)与周期（Period)，本文证明了。1，对任意非平凡有向图D,p(T(D))=1,k(T(D))≤max{2p(D)-1,2K(D) 1}，特别地，当D为本原有向图时，k(T(D))≤k(D) 1，当D不含有向圈时，k(T(D))=2k(D)-1；当D为有向圈Cn时，k(T(D))=2n-1.2。对任意非平凡强连通图D,k(T(D))≥Diam(D) 1。我们还证明了以上界是不可改进的最好界。     

连通的欧拉生成子图

本文证明了:若 G 是一个 p 个顶点的、2-边-连通简单图,其边数,q≥((p-4)/2)+7.则除 K_(2,5)外,G 有连通的欧拉生成子图.当 q=((p-4)/4)+6和 k(G)=2时,本文给出了全部6个极图.     

混合幂的除数和（英文）

令S_k(x)=∑d(n_1~2+n_2~2+n_3~k),3≤k∈N.1≤n_1,n_2≤x~(1/2)1≤n_3≤x~(1/k)本文得到了渐近公式S_k(x)=A(k)x~(1+1/k)logx+B(k)x~(1+1/k)+O(x~(1+1/k-δ(k)+ε)),这里A(k),B(k)是只与k有关的常数,δ(3)=5/(42),δ(4)=1/(16),δ(5)=1/(40),并且当6≤k≤7时δ(k)=1/(k2~(k-1)),当k≥8时δ(k)=1/(2k~2(k-1)).     

广义de Bruijn和Kautz有向图的距离控制数

对于任意的正整数(?),强连通图G的顶点子集D被称为距离(?)-控制集,是指对于任意顶点v(?)D,D中至少含有一个顶点u,使得距离dG(u,v)≤(?)．图G距离(?)- 控制数γe(G)是指G中所有距离(?)-控制集的基数的最小者．本文给出了广义de Bruijn 和广义Kautz有向图的距离(?)-控制数的上界和下界,并且给出当它们的距离2-控制数达到下界时的一个充分条件．从而得到对于de Bruijn有向图B(d,k)的距离2-控制数γ2(B(d,k))= ．在该文结尾,我们猜想Kautz有向图K(d,k)的距离2-控制数γ2(K(d,k))= .     

有向P2-路图的结构性质

一个有向图D的有向Pk-路图Pk(D)是通过把D中的所有有向k长路作为点集;两点u= x1x2…xk+1,v=y1y2…yk+1之间有弧uv当xi=yi-1,i=2,3,…,k+1.明显地,当k=1时Pk(D)就是通常的有向线图L(D).在[1,2]中,P2-路图得到完整刻画.在[3]中,Broersma等人研究了有向...     

一个素变量丢番图问题

设k和r是满足k≥3及r≥Ψ(k)+1的正整数,这里当3≤k≤4时,Ψ(k)=2~(k-1);而当k≥5时,Ψ(k)=1/2k(k+1).假定δ和ε是给定的足够小的正数,λ_1,λ_2,…,λ_(r+1)是不全同号且两两之比不全为有理数的非零实数.对于任意实数η与0σ2~(1-2k)/r-1,证明了:存在一个正数序列X→+∞,使得不等式|λ_1p_1~k+λ_2p_2~k+···+λ_rp_r~k+λ_(r+1)p_(r+1)+η|(max(1≤j≤r+1)p_j)~(-σ)有》■X~(■-(2~(1-2k))/(r-1)+ε组素数解(p_1,p_2,…,p_(r+1)),这里(δX)~(1/k)≤p_j≤X~(1/k)(1≤j≤r)及δX≤p_(r+1)≤X.这改进了之前的结果.     

有向图的L(j,k)数的上界

给定正整数j≥k,有向图D的一个L(j,k)-标号是指从V(D)到非负整数集的一个函数f,使得当x在D中邻接到y时|f(x)-f(y)|≥j,当x在D中到y距离为二时|f(x)-f(y)|≥k.f的像元素称为标号.L(j,k)一标号问题就是确定(?)j,k-数(?)j,k(D),这个参数等于(?) max{f(x)|x∈V(D)},这里f取遍D的所有L(j,k)-标号.本文根据有向图的有向着色数及最长有向路的长度来研究(?)j,k-数,证明了:(1)对任何有向着色数为(?)(D)的有向图D,(?)j,k(D)≤((?)(D)-1)j;(2)对任何最长有向路的长度为l的有向图D,如果不含有向圈或者D中最长有向圈长度为l 1,则(?)j,k(D)≤lj.并且这两个界都是可达的.最后我们对l=3的有向图给出了3j-L(j,k)-labelling的一个有效算法.     

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

有关Euler函数(n)的方程的正整数解

设(n)是Euler函数.主要研究了方程(xy)=3((x)+(y))的可解性问题,利用初等的方法给出了这一方程的所有的35组正整数解.对于任意素数k>3,(x,y)=(3k,4k),(4k,3k)是方程(xy)=k((x)+(y))的2个正整数解.证明了更为一般的结论:对于任意奇数k>3,当gcd(k,3)=1时,(x,y)=(3k,4k),(4k,3k)是方程(xy)=k((x)+(y))的2个正整数解.     

均衡二部图中含2k条指定边的k个独立圈及2-因子

得到了对于二部图G=(V_1,V_2;E),当|V_1|=|V_2|=n≥2k+1时的结果:对G中任意2k条独立边e_1,e_1~*,…,e_k,e_k~*,G中一定存在k个独立的4-圈C_1,C_2,…,C_k,使得对任意i∈{1,2,…,k}有{e_i,e_i~*}E(C_i).并在此基础上进一步证明了当|V_1|=|V_2|=n≥3k时若对任意两顶点x∈V_1,y∈V_2,都有d(x)+d(y)≥2n-k+1成立,则G有一个2-因子含有k+1个独立圈C_1,C_2,…,C_(k+1)使得对任意i∈{1,2,…,k}有{e_i,e_i~*}E(C_i)且|C_i|=4.     

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.     

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.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。     

Asymptotics of families of solutions of nonlinear difference equations

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.