Some Results Concerning Growth of Polynomials

Let P(z) be a polynomial of degree n having no zeros in |z|< 1, then for every real or complex number β with |β|≤ 1, and |z|=1, R ≥ 1, it is proved by Dewan et al. [4] that ︱P(Rz)+ β( R+1/2 )n P(z)︱≤ 1 /2 { (︱Rn + β(R+1/2 )n︱+︱1+ β (R + 1 /2 )n︱) max |z|=1 |P(z)︱-(︱Rn + β (R+1/2 )n︱-︱1+ β(R+1/2 )n︱) min|z|=1 |P(z)︱}.In this paper we generalize the above inequality for polynomials having no zeros in |z|相似文献   

一类无向Kautz图的k限制边连通度的上界

在Moor-Shannon网络模型中,k限制边连通度较大的网络一般有较好的可靠性和容错性.本文在无向Kautz图UK(2,n)中研究k限制边连通度的上界ξk,证明了ξ5(UK(2,3))=6,ξ5(UK(2,n))=8,n≥4,且当4≤k≤n时,ξk(UK(2,n))≤2(k-「k/3」).     

一道竞赛题的解答及推广

问题 证明:对任意正整数n,2n/3n+1≤3n∑k=n+1 1/k≤3n+1/4(n+1)成立.(2001年爱尔兰数学奥林匹克试题).     

中心对称本原矩阵的k点指数集

Let G = (V, E) be a primitive digraph. The vertex exponent of G at a vertex v ∈ V, denoted by expG(v), is the least integer p such that there is a v → u walk of length p for each u ∈ V. We choose to order the vertices of G in the k-point exponent of G and is denoted by expG(k), 1 ≤ k ≤ n. We define the k-point exponent set E(n, k) := {expG(k)| G = G(A) with A ∈ CSP(n)}, where CSP(n) is the set of all n × n central symmetric primitive matrices and G(A) is the associated graph of the matrix A. In this paper, we describe E(n,k) for all n, k with 1 ≤ k ≤ n except n ≡ 1(mod 2) and 1 ≤ k ≤ n - 4. We also characterize the extremal graphs when k = 1.     

P(n，k)的计数及其良域

设P(n,k)为整数n分为k部的无序分拆的个数,每个分部≥1;P(n)为n的全分拆的个数.P(n,k)是用途广泛的、且又十分难予计算的数.本文证明了下述定理：当n＜k,P(n,k)=0;当k≤n≤2k,P(n,k)=P(n-k);当k=1,4≤n≤5,或者当k≥2,2k+1≤n≤3k+2,P(n,k)=P(n-k)-(?)P(t)还定义了P(n,k)的良城,因面可借助若干个P(n)的值,迅速地计算大量的P(n,k)的值.     

On Some Cycles in Wenger Graphs

Let p be a prime,q be a power of p,and let Fq be the field of q elements.For any positive integer n,the Wenger graph Wn(q)is defined as follows:it is a bipartite graph with the vertex partitions being two copies of the(n+1)-dimensional vector space Fq^n+1,and two vertices p=(p(1),…,p(n+1))and l=[l(1),…,l(n+1)]being adjacent if p(i)+l(i)=p(1)l(1)i-1,for all i=2,3,…,n+1.In 2008,Shao,He and Shan showed that for n≥2,Wn(q)contains a cycle of length 2 k where 4≤k≤2 p and k≠5.In this paper we extend their results by showing that(i)for n≥2 and p≥3,Wn(q)contains cycles of length 2k,where 4≤k≤4 p+1 and k≠5;(ii)for q≥5,0相似文献   

具有固定行列和k的阶为2k-2的(0,1)-矩阵的最大跳跃数

1992年Brualdi与Jung首次引出了最大跳跃数M(n,k),即每行每列均含k个1的阶为n的(0,1)-矩阵的跳跃数的极大数,给出了满足条件1≤k ≤n ≤10的(0,1)-矩阵的最大跳跃数M(n,k)的一个表,并提出了几个猜想,其中包括猜想M(2k-2,k)=3k-4 [k-2/2].本文证明了当k≥11时,对每个A∈∧(2k-2,k)有b(A)≥4.还得到了该猜想的另一个反例.     

半群O_n(k)的秩

设O_n是有限链[n]上的保序变换半群.对任意1≤k≤n-1,研究半群O_n(k)={α∈O_n:(x∈[n]x≤k→xα≤k}的秩和幂等元秩,证明了半群O_n(k)的秩为2n-3.进一步,得到了半群O_n(k)(2≤k≤n-1)的幂等元秩为n和半群O_n(1)的幂等元秩为n-1.     

一类本原无向图的广义上指数的极图

设R（n,d)表示由全体恰含d个环点的n(n≥3）阶本原无向图所构成的集合,F(n,d,k)为R(n,d)中图的第k重上广义本原指数的量大值,1≤d≤n,2≤k≤n-1。本文给出了第k重上广义本原指数达到F(n,d,k)的极图的完全刻画。     

恰有k个悬挂点的n阶双圈和三圈图的拟拉普拉斯谱半径

设k,n为两个确定的正整数.本文得到了当1≤k≤n-7时恰有k个悬挂点的n阶连通三圈图的最大拟拉普拉斯谱半径的唯一极图,也得到了当1≤k≤n-5时恰有k个悬挂点的n阶连通双圈图的最大拟拉普拉斯谱半径的唯一极图.     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.     

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。