高阶亚纯函数系数微分方程的解及其导数的不动点

研究了高阶线性微分方程f~(k)+A_(k-1)(z)f~(k-1)+…+A_1(z)f′+A_0(z)f=0的非零解f,及其一阶、二阶导数,f~(i)(i=1,2)的不动点性质,这里A_j(z)(j=0,1,…k-1)为亚纯函数,得到了若δ(∞,A_0)>0,且满足max{i(A1),i(A2),…,i(A_(k-1))}相似文献   

线性流形上双对称阵逆特征值问题

１．引言 令Ｒ表示所有ｎ×ｍ阶实对称阵集合,Ｒ＝Ｒ,Ｒ表示Ｒ中秩为ｒ的子集; ＯＲ是ｎ阶正交阵之集; Ａ＋表示Ａ的Ｍｏｏｒｓ－ｐｅｎｒｏｓｅ广义逆;Ｉｋ表示ｋ阶单位阵; ＳＲ表示 ｎ×ｎ表示ｎ阶实对称阵的全体; Ｒ（Ａ）表示 Ａ的列空间; Ｎ（Ａ）表示 Ａ的零空间; ｒａｎｋ（Ａ）表示 Ａ的秩,对 Ａ＝（ａｉｊ）, Ｂ＝（ｂｉｊ） Ｒ, Ａ＊ Ｂ表示 Ａ与 Ｂ的 Ｈａｄａｍａｒｄ乘积,其定义为 Ａ＊ Ｂ＝（ａｉｊ　ｂｉｊ）,并且定义 Ａ与 Ｂ的内积为（Ａ,Ｂ）＝ｔ,（ＢＡ）,由此内积导出的范数为（Ａ,Ａ）＝（ｔ,（Ａ…     

关于KAPLAN-MEIER估计的二阶EDGEWORTH展开

定义F={t>0,F(t)=1},设t<τ     

关于排队过程GI/E_k/l的若干結果

<正> §1.引言 采用Kendall的記号,所謂GI/E_k/1是指由下述条件規定的一个排队过程: (i)若用t_n表第n个顾客来到服务系统的时刻,而用ui=ti-t_(i-1)山表示相紕两顾客到达时刻間的間隔(簡称到达間隔),則这些u互相独立,并且服从同一分布     

一类Lyness方程解的性质

考虑差分方程xn+1=a+b0xn+b1xn-1+…+bk-1xn-(k-1)xn-k其中a,bi是非负实数,a+∑k-1i=0bi>0,k∈{1,2,…}.证明了当k+1为素数时,方程的任半环不超过(2k+2)项;当k+1为合数且只有一个bi≠0时,方程的任半环不超过2k+1+km+0 1项,其中m0=min{m m为k+1的大于1的因数}.结果部分回答了C.Darwen and W.T.Patula提出的公开问题.     

对Baker~[1]-Mahler~[2]一个定理的注记

<正> 对任意实数x,定义‖x‖=max(x-[x],[x]+1-x).设a_1,…,a_(k-1)是互不相等的非零整数,a是适合(a,a_1,…,a_(k-1)=1的正整数,r是正整数.置     

一类Y~(SG)(γλ,n)∪βS_n~G形图簇的伴随分解及其补图的色等价性

设G是m阶连同图,我们用S_n~G(n=km+1)表示把kG的每个分支的d_i度点分别与星图S_k+1的k个1度点重迭后得到的图,Y~(SG)(r_1n,n)表示把r_1S_n~G中每个分支的k度点依次与图的k度点邻接后得到的图,Y~(SG)(r_2λ_1,n)表示把τ_2Y~(SG)(τ_1n,n)中每个分支的r_1+k度点依次与图S_n~G的k度点邻接后得到的图,若k≥3,用Y~(sG)(r_kλ__(k-1),n)表示把τ_kY~(sG)(r_(k-1)λ_(k-2),n)中每个分支的τ_(k-1)+k度顶点依次与图S_n~G的k度点邻接后得到的图,这里λ_k=r_kλ_(k-1)+n.运用图的伴随多项式的性质,证明了一类新的图簇Y~(sG)(r_kλ__(k-1),n)∪β_kS_n~G的伴随多项式的因式分解定理,进而得到了这类图的补图的色等价图.     

关于整数和集的定理的推广

本文主要利用加性数论的理论考察整数和集,稚广了Vscvolod F．Lev的关于整数和的定理：设n≥1,B增包含[1,n],｜B｜〉n/4,k=｜B｜＋1,则 （1）当1≤n≤2k-3时,有ia^s能写成两个不同B中元之和。 （2）当2k-2≤,1〈3k-3时,有ia^s能写成最多四个B中元之和。 （3）当3k-3≤n〈4k-4时,有ia^s能写成最多2h个B中元之和。 其中h=max[2k/4k-4-n],i=1,2,3,4,6     

一类非线性微分方程空间周期解的存在性及唯一性

利用Bendixson-Dulac定理,讨论系统     

Hammerstein型非线性积分方程正解的个数

<正> 本文是作者工作[8]、[9]的继续.在[9]中作者利用Leray-Schauder拓扑度理论研究了多项式型Hammerstein非线性积分方程的固有值,即设     

Codegree Threshold for Tiling k-graphs with Two Edges Sharing Exactly ℓ Vertices

Given integer k and a k-graph F,let t(k-1)(n,F)be the minimum integer t such that every k-graph H on n vertices with codegree at least t contains an F-factor.For integers k>3 and 0≤l≤k-1,let y(k,l)be a k-graph with two edges that shares exactly l vertices.Han and Zhao(J.Combin.Theory Ser.A,(2015))asked the following question:For all k≥3,0≤l≤k-1 and sufficiently large n divisible by 2 k-l,determine the exact value of t_k-1(n,y(k,l)).In this paper,we show that t(k-1)(n,y(k,l))=n/(2 k-l)for k>3 and 1≤l≤k-2,combining with two previously known results of R?dl,Rucinski and Szemeredi(J.Combin.Theory Ser.A,(2009))and Gao,Han and Zhao(Combinatorics,Probability and Computing,(2019)),the question of Han and Zhao is solved completely.     

AN INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES

Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk+1,nA new inverse eigenvalues problem has put forward as follows: How do we construct anunreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: theeigenvalues of T1,n, the eigenvalues of Ti,k-1 and the eigenvalues of Tk+1,n?Namely if we only know the data: A1, A2, An,how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm ofsolving such problem, are given in this paper.     

高阶复微分方程关于迭代级的辐角分布

设Aj是整函数(j=0,1,…,k-2),其中i(A0)=p,i(Aj)＜p,或σp(Aj)＜σp(A0)(j=1,2,…,k-2),0＜p＜+∞.本文研究微分方程f(k)+Ak-2f(k-2)+…+A0f=0(k≥2)解的辐角分布并得出零点聚值线和Borel方向之间的关系.所得结论推广了先前的结果.     

COMPUTING THE NEAREST BISYMMETRIC POSITIVE SEMIDEFINITE MATRIX UNDER THE SPECTRAL RESTRICTION

Let A and C denote real n × n matrices. Given real n-vectors x1, ... ,xm, m ≤ n, and a set of numbers L = {λ1,λ2,... ,λm}. We describe (I) the set (?) of all real n × n bisymmetric positive seidefinite matrices A such that Axi is the "best" approximate to λixi, i = 1,2,...,m in Frobenius norm and (II) the Y in set (?) which minimize Frobenius norm of ||C - Y||.An existence theorem of the solutions for Problem I and Problem II is given and the general expression of solutions for Problem I is derived. Some sufficient conditions under which Problem I and Problem II have an explicit solution is provided. A numerical algorithm of the solution for Problem II has been presented.     

一般退化时滞差分系统解的存在性及通解

本文研究退化时滞差分系统Ex(k+ 1)= Ax(k)+ ∑li= 1Bix(k- i)+ f(k) (k= 0,1,2,…),x(k)= φ(k) (k= 0,- 1,- 2,…,- l),其中E、A、Bi∈Rm ×n,x(k)∈Rn,f(k)∈Rm ,rank(E)< n.给出了上述系统解的存在性条件及通解表达式.     

On approximation of smooth functions from null spaces of optimal linear differential operators with constant coefficients

For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln(ψ) = n ∑ k=0 akψ(k), where the constant coefficients ak ∈ R may be adapted to f . We prove that for each f ∈ C(n)(I), there is a selection of coefficients {a1, ,an} and a corresponding linear combination Sn( f ,t) = n ∑ k=1 bkeλkt of functions ψk(t) = eλkt in the nullity of L which satisfies the following Jackson’s type inequality: f (m) Sn(m )( f ,t) ∞≤ |an|2n|Im|1/1q/ep|λ|λn|n|I||nm1 Ln( f ) p, where |λn| = mka x|λk|, 0 ≤ m ≤ n 1, p,q ≥ 1, and 1p + q1 = 1. For the particular operator Mn(f) = f + 1/(2n) f(2n) the rate of approximation by the eigenvalues of Mn for non-periodic analytic functions on intervals of restricted length is established to be exponential. Applications in algorithms and numerical examples are discussed.     

一类加强不等式的推广

本文给出了 n个正数 x1 ,x2 ,… ,xn 的如下不等式 :∏nk=1( xαk+x-αk )≥ ( Aαn( x) +A-αn ( x) ) n ,每个 xk≤ xα,∏nk=1( xαk+x-αk )≤ ( Aαn( x) +A-αn ( x) ) n ,每个 xk≥ e.其中 α>0 ,xα=[4α2 +1 +2 α]12α ,常数 e=2 .71 81 82 81 8… ,An( x) =1n∑nk=1xk.     

一类Clifford半群的刻画

G是一个群,I是一个指标集.令CG=G×I={(g,i):g∈G,i∈I};(a,i)(b,j)=(ab,k)with k=min{i,j}则CG是一个半群.事实上,CG是Clifford半群,并且CG代表了一类特殊的Clifford半群.     

复合型脆断的应变能判据

本文提出一个十分简单的复合型脆断判据,即应变能判据。该判据可以表示成:(K_Ⅰ/K_Ⅰc)2+(K_Ⅱ/K_ⅡC)2+(K_Ⅲ/K_ⅢC)2=1,它与文献中的实验数据非常一致,是一个实用的判据。本文还提出一个经验判据:(K_Ⅰ/K_Ⅰc)m+(K_Ⅱ/K_ⅡC)n=1,1≤≤2。     

关于正定厄米特矩阵的一个不等式的推广

本文推广了正定厄米特矩阵的一个不等式 ,得到以下结果 :设 A( i) ,B( i) ,… ,C( i) ( i=1 ,2 ,… ,m)都是 n阶正定厄米特矩阵 ,A( i)11,B( i)11,… ,C( i)11为其相应矩阵的 k阶顺序主子阵 ,1≤ k≤ n-1 ,α,β,… ,γ都是正实数 ,且 α+β+… +γ=p≥ 1 ,则有∑mi=1|A( i) |α|A( i)11|α,|B( i) |β|B( i)11|β… |C( i) |γ|C( i)11|γ) <∑mi=1A( i) α∑mi=1A( i)11α.∑mi=1B( i) β∑mi=1B( i)11β…∑mi=1C( i) γ∑mi=1C( i)11γ