S[a,b]类中边界Nevanlinna-Pick插值(Ⅱ)

继续作者最近的研究,用所谓的Hankel向量方法建立S[a,b]函数类中带边界插值数据的Nevanlinna-Pick插值问题与[a,b]上的某种带约束条件的Hausdorff矩量问题之间解集之间明确的一一对应关系.通过N[a,b]函数类与S[a,b]函数类之间的联系,从而由BNP(N[a,b])问题的可解性准则和解的参数化描述获得BNP(S[a,b)问题的可解性准则和解的参数化表示.     

E_m函数类中Nevanlinna-Pick插值与广义Stieltjes矩量问题

令E\-m=(-∞,∞)＼∪[DD(]m[]j=1[DD)](α\-j,β\-j).函数类[WTHT]N[WTBX](E\-m)表示在上半复平面解析且虚部非负,在诸(α\-j,β\-j)(j=1,…,m)内解析且为实值的函数全体.该文用Hankel 向量方法建立[WTHT]N[WTBX](E\-m)函数类 中含有限(或无限可数)插值点的Nevanlinna Pick 问题与集合E\-m上 相关的非标准截断(或全)广义Stieltjes 矩量问题解集之间的一一对应.用类似于Riesz的办法建立E\-m上非标准截断广义Stieltjes矩量问题的可解性准则,从而获得了[WTHT]N[WTBX](E\-m)函数类中Nevanlinna Pick问题的可解性准则.     

一类具有对称与中心对称性的有理函数双边留数插值问题

获得了在Sl^(s)[a,b]函数类中具有对称与中心对称性质的矩阵值两边留数插值问题的可解性条件。给出该问题所有解的一个线性分式变换表达形式．所用的方法是构造相同的矩阵函数作为线性分式变换的系数矩阵。     

再生核构造的一种新方法

本文利用微分算子插值样条函数的方法给出了W12[a,b]空间再生核构造的新方法,证实了求解微分方程边值问题的方法([1]再生核空间数值分析[M].科学出版社,2004),其实是本文方法的一种特例.     

最小度和[a,b]-对等图

既是[a,b]-覆盖又是[a,b]-消去的图称为[a,b]-对等图.本文研究了最小度和[a,b]-对等图之间的关系,给出了一个图是[a,b]-对等图的关于最小度的充分条件.     

图有[a,b]因子的邻域条件

不含有图K1，R的图称为K1,r-free图，设G是一个具有顶点集V（G）的图，设n(≥3),a和b是整数，使得b≥a≥1，若b是奇数，设b≥n-1。我们证明了每个连通的K1,r-free图G在b|V(G)|为偶数，它的最小度至少是a n-1,|V(G）≥ （2(a b)-1)(a b-1)/b，以及|NG(x）∪NG（y)|≥a|V(G)|a b对V的任意两个不邻接的点x和y都成立时，G有一个[a,b]因子。     

独立数与最小度和[a，b]-因子

设G是一个图,a,b是整数且0≤a≤b,G的一个支撑子图F称为一个[a,b]-因子,若对任意的v∈V(G)有a≤dF(v)≤b.在本文中,我们给出了图存在[a,b]-因子涉及到独立数和最小度的一个充分条件,推广了前人的结果.     

Degree Conditions for k-Hamiltonian [a,b]-factors

Let a,b,k be nonnegative integers with 2≤a相似文献   

[a,b]-因子存在性的范-型条件

设G是一个图,a,b是整数且满足0≤a≤b.如果存在G的一个支撑子图F,使对任意的x∈V(G)有a≤d_F(x)≤b,则称F是G的一个[a,b]-因子.本文给出图中具有特定性质的[a,b]-因子的范-型条件.进一步指出这个结果是最好的.     

[a,b]-对等图的范-型条件

既是[a,b]-覆盖又是[a,b]-消去的图称为[a,b]-对等图.设1≤aan+1a+b,则G为[a,b]-对等图.给出了一个图是[a,b]-对等图的关于范-型条件及邻域并的若干充分条件,并指出定理中的条件在一定意义上是最好可能的.     

POSITIVE SOLUTIONS TO(k,n-k) NONHOMOGENEOUS BOUNDARYVALUE PROBLEM

By the Schauder fixed point theory,this paper establishes the existence of positive solutions to a(k,n k) m-point boundary value problem.We show that there exists a positive constant b such that the problem has at least one positive solution when the homogeneous boundary parameter is smaller than b,and no positive solution when this parameter is greater than b.     

Toughness and [a,b]-factors with inclusion/exclusion properties

In this paper, we investigate the existence of [a,b]-factors with inclusion/exclusion properties under the toughness condition. We prove that if an incomplete graph G satisfies t(G) (a-1) + ab and a,b are two integers with b > a > 1, then for any two given edges e1 and e2, there exist an [a,b]-factor including e1,e2; and an [a,b]-factor including e1 and excluding e2; as well as an [a,b]-factor excluding e1,e2 unless e1 and e2 have a common end in the case of a = 2. For complete graphs, we obtain a similar r...     

Extremal points and optimal solutions for general capacity problems

This paper studies the infinite dimensional linear programming problems in the integration type. The variable is taken in the space of bounded regular Borel measures on compact Hausdorff spaces. It will find an optimal measure for a constrained optimization problem, namely a capacity problem. Relations between extremal points of the feasible region and optimal solutions of the optimization problem are investigated. The necessary/sufficient conditions for a measure to be optimal are established. The algorithm for optimal solution of the general capacity problem onX = Y = [0, 1] is formulated.     

集值映射的广义对称向量拟平衡问题

本文提出了一类集值映射的广义对称向量拟平衡问题．利用非线性标量化函数,分别在局部凸Hausdorff拓扑向量空间和一般的Hausdorff拓扑向量空间中,证明了广义对称向量拟平衡问题解的存在性定理．     

A blow-up criterion for 3D compressible viscoelastic flow with large initial data

In this paper, we consider a Cauchy problem for the three-dimensional compressible viscoelastic flow with large initial data. We establish a blow-up criterion for the strong solutions in terms of the gradient of velocity only, which is similar to the Beale-Kato-Majda criterion for ideal incompressible flow (cf. Beale et al. (1984) [20]) and the blow-up criterion for the compressible Navier-Stokes equations (cf. Huang et al. (2011) [21]).     

关于双曲型方程解的爆破

在RNR+(N2)中考虑非线性双曲型方程 utt-DI(aij(x)Dju)=|u|p-1u.Kato1980年证明了当1<p [SX(]N+1[]N-1[SX)]时,Cauchy问题的解可能在有限时刻爆破.本文使用不同的方法估计, 把Kato的结果改进为1<p<[SX(]N+3[]N-1[SX)].     

Error estimates for oscillatory solutions to hyperbolic systems of conservation laws

This paper deals with oscillatory solutions of one dimensional syterns of conservation laws endowed with one linearly degenerate characteristic field. Recently, Weinan E (cf. [3]) and D. Sene (cf. [11]) derived a system of homogenized equations, by using a multiple scale analysis. Our goal is to prove rigourous error estimates in order to justify the validity of these equations, at least when initial data are smooth.