计算周期三对角矩阵行列式和逆矩阵的新算法

给出了一种计算周期三对角矩阵行列式和逆矩阵的新递推算法,它们的运算复杂度分别为O(n)和O(n2),该算法是文献[5]和[6]中相关算法的拓广.     

[0,1]上带参数光滑自映射不动点的图论性质及其应用

设f:I×I是光滑的,f=f(x,y),I=[o,1],y为参数,本文证明f的不动点组成的图有连通分枝.作为应用,给出了二维Brouwer不动点定理的新证明.这是迄今为止最直接的证明.,The graph properties of the fixed points of a continuous self-mapping on unit closed interval with a parameter were studied. The existence of some kind of connected branch was shown. By this result, a new proof of two dimensional Brouwer's fixed point theorem was given.     

The connectivity of a graph on uniform points on [0,1]

A random graph G_n(x) is constructed on independent random points U₁,…,U_n distributed uniformly on [0,1]^d, d1, in which two distinct such points are joined by an edge if the l_∞-distance between them is at most some prescribed value 0<x<1. The connectivity distance c_n, the smallest x for which G_n(x) is connected, is shown to satisfy

(1)

For d2, the random graph G_n(x) behaves like a d-dimensional version of the random graphs of Erdös and Rényi, despite the fact that its edges are not independent: c_n/d_n→1, a.s., as n→∞, where d_n is the largest nearest-neighbor link, the smallest x for which G_n(x) has no isolated vertices.     

Topological Structure of Non-wandering Set of a Graph Map

Let G be a graph （i.e., a finite one-dimensional polyhedron） and f ： G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non-wandering point; every accumulation point of the set of non-wandering points of f with infinite orbit is a two-order accumulation point of the set of recurrent points of f; the derived set of an ω-limit set of f is equal to the derived set of an the set of recurrent points of f; and the two-order derived set of non-wandering set of f is equal to the two-order derived set of the set of recurrent points of f.     

An optimal sequential algorithm for the uniform approximation of convex functions on [0,1]2

In this paper an algorithm is given for the sequential selection ofN nodes (i.e., measurement points) for the uniform approximation (recovery) of convex functions over [0, 1]², which has almost optimal order global error, (≦c ₁ N ^?1 lgN), over a naturally defined class of convex functions. This shows the essential superiority of sequential algorithms for this class of approximation problems because any simultaneous choice ofN nodes leads to a global error >c ₀ N ^?1/2. New construction and estimation methods are presented, with possible (e.g., multidimensional) generalizations.     

The norm of the Riemann-Liouville operator on Lp[0,1]: a probabilistic approach

We obtain explicit lower and upper bounds for the norm of theRiemann–Liouville operator V^s on L^p[0, 1] which are asymptoticallysharp, thus completing previous results by Eveson. Similar statementsare shown with respect to the norms ||V^s f||_p, whenever f satisfiescertain smoothness properties. It turns out that the correctrate of convergence of ||V^s f||_p as s depends both on theinfimum of the support of f and on the degree of smoothnessof f. We use a probabilistic approach which allows us to giveunified proofs.     

求数列极限的两个定理

本文给出关于数列极限的两个定理 .     

树映射的单侧γ-极限点集与拓扑熵

本文讨论了树映射的单侧γ-极限点集与吸引中心的关系，得到了树映射具有正拓扑熵的几个等价条件．此外，还得到了树映射是强非混沌以及逐片单调树映射的拓扑熵为零的几个等价条件．     

The Existence of a Waver Point on the Omitted Arc of a Support Point of the Class S

The purpose of this article is to present new information about the geometry of the omitted arc of a support point of the class S. We provide an example of an omitted arc whose tangent vector reverses direction from clockwise to counterclockwise at an interior point of the arc.     

Counterexample to a Conjecture on the Algebraic Limit Cycles of Polynomial Vector Fields

In Geometriae Dedicata 79 (2000), 101–108, Rudolf Winkel conjectured: for a given algebraic curve f=0 of degree m 4 there is in general no polynomial vector field of degree less than 2m -1 leaving invariant f=0 and having exactly the ovals of f=0 as limit cycles. Here we show that this conjecture is not true. Mathematics Subject Classifications (2000). Primary 14P25, 34C05, 34A34.     

Some properties of the injective tensor product of L[0,1] and a Banach space

Let X be a (real or complex) Banach space and 1<p,p′<∞ such that 1/p+1/p′=1. Then , the injective tensor product of L^p[0,1] and X, has the Radon-Nikodym property (resp. the analytic Radon-Nikodym property, the near Radon-Nikodym property, contains no copy of c₀, is weakly sequentially complete) if and only if X has the same property and each continuous linear operator from L^p′[0,1] to X is compact.     

An Equivalent Theorem on Connectedness of the Weakly Cone-Efficient Sets

利用连通集上有关上半连续点集映射的连通性质，本文证明了拓扑向量空间中向量最优化问题的弱锥－有效解集与相应目标空间中的弱锥－有效点集连通性之间的一个等价定理．     

洛必达(L’Hospital)法则在求[1~∞]型极限中的应用

给出了求不定式[1∞]型极限的一个定理,同时通过历年考研试题的应用,说明此定理是有效的、简单的.     

解析辊拔问题的变上限与参变量积分

本文建立与Ａｖｉｔｚｕｒ不同的直角坐标系速度场与应变速率场，并采用变上限积分与参变量积分获得辊拔力的上界解析解。     

On the Limit as the Density Ratio Tends to Zero for Two Perfect Incompressible Fluids Separated by a Surface of Discontinuity

We study the asymptotic limit as the density ratio ρ^?/ρ⁺ → 0, where ρ⁺ and ρ^? are the densities of two perfect incompressible 2-D/3-D fluids, separated by a surface of discontinuity along which the pressure jump is proportional to the mean curvature of the moving surface. Mathematically, the fluid motion is governed by the two-phase incompressible Euler equations with vortex sheet data. By rescaling, we assume the density ρ⁺ of the inner fluid is fixed, while the density ρ^? of the outer fluid is set to ε. We prove that solutions of the free-boundary Euler equations in vacuum are obtained in the limit as ε → 0.     

基于有限集[N]上相交关系构作的二元等重码

对于自然数s,r,k,N,0＜s≤r＜k≤N,根据基集[N]={1,2,…,N}上两个不同子集的相交关系构作了一个关联矩阵,证明了这个关联矩阵是一个二元等重码,给出了它成为最佳等重码的条件,研究了它的检错性.     

Tensor Fields of Type (0, 2) on the Tangent Bundle of a Riemannian Manifold

To any (0, 2)-tensor field on the tangent bundle of a Riemannian manifold, we associate a global matrix function. Based on this fact, natural tensor fields are defined and characterized, essentially by means of well-known algebraic results. In the symmetric case, this classification coincides with the one given by Kowalski–Sekizawa; in the skew-symmetric one, it does with that obtained by Janyka.     

Limit behaviour of the solution of an evolution boundary‐value problem involving the p‐Laplacian operator for the case of an equivalued condition on a shrinking surface

In this paper, we discuss the limit behaviour of the solution of an evolution boundary‐value problem involving the p‐Laplacian operator for the case of an equivalued condition on a shrinking surface. Copyright © 2004 John Wiley & Sons, Ltd.     

图的[a,b]-因子存在性的两个结果

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≤dF(x)≤b,则称F是G的—个[a,b]-因子.本文给出图中具有特定性质的[a,b]-因子的两个充分条件.