L~2[0,1]上的正交小波基

从尺度因子 M =4的正交小波基出发 ,利用折叠方法得到了 L 2 [0 ,1 ]空间的正交小波基 .这种小波不同于折叠前的小波基 ,它是完全限制在有限区间 [0 ,1 ]上 ,且保持小波基的正交性 ,并在使用过程中拥有更大的灵活性 .也可用类似方法对一般尺度小波进行折叠     

BKW-operators on the interval [0,1]

Uniqueness sets inC([0, 1]) are studied for test functions {1,t,…,t ⁿ}. As an application, we investigateBKW-operators on the interval [0,1].     

Wentzell-Robin boundary conditions on C[0,1]

Given a ∈ C ¹[0,1], a(x) ≥ α > 0, we prove that the second order differential operator on C[0,1] defined by A _W u := (au′)′ with Wentzell-Robin boundary conditions $$\left( {au'} \right)^\prime \left( j \right) + \beta _j u'\left( j \right) + \gamma _j u\left( j \right) = 0, j = 0,1,$$ where β _j and γ _j are real numbers, generates a holomorphic C ₀-semigroup on C[0,1].     

[0,1]-拓扑空间中的Starplus-连通性

本文在I-拓扑空间中引入Starplus-连通性的概念,并且研究它的性质.借助于水平拓扑,得到了下面结果:Starplus-连通性是一般拓扑学中连通性的好推广而且被连续映射保持.一个Starplus-连通的模糊集一定是O-连通的.另外,模糊单位区间和模糊实直线是Starplus-连通的.     

A family of Bernstein quasi-interpolants on [0,1]

Suppose that we want to approximate f∈C[0,1] by polynomials inP, using only its values on X_n={i/n, 0≤i≤n}. This can be done by the Lagrange interpolant L_n f or the classical Bernstein polynomial B_n f. But, when n tends to infinity, L_n f does not converge to f in general and the convergence of B_n f to f is very slow. We define a family of operators B _n ^(k) , n≥k, which are intermediate ones between B _n ⁽⁰⁾ =B _n ⁽¹⁾ =B_n and B _n ⁽ⁿ⁾ =L_n, and we study some of their properties. In particular, we prove a Voronovskaja-type theorem which asserts that B _n ^(k) f−f=O(n^−[(k+2)/2]) for f sufficiently regular. Moreover, B _n ^(k) f uses only values of B_n f and its derivaties and can be computed by De Casteljau or subdivision algorithms.     

论域为区间[0,1]上的三角形模糊数的比较

利用包含度(小于度)理论,建立了一个全新的模糊数之间的关系,即,“β-小于等于”关系。研究了其相关性质,并且在此基础上讨论了论域为区间[0,1]上的三角形模糊数的比较。最后利用β-小于等于关系给出了模糊线性规划问题的一种新解法。     

Wentzell-Robin Boundary Conditions on C [0,1]

   Abstract. Given a∈ C ¹ [0,1], a(x)≥ α >0 , we prove that the second order differential operator on C[0,1] defined by A _W u:=(au')' with Wentzell-Robin boundary conditions

闭区间[0,1]上的分形插值函数的分数阶积分

介绍了分形插值函数和迭代函数系统以及v阶黎曼-刘准尔分数阶积分的概念及相关定理.利用这些概念及定理讨论了分形插值函数的分数阶积分在[0,1]上连续性及判定[0,1]上的分形插值函数的分数阶积分也是[0,1]上的分形插值函数,并给予了证明.     

[0,1]区间上的r重正交多小波基

本文利用L2（R）上的紧支撑正交的多尺度函数和多小波构造出有限区间[0,1]上的正交多尺度函数及相应的正交多小波.本文构造的逼近空间Vj[0,1]与相应的小波子空间Wj[0,1]具有维数相同的特点,从而给它的应用带来巨大方便.最后给出重数为2时的[0,1]区间上的正交多小波基构造算例.     

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.     

ESTIMATES OF LINEAR RELATIVE n-WIDTHS IN L~p [0,1]

In this paper we will show that if an approximation process { L n }n ∈ N is shapepreserving relative to the cone of all k-times differentiable functions with non-negative k-th derivative on [0,1],and the operators L n are assumed to be of finite rank n,then the order of convergence of D k L n f to D k f cannot be better than n 2 even for the functions x k,x k+1,x k+2 on any subset of [0,1] with positive measure.Taking into account this fact,we will be able to find some asymptotic estimates of linear relative n-width of sets of differentiable functions in the space L p [0,1],p ∈ N.     

Nonstandard Analysis Methods for Separations in [0,1]-topological Spaces

In nonstandard enlargement,the separations are characterized by non-standard analysis methods in [0,1]-topological spaces.Firstly,the monads of fuzzy point in [0,1]-topological spaces are described wit...     

R_0-代数[0,1]的子代数与广义重言式

本文是对修正的Kleene系统中广义重言式理论的推广,讨论了R_0-代数[0,1]的各类无限子R_0-代数中的广义重言式,证明了在子R_0-代数E_2中,中存在着可数多个不同的广义重言式。     

Nonstandard Analysis Methods for Separations in[0,1]-topological Spaces

In nonstandard enlargement,the separations are characterized by nonstandard analysis methods in[0,l]-topological spaces.Firstly,the monads of fuzzy point in[0,l]-topological spaces are described with remote-neighborhoods in nonstandard enlarged model.Then the nonstandard characterizations of separations in [0,l]-topological space are given by the monads.At last,relations of these separations are investigated.     

The law of the iterated logarithm in C[0,1]

The law of the iterated logarithm is proved for C[0,1] valued random variables under conditions related to those used to establish the central limit theorem.Supported in part by NSF Grant GP 18759.     

THE GLOBAL APPROXIMATION BY LEFT-BERNSTEIN-DURRMEYER QUASI-INTERPOLANTS IN Lp[0,1]

In this paper, we will use the 2r-th Ditzian-Totik modulus of smoothness wψ2r(f,t)p to discuss the direct and inverse theorem of approximation by Left-Bernstein-Durrmeyer quasi-interpolants Mn[2r-1]f for functions of the space Lp[0,1] (1≤ p≤ +∞).     

The existence of invariant measures forC[0,1]-valued diffusions

Summary We prove the existence of an invariant measure for processes arising from a perturbation of theC[0,1]-valued Ornstein-Uhlenbeck process with a drift taking values in the Cameron-Martin space. We study the infinitesimal generator, and a partial integration onC[0,1] will yield conditions on the drift which enable us to use arguments of perturbation theory to prove the existence of an invariant measure which is absolutely continuous with respect to the Wiener measure.