二元对角向量值有理插值的算法

首先提出了二元对角向量值有理插值问题,它包括主对角和副对角两种向量值有理插值,并分别给出了主对角线和副对角线上向量值有理插值的两种算法,即直接求系数bi,j的算法和基于Samelson广义逆所定义的特殊初等变换的矩阵算法.然后构造了在预给极点情况下求主对角线和副对角线上向量值有理插值的矩阵算法.最后给出多个数值例子说明上述算法的有效性.     

高阶导数切触有理插值算法

已有关于高阶导数有理插值方法的研究大都是基于广义范德蒙逆矩阵的思想,计算复杂度较高.本文利用埃米特插值基函数的方法和多项式插值的误差性质,给出一种满足高阶导数插值条件的切触有理插值算法,并且适用于向量值切触有理插值及插值重度不相等的情形,解决切触有理插值函数的存在性及算法复杂性问题.较之其他算法,具有计算复杂度较低,便于实际应用等特点.最后通过数值例子说明该算法的有效性.     

矩形网格上的二元切触有理插值

二元切触有理插值是有理插值的一个重要内容,而降低其函数的次数和解决其函数的存在性是有理插值的一个重要问题.二元切触有理插值算法的可行性大都是有条件的,且计算复杂度较大,有理函数的次数较高.利用二元Hermite（埃米特）插值基函数的方法和二元多项式插值误差性质,构造出了一种二元切触有理插值算法并将其推广到向量值情形.较之其它算法,有理插值函数的次数和计算量较低.最后通过数值实例说明该算法的可行性是无条件的,且计算量低.     

切触有理插值函数的新算法

切触有理插值函数的算法大都是基于连分式进行的,其算法的可行性大都是有条件的,且有理函数次数较高,计算量较大.文章利用拉格朗日插值的性质和分段组合的方法,给出了一种新的切触有理插值算法,并给出误差估计且将其推广到向量值切触有理插值情形.较之其他算法,具有有理函数次数较低、计算量较小、算法无条件性、无极点、满足高阶导数插值条件等优点.     

向量值有理插值存在性的一种判别方法

对于向量值有理插值的计算,目前已经有多种求解算法.但其存在性的判别方法及其证明在现有的文献中还没有见到.这里利用标量有理插值函数插值存在性的思想,引入Newton基函数,给出并证明了向量值有理插值存在性的一种判别方法.同时给出有理插值函数的分子和分母的显式表达式,最后的实例说明了它的有效性.     

三元向量值混合有理插值及其算法

本文第一节利用 Samelson逆、混合偏差商以及 Thiele-型分叉连分式构造三元向量值混合有理插值 ,第二节给出了一种计算三元向量值混合有理插值的算法 ,第三节给出了一个数值例子 .     

二元向量值有理插值存在性的一种判别方法

文章给出了对于矩形网格上基于二元Newton插值公式的二元向量值有理插值存在性的充要条件.在存在的情况下,建立了具有显式表达式的不同于向量连分式的二元向量值有理插值函数,并且这种方法具有承袭性.最后给出的实例说明了这种算法的有效性.     

基于向量值有理插值的最优预测算法研究及陶瓷需求量预测的应用

通过对高维数据整体表达式建模预测方法和分区间等预测算法的缺陷分析,提出基于向量值有理插值的最优预测算法,通过有理向量插值函数和各分量的误差限得到向量之间的相似性,克服了其它很多算法利用向量的整体表达式方法而产生预测的偏差;另外,通过向量的误差限与训练样本所得向量值有理插值函数及迭代仿真方法来确定预测样本向量所对应的最优预测值.通过实例,算法所得预测值的精度比其他算法更高,并且分析了误差限和迭代步长对算法性能的影响.     

三元向量值混合有理插值及其算法

本第一节利用Samelson逆,混合偏差商以及Thiele-型分叉连分布构造三元向量值混合有理插值,第二节给出了一种计算三元向量值混合有理插值的算法,第三节给出了一个数值例子。     

具有承袭性的高阶导数有理插值算法

切触有理插值是函数逼近的一个重要内容,而降低切触有理插值的次数和解决切触有理插值函数的存在性是有理插值的一个重要问题.切触有理插值函数的算法大都是基于连分式进行的,其算法可行性是有条件的,且计算量较大.利用Newton(牛顿)多项式插值的承袭性和分段组合的方法,构造出了一种无极点且满足高阶导数插值条件的切触有理插值函数,并推广到向量值切触有理插值情形;既解决了切触有理插值函数存在性问题,又降低了切触有理插值函数的次数.最后给出误差估计,并通过数值实例说明该算法具有承袭性、计算量低、便于编程等特点.     

Symmetries between two Ramsey properties

In this article we compare the well-known Ramsey property with a dual form of it, the so called dual-Ramsey property (which was suggested first by Carlson and Simpson). Even if the two properties are different, it can be shown that all classical results known for the Ramsey property also hold for the dual-Ramsey property. We will also show that the dual-Ramsey property is closed under a generalized Suslin operation (the similar result for the Ramsey property was proved by Matet). Further we compare two notions of forcing, the Mathias forcing and a dual form of it, and will give some symmetries between them. Finally we give some relationships between the dual-Mathias forcing and the dual-Ramsey property. Received: July 1, 1996     

Pseudofinite homogeneity, isolation, and reducibility

It has been proved (by S. M. Dudakov and M. A. Taitslin) that the reducibility of some models of a theory implies the second pseudofinite homogeneity property for this theory. We prove the converse, namely, that any theory with the first or the second pseudofinite homogeneity property has a reducible model and, therefore, possesses the second isolation property. This also proves the equivalence of the second isolation property and the second pseudofinite homogeneity property, in contrast to the first pseudofinite homogeneity property, which is more general than the first isolation property (this was established by O. V. Belegradek, A. P. Stolboushin, and M. A. Taitslin).     

The weak metric approximation property

We introduce and investigate the weak metric approximation property of Banach spaces which is strictly stronger than the approximation property and at least formally weaker than the metric approximation property. Among others, we show that if a Banach space has the approximation property and is 1-complemented in its bidual, then it has the weak metric approximation property. We also study the lifting of the weak metric approximation property from Banach spaces to their dual spaces. This enables us, in particular, to show that the subspace of c₀, constructed by Johnson and Schechtman, does not have the weak metric approximation property. The research of the second-named author was partially supported by Estonian Science Foundation Grant 5704 and the Norwegian Academy of Science and Letters.     

两水平无重复因析试验散度效应BH估计的性质

本文研究了两水平无重复因析试验散度效应BH估计的性质,给出了BH估计无偏性的充分必要条件,求得了它的近似方差.并在多个模型下对BH与MH估计进行了模拟比较.     

Persistence Approximation Property for Maximal Roe Algebras

Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then C_(max)~*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.     

Lifting of the approximation property from Banach spaces to their dual spaces

Inspired by the principle of local reflexivity, due to Lindenstrauss and Rosenthal, a new geometric property of Banach spaces, the extendable local reflexivity, was recently introduced by Rosenthal. Johnson and Oikhberg proved that the extendable local reflexivity permits lifting the bounded approximation property from Banach spaces to their dual spaces. It is not known whether the extendable local reflexivity permits lifting the approximation property. We prove that it does whenever the space is complemented in its bidual. This involves the concept of the weak bounded approximation property, introduced by Lima and Oja.

     

Weak and quasi approximation properties in Banach spaces

In this paper, we introduce weak versions (the weak approximation property, the bounded weak approximation property, and the quasi approximation property) of the approximation property and derive various characterizations of these properties. And we show that if the dual of a Banach space X has the weak approximation property (respectively the bounded weak approximation property), then X itself has the weak approximation property (respectively the bounded weak approximation property). Also we observe that the bounded weak approximation property is closely related to the quasi approximation property.     

On the normalizer problem for integral group rings of torsion groups

In this paper, we investigate the normalizer property for the integral group ring of a torsion group. We show that this property holds for locally finite nilpotent groups. A necessary and sufficient condition for this property to hold for any torsion group is also given. This research was supported in part by a research grant from the Natural Sciences and Engineering Research Council of Canada.     

一般混合线性模型联合估计的一个最优性

本文从一个新的角度 ,刻划了一般的混合线性模型的一个最优性质 .这一性质比最小方差性更为直观 .     

A property of certain multistage linear programs and some applications

In this paper, we present a property of certain linear multistage problems. To solve them, a method which takes this property into account is presented. It requires the resolution of 2N–1 subproblems, if there areN stages in the original problem. A sufficient condition is given on the matrix of the constraints for the property to be true. When only a submatrix has this property, we propose to use the Dantzig-Wolfe decomposition principle. We then can solve the subproblem with the proposed method. Applications to linear and nonlinear programming are presented.This work was done while the author was Visiting Scholar at the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California.