关于q—Bernstein多项式及其Boole和迭代

本文对q-Bernstein多项式Bn(f,q,x)收敛于B∞(f,q,x)的加速问题进行研究,同时对其Boolean和迭代的收敛性问题进行考虑.采用精细估计,并应用光滑模理论等手段,得到相应的逼近速度估计.结果表明:q-Bernstein多项式在这两个问题上与传统Bernstein多项式有着类似的结果.     

Skew Boolean algebras and discriminator varieties

We investigate the class of skew Boolean algebras which are also meet semilattices under the natural skew lattice partial order. Such algebras, called hereskew Boolean -algebras, are quite common. Indeed, any algebra A in a discriminator variety with a constant term has a skew Boolean -algebra polynomial reduct whose congruences coincide with those of A.Presented by S. Burris.     

Mean covariogram of cylinders and applications to Boolean random sets

This work focuses on the variance properties of isotropic Boolean random sets containing randomly-oriented cylinders with circular cross-section. Emphasis is put on cylinders with large aspect ratios, of the oblate and prolate types. A link is established between the power law decay of the covariance function and the variance of the estimates of the volume fraction of cylinders. The covariance and integral range of the Boolean mixtures are expressed in terms of the orientation-averaged covariogram of cylinders, for which exact analytical formulas and approximate expressions are provided.     

Iterated probability distributions and extremes with random sample size

In this paper the possible nondegenerated limit distributions for the n-fold mapping of a given probability distribution are considered. If the mapping used for the iteration procedure is a probability generating function of a positive integer-valued random variable then the results can be applied to the max-stability of distributions of random variables with random sample size.     

LS algebras and application to Schubert varieties

In this paper we introduce LS algebras. We study their general properties and apply these results to Schubert varieties. Our main achievement is that any Schubert variety admits a flat deformation to a union of normal toric varieties. A new proof of Cohen-Macaulayness (and thus normality) for Schubert varieties is also obtained.     

Truncated random variables with application to random surfaces

There has been considerable interest in obtaining discrete results for random surfaces. Standard results have been published in journals of physics or engineering which have emphasised the applications. This paper gives a detailed background of the mathematical methods needed so that the central connection, namely truncated random variables, between these standard results can be understood. Distributions of discrete peak measures are obtained from the distributions of discrete profile measures of a random Gaussian surface by applying results for the distributions of truncated random variables. This enable the moments to be obtained from known results for the truncated distributions.     

Elementary generation and canonicity for varieties of Boolean algebras with operators

Dedicated to the memory of Alan Day     

Iterated expansions of models for countable theories and their applications

An expansion of a countable model by relations for incomplete types realized in the model is constructed. Theories of models obtained by iterating the expansion defined over countable ordinals are investigated. Theorems concerning the atomicity of countable models in a suitable -expansion are proved, and we settle the question of whether or not -expansions have atomic models. A theorem on the realization and omission of generalized types is presented. The resulis obtained are then used to give a direct proof of a theorem of Morley on the number of countable models and to state that Ehrenfeucht theories have finite type rank.Translated fromAlgebra i Logika, Vol. 34, No. 6, pp. 623-645, November-December, 1995.Supported by RFFR grant No. 93-01-01506.     

The method of Iterated Defect-Correction and its application to two-point boundary value problems

Summary In Part II of this paper we present a rigorous analysis of the Iterated Defect-Correction — applied to two-point boundary value problems — which was introduced in Part I of this paper [1]. A complete proof of Theorem 5. 1 of [1] is given.     

Estimation of Iterated Matrices,with application to the von Neumann condition

Ohne Zusammenfassung     

Precise asymptotics for random matrices and random growth models

The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.     

A Laplace transform method for order statistics from nonidentical random variables and its application in Phase-type distribution

In this paper, we derive a method for obtaining the Laplace transform of order statistics (o.s.) arising from general independent nonidentically distributed random variables (r.v.’s). A survey of the most important properties, applications and the o.s. of a Phase-type (PH) distribution are also presented. Two illustrative examples are provided.     

Approximations to the probabilities of binomial and multinomial random variables and chi-square type statistics

Summary New lower and upper bounds are given to the probabilities of binomial and multinomial random variables. Exact bounds are also presented for the sampling distributions of chi-square type statistics and the K-L information number from a multinomial distribution. The Institute of Statistical Mathematics