On the fixing of values of sequences of seminorms

Theorems on the fixing of values of sequences of continuous seminorms on certain sets in Banach spaces are proved, enabling one to obtain new results on the asymptotic behavior of approximations of individual functions and on the convergence of interpolation processes on classes of functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 467–474, April, 1992.     

Behavior of zeros of polynomials of near best approximation

The purpose of this paper is to study the asymptotic behavior of the zeros of polynomials of near best approximation to continuous functions f on a compact set E in the case when f is analytic on the interior of E but not everywhere on the boundary. For example, suppose E is a finite union of compact intervals of the real line and f is a continuous function on E, but is not analytic on E; then we show (cf. Corollary 2.2) that every point of E is a limit point of zeros of the polynomials of best uniform approximation to f on E. This fact answers a question posed by P. Borwein who showed that, for the case when E is a single interval and f is real-valued, then the above hypotheses on f imply that at least one point of E is the limit point of zeros of such polynomials.     

An extension of a theorem of Banach

Summary Via porosity a well-known theorem of Banach on bounded real valued continuous functions defined on [0, 1] is extended to higher dimensions. Summary. Via porosity a well-known theorem of Banach on bounded real valued continuous functions defined on [0, 1] is extended to higher dimensions.     

A new class of operators and a description of adjoints of composition operators

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toeplitz operators to include symbols that are multiple-valued functions. These definitions can be made on any Banach space of analytic functions on a plane domain, but in this work, our attention is focused on the basic properties needed for the application to operators on the standard Hardy and Bergman Hilbert spaces on the unit disk.     

一类初等微分几何定理机器证明的算法与实现

空间曲面上的曲线论是初等微分几何的重要部分．作者提出了一种以外微分运算和向量计算为主要工具,可以进行有关曲面上曲线局部性质的定理机器证明的算法．该算法结合了曲面上的活动标架,曲面上曲线的测地标架和曲线自身的Frenet标架,在Maple 9下得到实现．对20个例子进行的测试表明,由该算法生成的自动证明简短可读．     

Estimation of dependences based on Bayesian correction of a committee of classification algorithms

Estimation of dependence of a scalar variable on the vector of independent variables based on a training sample is considered. No a priori conditions are imposed on the form of the function. An approach to the estimation of the functional dependence is proposed based on the solution of a finite number of special classification problems constructed on the basis of the training sample and on the subsequent prediction of the value of the function as a group decision. A statistical model and Bayes’ formula are used to combine the recognition results. A generic algorithm for constructing the regression is proposed for different approaches to the selection of the committee of classification algorithms and to the estimation of their probabilistic characteristics. Comparison results of the proposed approach with the results obtained using other models for the estimation of dependences are presented.     

Experimental determination of the life of oriented molecules of higher fatty acids under conditions of surface friction of polymers against steel

It is shown that the life of boundary lubricants is much greater on polymers than on steel, and a hypothesis is put forward, and experimentally confirmed, to explain the causes of the breakdown of boundary lubricants on polymer and steel surfaces.Mekhanika Polimerov, Vol. 1, No. 5, pp. 101–106, 1965     

Homology of algebras of families of pseudodifferential operators

We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology degenerates at E² and converges to Hochschild homology. As a byproduct, we identify the space of residue traces on fibrations by manifolds with corners. In the process, we prove some structural results about algebras of complete symbols on manifolds with corners.     

On domains of regularity of the solutions of some special classes of Monge-Ampère-type equations

We present several results on estimates from above of the regularity domains for special classes of solutions to Monge-Ampère-type equations (in particular, periodic at least in one variable). Also, we present some geometrical and geophysical applications. Namely, we are concerned with the problem on dimensions of a single-valued projection on a plane of a surface with separated-from-zero negative Gaussian curvature and discuss the existence or nonexistence of a solution to the pressure-wind balance equation on a torus. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 1, pp. 237–246, 2006.     

Application of tests of chi-square type

Some recent results on the theory of chi-square tests are given. Remarks of practical character on the use of these tests are made, reflecting on a large number of applied papers.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 49–71, 1987.     

Criteria of the long-time strength of polymers

Based on dimensional analysis, a generalization of phenomenological estimations of the long-time strength of polymers is presented.Mekhanika Polimerov, Vol. 2, No. 6, pp. 828–832, 1966Paper read on 7 June 1966 at the VII Scientific Conference on Thermal Stresses in Kanev, UkrSSR.     

Dependence of the Nature of Equilibrium States of a Two-Phase Medium on the Parameters of the Problem

Under general assumptions on the densities of the energy of deformation, which depend on parameters, zones of the values of parameters are determined for which one-phase or two-phase equilibrium states are realized. It is proved that the boundary between these zones is Lipschitz. The nature of an equilibrium of a two-phase medium is studied for parameters lying on the line of demarcation of the zones. Bibliography: 1 title.     

On the number of essential arguments of homomorphisms between products of median algebras

In this paper we characterize classes of median-homomorphisms between products of median algebras, that depend on a given number of arguments, by means of necessary and sufficent conditions that rely on the underlying algebraic and on the underlying order structure of median algebras. In particular, we show that a median-homomorphism that take values in a median algebra that does not contain a subalgebra isomorphic to the m-dimensional Boolean algebra as a subalgebra cannot depend on more than \(m-1\) arguments. In view of this result, we also characterize the latter class of median algebras. We also discuss extensions of our framework on homomorphisms over median algebras to wider classes of algebras.     

Strong convergence of weighted sums of random elements through the equivalence of sequences of distributions

The equivalence of sequences of probability measures jointly with the extension of Skorohod's representation theorem due to Blackwell and Dubins is used to obtain strong convergence of weighted sums of random elements in a separable Banach space. Our results include most of the known work on this topic without geometric restrictions on the space. The simple technique developed gives a unified method to extend results on this topic for real random variables to Banach-valued random elements. This technique is also applied to the proof of strong convergence of some statistical functionals.     

Groups of Symmetries of the Set of Zeros of Polynomial Functionals on Complex Banach Spaces

We describe groups of symmetries on the set of zeros of polynomial functionals on complex Banach spaces and establish the connection between symmetries of polynomial functionals and their kernels.     

On the rate of superlinear convergence of a class of variable metric methods

Summary This paper considers a class of variable metric methods for unconstrained minimization. Without requiring exact line searches each algorithm in this class converges globally and superlinearly on convex functions. Various results on the rate of the superlinear convergence are obtained.Dedicated to Professor Dr. H. Görtler on the occasion of his seventieth birthday     

广义流体动力学守恒方程组的弱解的存在性和唯一性问题

本文讨论了非定常广义流体动力学方程组在大尺度情况下平均流动参数所应满足的条件,提出了相应的假设,证明了大尺度平均流动参数弱解的存在性和唯一性。     

A report on polarography of nitro derivatives of arylazopyrazoles

In an earlier communication¹ we reported our results on the effect of electron donating substituents on the polarographic reduction of 4-phenylazopyrazole. In this communication we report our results on the effect of an electron withdrawing substituent on the E_1/2 of 1-thiocarbamoyl-3, 5-diphenyl-4-phenylazopyrazole. The studies were carried out in non-aqueous medium due to water insoluble nature of these compounds.