Synthesis and Structural Study of 3,5-Cyclophosphorus Derivatives of 1,2-O-Alkylidene-6-Desoxy-6-Halogeno-α-D-Glucofuranoses

Abstract

Reactions of 3,5-halogenocyclophosphata of 1,2-O-alkylidene-6-desoxy-6-halogeno-α-D-glucofuranoses with water, alcohols, and amines were studied, which permit the obtaining of corresponding 3,5-cyclophosphates, their salts, and amides:     

Mobility and reactivity of lattice oxygen in Gd-doped ceria promoted by Pt

Summary For samples of the Ce_1-xGd_xO_2-y system prepared by the Pechini route and promoted with Pt, the mobility and reactivity of lattice oxygen were found to correlate with the density of surface and bulk anion vacancies.     

Analysis of spectra of acoustic signals generated by high-power pulsed laser radiation propagating in the atmosphere. I. Spectra of local plasma formations

Results of theoretical and experimental investigations into the spectra of acoustic signals generated by high-power pulsed laser radiation propagating in the atmosphere in the breakdown mode are given in the present paper. In Part I, results of theoretical and experimental investigations into the spectra of acoustic signals from laser breakdown initiated on a single solid aerosol particle and an ensemble of monodisperse particles depending on the particle material and sizes are presented. In Part II, spectra of acoustic signals from laser sparks in the atmosphere are analyzed, and the special features of the spectra of acoustic signals from individual plasma formations and discrete laser sparks are discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 74–80, November, 2005.     

Example of a Gaussian Self-Similar Field With Stationary Rectangular Increments That Is Not a Fractional Brownian Sheet

We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet (fBs). This Gaussian field is an extension of fractional Brownian motion. It is well known that the fractional Brownian motion is a unique Gaussian self-similar process with stationary increments. The main result of this article is an example of a Gaussian self-similar field with stationary rectangular increments that is not an fBs. So we proved that the structure of self-similar Gaussian fields can be substantially more involved then the structure of self-similar Gaussian processes. In order to establish the main result, we prove some properties of covariance function for self-similar fields with rectangular increments. Also, using Lamperti transformation, we obtain properties of covariance function for the corresponding stationary fields.     

On functions with given spherical means on symmetric spaces

The inversion problem for a local Pompeiu transformation of rank one on sym- metric spaces X of the noncompact type is studied. The reconstruction of a function defined in the ball B _R ⊂ X by its averages on balls of two fixed radii lying in B _R is obtained.     

Some Identities in Algebras Obtained by the Cayley-Dickson Process

Polynomial identities in algebras are the central objects of Polynomial Identities Theory. They play an important role in learning of algebras properties. In particular, the Hall identity is fulfilled in the quaternion algebra and does not hold in other non-commutative associative algebras. For this reason, the Hall identity is important for the quaternion algebra. The idea of this work is to generalize the Hall identity to algebras obtained by the Cayley-Dickson process. Starting from the above remarks, in this paper, we prove that the Hall identity is true in all algebras obtained by the Cayley-Dickson process and, in some conditions, the converse of this statement is also true for split quaternion algebras. From Hall identity, we will find some new properties and identities in algebras obtained by the Cayley-Dickson process.