Damping of persistent oscillations of quadratic optical solitons

We investigate the dynamics of optical soliton formation in media with quadratic nonlinearity under conditions of long-living oscillations produced by the soliton's internal modes. We compare the predictions of the second-order perturbation approach, combining it with the energy conservation law, with the direct numerical simulations using the transparent boundary conditions. We demonstrate that these two approaches correlate well and describe the nonlinear radiation damping of the internal modes.     

Inversion of the local Pompeiu transformation on Riemannian symmetric spaces of rank one

We study the problem of inversion of the local Pompeiu transform on Riemannian symmetric spaces of rank one. The explicit formula for the reconstruction of a function by its averages over balls and spheres with a single fixed radius is obtained.     

On the connected stability of the large-scale systems of dynamical equations on the time scale in critical cases

The connected stability of a large-scale system of dynamical equations on the time scale is investigated. The case where the trivial zero solution of the system is non-asymptotically stable in the linear approximation is considered. The sufficient conditions for the connected asymptotic stability of the zero solution of the system are obtained on the basis of the Lyapunov direct method.     

Hybrid iodobismuthates code: adapting the geometry of Bi polyhedra to weak interactions

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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.     

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.     

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.