Temporal characteristics of picosecond stimulated Raman scattering in oxide crystals

The temporal characteristics of stimulated Raman scattering (SRS) under 22-ps laser excitation were studied in eight oxide crystals with a T ₂ optical-phonon dephasing time variable by up to two orders of magnitude. The measured SRS pulse width was shortened from 13.8 ps for Ba(NO₃)₂ (T ₂ = 26.5 ps) to 4 ps for the LiNbO₃ (T ₂ = 0.38 ps) crystal. The dependence of SRS pulse width on the dephasing time was analyzed in the framework of the known SRS theory.     

About Regularity of Collections of Sets

The paper continues investigations of stationarity and regularity properties of collections of sets in normed spaces. It contains a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a collection of sets to be regular.     

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.     

An axially symmetric contact problem for a half-space with an elastically reinforced cylindrical cavity

We consider the pressure of a plate on a half-space with a round cylindrical cavity. The surface of the cavity is reinforced by elastic elements that are modeled by very general operators. The problem is reduced to a Fredholm integral equation of second kind. A detailed study is made of the case of reinforcement described by the Winkler law. An approximate solution is obtained in the form of the asymptotics with respect to the radii of the plate and the cavity.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 80–85.     

Investigation of radical decay mechanisms in a glow-discharge plasma in carbon tetrafluoride

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 1004–1010, June, 1991.     

An approach to numerical solution of multipoint boundary-value problems

An approach is proposed to solving multipoint boundary-value problems for linear differential equation of w-th order, based on reduction to two-point boundary-value problems. The two-point problems are solved by the stable discrete orthogonalization method. Some numerical examples are considered.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 36–45, 1986.     

Stochastic Stability of Processes Determined by Poisson Differential Equations with Delay

We prove an existence theorem and establish the property of stochastic stability for processes determined by the Poisson stochastic differential equations with delay.     

Axisymmetric excitation of a dielectric torus: Numerical solution

The article considers the mathematical model of a lens antenna in the shape of a homogeneous dielectric torus excited by an axial magnetic dipole. The boundary-value problem for an elliptical differential equation is posed and reduced by the fundamental solution method to an integral equation of 2nd kind over the torus section. A numerical algorithm is proposed, and the numerical results are compared with experimental findings. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 109–115.