Effect of Heat Treatment of Molten Bi2O3 Containing 22 mol % SiO2 on the State of the Metastable δ*-Phase Forming during Solidification

Inorganic Materials - We have studied the effect of isothermal holding of a melt containing 78 mol % Bi2O3 and 22 mol % SiO2 and various melt cooling schedules on the morphology, microstructure,...     

Stochastic <Emphasis Type="Italic">m</Emphasis>-Point Cauchy Problem for Parabolic Equation with Semi-Wiener Perturbations

The authors consider the problem of the existence, with probability 1, of Green’s function of a stochastic m-point Cauchy problem for a higher-order parabolic equation with white noise perturbations taken with negative values only. Estimates are obtained in spaces of functions whose norm contains the mathematical expectation.     

Analysis of Exponential Stability of a Linear Stochastic Oscillator under Small Diffusive Disturbances

The necessary and sufficient conditions of exponential stability in the quadratic mean are obtained for a stochastic oscillator under small diffusive disturbances.     

Mean square stability of the solutions of autonomous dynamic diffusion systems with finite aftereffect with regard for random factors

The necessary and sufficient conditions are obtained for the asymptotic mean square stability of strong solutions of autonomous diffusion stochastic functional-differential equations with finite aftereffect and random factors (random functions with different distribution) taken into account.     

Analysis of oscillations in quasilinear stochastic dynamic hereditary systems

Oscillations in quasilinear stochastic hereditary systems and their application to specific problems are investigated. The algorithm of transition to a standard system with the help of the averaging method with small parameter in the presence of fast time is justified.     

Stability of stochastic dynamic random-structure systems with aftereffect and Markov switchings

Using the second Lyapunov–Krasovskii method, sufficient conditions are obtained for the asymptotic stochastic global stability, for the global stability, and mean-square stability of trivial solutions to systems of diffusion stochastic functional–differential equations with Markov switchings, and the theory is illustrated by two model problems.     

Parametric continuity of solutions to stochastic functional differential equations with poisson perturbations

The small-parameter method and the notion of averaged system are used to analyze the asymptotic stability in the mean square of the original system of stochastic differential equations. The stability of a system with continuous perturbations is considered. It is proved that the small-parameter method can be applied to stochastic differential equations with discontinuous trajectories, i.e., that stochastic differential depends on the Poisson integral.     

Optimal linear filtering for systems of stochastic differential equations with poisson perturbations

The Kalman–Bucy filter that can be modeled by computer statistical design is constructed for stochastic dynamic systems with Poisson perturbations. It is proved that a stationary filter coincides with the Wiener filter for the optimal mean-square filtering of stationary sequences in the absence of Poisson perturbations.     

Periodic solutions for a class of nonlinear hyperbolic evolution equations

The existence of periodic solutions is constructively substantiated for a class of nonlinear hyperbolic evolution equations. A priori estimates are obtained. Examples are given to illustrate the results.