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In this paper a robust sequential test is constructed for a discrete observation model, for which probabilities of first-type and second-type errors under Tukey-Huber type distortions do not exceed the specified values. No additional 'commensurability' condition is imposed on the model, and test construction does not require cumbersome calculations. Theoretically studied properties of the constructed test are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In the present paper, we describe the fascinating 150-year history of vortex dynamics, which started from the classical work by H. Helmholtz (1858). This work contains not only the general theorems on vortex motion, but also a special section devoted to axisymmetric circular vortex filaments and, in particular, to vortex rings. The aim of our investigation is both to clarify some purely mathematical questions connected with the Dyson model for coaxial vortex rings with a small circular cross-section in an ideal incompressible fluid and to provide a historical overview of the achievements in experimental, analytical, and numerical studies of the interaction of vortex rings. The model is illustrated by several examples of the motion of vortex rings. Finally, we present a complete classification of the interactions of two coaxial vortex rings in an ideal fluid. [ABSTRACT FROM AUTHOR]

A mathematical model is proposed to describe the process of crystallization. This model reflects experimentally established properties of structure formation in instability zones. Contemporary approaches to the theoretical description of crystallization yield values of the solid phase growth rate that differ, by several orders, from those observed in experiments. This fact stimulated the construction of a mathematical object that reproduces the basic instabilities of the process and stabilizes their feedback. The creation of this object required matching between the micro and the macro scales, as well as between wave and diffusion processes. The paper also gives a physical interpretation and results of the numerical analysis of the said model. [ABSTRACT FROM AUTHOR]

The authors study small vibrations of a mixture (emulsion) of two weakly viscous compressible fluids, construct a macroscopic (homogenized) model of emulsion, and establish convergence (with respect to a small parameter) of solutions of the original boundary value problem for a two-phase fluid to solutions of the corresponding homogenized problem. The paper also describes the results of qualitative analysis of the spectrum of the macroscopic acoustic equation (the dynamical Darcy's law), as well as typical spectral pictures obtained by numerical experiments. [ABSTRACT FROM AUTHOR]

This paper considers the Kipriyanov–Radon transform constructed as a special Radon transform adopted for dealing with singular Bessel differential operators of the corresponding indices acting on a part of the variables. The authors obtain inversion formulas generalizing the classical formulas for the Radon transform of axially-symmetric functions and relating to the integro-differentiation of fractional order in a one-dimensional parameter. [ABSTRACT FROM AUTHOR]

This paper considers the control problem with boundary condition for the one-dimensional parabolic equation on a bounded interval. For the quadratic cost functional, the author proves the existence of a minimizing function. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 54, Suzdal Conference–2006, Part 2, 2008. [ABSTRACT FROM AUTHOR]