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**Редакційна колегія (UA)**,*P. 2.*[ (PDF) ] **Contents / Зміст (UA)**,*P. 3.*[ (PDF) ]**V. Kadets,**Statistical convergence cannot be generated by a single statistical measure,*P. 4-8.*[ Abstract ] [ Full-text available (PDF) ]**S.Yu. Ignatovich,**Approximation of autonomous affine control systems in the sense of time optimality and algebraic approximation,*P. 9–21.*[ Abstract ] [ Full-text available (PDF) ]**N.V. Zhogoleva, V.F. Shcherbak,**Identification of characteristics of coupled oscillators,*P. 22-30.*[ Abstract ] [ Full-text available (PDF) ]**K. Stiepanova,**Semi-classical analysis for proof extinction-property in finite time of solutions for parabolic equations with homogeneous main part and degenerate absorption potential,*P. 31-45.*[ Abstract ] [ Full-text available (PDF) ]**I.D. Borisov, S.I. Potseluiev,**Rozensweig instability of two-layer system of immiscible ferrofluid,*P. 46-60.*[ Abstract ] [ Full-text available (PDF) ]**I.V. Brysina, V.A. Makarichev,**Approximation properties of generalized Fup-functions,*P.61-92.*[ Abstract ] [ Full-text available (PDF) ]**L.O. Khilkova,**Homogenization of the diffusion equation in domains with the fine-grained boundary with the nonlinear boundary Robin condition,*P.93-111.*[ Abstract ] [ Full-text available (PDF) ]**V.D. Gordevskyy, O.S. Sazonova,**Continual distribution with screw modes,*P.112-122.*[ Abstract ] [ Full-text available (PDF) ]**Korobov Valeriy Ivanovich,**On his 75th birthday,*P.123-124.*[ Abstract ] [ Full-text available (PDF) ]

We demonstrate that statistical convergence cannot be generated by a single statistical measure, thus solving in negative a question from recent paper by Li Xin Cheng, Li Hua Lin, and Xian Geng Zhou.

*Keywords:* filter convergence, statistical convergence, statistical
measure.

2000 Mathematics Subject Classification: 40A35, 54A20. [ Full-text available (PDF) ] Top of the page.

In the paper conditions are given under which, for autonomous affine control systems, approximation in the sense of time optimality implies the algebraic approximation.

*Keywords:* control systems, time optimality, explicit solution.

2000 Mathematics Subject Classification: 93B10, 93B25 [ Full-text available (PDF) ] Top of the page.

The observation and identification problem for mathematical model of coupled Van der Pol oscillators is considered. Such systems arise under modeling of many cyclical biological processes. The synthesis of invariant relationships method is used developed for the solution of inverse control problems. The method allows to synthesize additional relations between the known and unknown quantities of the mathematical model of the object.

*Keywords:* Observer, identification of parameters, invariant relations, Van
der Pol oscillator

2000 Mathematics Subject Classification: 15A24, 34В15, 34C25. [ Full-text available (PDF) ] Top of the page.

We study the behavior of solutions of parabolic equation with double nonlinearity and a degenerate absorption term. The main topic of interest is the property of finite time extinction, i.e., the solution vanish after finite time.

*Keywords:* degenerate nonlinear parabolic equation, diffusion--absorption,
extinction-property of solutions, semi-classical analysis.

2000 Mathematics Subject Classification: 35A25, 35B40. [ Full-text available (PDF) ] Top of the page.

The stability of equilibrium for two-layer system of immiscible ferrofluids, separated by thin horizontal plate with a hole is considered. A numerical method for calculation of stability boundary in the space of dimensionless physical parameters of the system is proposed. In the case of circular hole the stability boundary and the most rapidly growing perturbations were calculated.

*Keywords:* ferrofluid, equilibrium forms, stability of equilibrium.

2000 Mathematics Subject Classification: 76W05. [ Full-text available (PDF) ] Top of the page.

Generalized Fup-functions are considered. Almost-trigonometric basis theorem is proved. Spaces of linear combinations of shifts of the generalized Fup-functions are constructed and an upper estimate of the best approximation of classes of periodic differentiable functions by these spaces in the norm of $L_2[-\pi,\pi]$ is obtained.

*Keywords:* function with a compact support, approximation of periodic
functions, up-function, Kolmogorov width, best approximation, generalized
Fup-function.

2000 Mathematics Subject Classification: 41A30, 41A50. [ Full-text available (PDF) ] Top of the page.

In this paper we consider the boundary-value problem for the stationary diffusion equation in perforated domains, which are additional of a large number non-overlapping small balls on the surface of which is given the nonlinear Robin condition. We study the asymptotic behavior of the solution of the problem. We derive homogenization equations describing the principal term of the asymptotic of the solutions.

*Keywords:* homogenization, diffusion, Robin condition, quasisolutions.

2000 Mathematics Subject Classification: : 35J65, 35Q80. [ Full-text available (PDF) ] Top of the page.

Explicit approximate solution of the Boltzmann equation for the hardsphere model are built. It has the kind of continual distribution in the case of local Maxwellians of special form describing the screw-shaped stationary equilibrium states of a gas. Some limited cases, in which this distribution minimized the uniform-integral remainder between the sides of this equation are obtained.

*Keywords:* hard spheres, Boltzmann equation, Maxwellian, screws,
uniformintegral remainder, continual distribution.

2000 Mathematics Subject Classification: 76P05; 45K05; 82C40; 35Q55. [ Full-text available (PDF) ] Top of the page.

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