Mathematics

On Equivalence of the Method of Steepest Descent and the Method of Hypodifferential Descent in Some Constrained Optimization Problems

Authors: Dolgopolik M. V., Tamasyan G. S.

The method of exact penalty functions is widely used for the study of constrained optimization problems. The approach based on exact penalization was successfully applied to the study of optimal control problems and various problems of the calculus of variations, computational geometry and mathematical diagnostics. It is worth mentioning that even if the constrained optimization problem under consideration is smooth, the equivalent unconstrained optimization problems constructed via exact penalization technique is

About the Retrofit of the Valle’e-Poussin’s Algorithm for Approximations of Multivalued Mappings by Algebraic Polynomial with Type Constraint Equality

Authors: Vygodchikova I. Y.

The discrete approximation of noisy data by algebraic polynomial with restriction of type equality is studied. The aimof the investigation is to obtain the fundamental properties of solution of the problem and development by them the new algorithm, more effective, in comparison with existing methods of the solution. The tasks of the research — gets the properties of the solution of the problem, presentation of the algorithm and the demonstration of its implementation. Research methodology continues P. L. Chebyshjov’s and Valle-Pussen’s method. Results.

Embedding Theorems for P-nary Hardy and VMO Spaces

Authors: Volosivets S. S.

In the present paper several embedding theorems of P. L. Ul’yanov type for H¨older spaces connected with P-nary Hardy, VMO, L1 and uniform metric on Vilenkin groups are proved. Its sharpness is also established. The sufficient conditions for the convergence of Fourier series with respect to multiplicative systems in Hardy space and uniform metric are also given.

MRA on Local Fields of Positive Characteristic

Authors: Lukomskii S. F., Vodolasov A. M.

We prove that the local field of positive characteristic is a vector space over a finite field.

Systems of Scales and Shifts in the Problem Still Image Compression

Authors: Baryshev A. A., Lukomskii S. F., Lukomskii D. S.

A new approach to the construction of two-dimensional Haar and Vilenkin considered. To the obtained systems fast algorithms Fourier – Haar and Fourier – Vilenkin developed. Comparative analysis of algorithms developed in the problemstill image compression performed.

On Divergence Almost Everywhere of Fourier Series of Continuous Functions of Two Variables

Authors: Antonov N. Y.

We consider one type of convergence of double trigonometric Fourier series intermediate between convergence over squares and λ-convergence for λ> 1. We construct an example of continuous functions of two variables, Fourier series of which diverges in this sense, almost everywhere.

Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces

Authors: Alimov A. R.

The well-known Tsar’kov’s characterisation of finite-dimensional Banach spaces in which every bounded Chebyshev set (bounded P-acyclic set) is convex is extended to the asymmetrical setting.

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