For the Jubilee of Vladimir Mikhailovich Chernov

On April 25, 2019, Vladimir Chernov celebrated his 70th birthday, Doctor of Physics and Mathematics, Chief Researcher at the Laboratory of Mathematical Methods of Image Processing of the Image Processing Systems Institute of the Russian Academy of Sciences (IPSI RAS), a branch of the Federal Science Research Center "Crystallography and Photonics RAS and part-Time Professor at the Department of Geoinformatics and Information Security of the Samara National Research University named after academician S.P. Korolev (Samara University). The article briefly describes the scientific and pedagogical achievements of the hero of the day. © Published under licence by IOP Publishing Ltd

Entropy and growth rate of periodic points of algebraic Z^d-actions

Expansive algebraic Z^d-actions corresponding to ideals are characterized by the property that the complex variety of the ideal is disjoint from the multiplicative unit torus. For such actions it is known that the limit for the growth rate of periodic points exists and equals the entropy of the action. We extend this result to actions for which the complex variety intersects the multiplicative torus in a finite set. The main technical tool is the use of homoclinic points which decay rapidly enough to be summable.Comment: 17 page

On quaternary complex Hadamard matrices of small orders

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.Comment: 7 page

Intelligent OFDM telecommunication system. Part 2. Examples of complex and quaternion many-parameter transforms

In this paper, we propose unified mathematical forms of many-parametric complex and quaternion Fourier transforms for novel Intelligent OFDM-telecommunication systems (OFDM-TCS). Each many-parametric transform (MPT) depends on many free angle parameters. When parameters are changed in some way, the type and form of transform are changed as well. For example, MPT may be the Fourier transform for one set of parameters, wavelet transform for other parameters and other transforms for other values of parameters. The new Intelligent-OFDM-TCS uses inverse MPT for modulation at the transmitter and direct MPT for demodulation at the receiver. © 2019 IOP Publishing Ltd. All rights reserved

Frequency response modeling and control of flexible structures: Computational methods

The dynamics of vibrations in flexible structures can be conventiently modeled in terms of frequency response models. For structural control such models capture the distributed parameter dynamics of the elastic structural response as an irrational transfer function. For most flexible structures arising in aerospace applications the irrational transfer functions which arise are of a special class of pseudo-meromorphic functions which have only a finite number of right half place poles. Computational algorithms are demonstrated for design of multiloop control laws for such models based on optimal Wiener-Hopf control of the frequency responses. The algorithms employ a sampled-data representation of irrational transfer functions which is particularly attractive for numerical computation. One key algorithm for the solution of the optimal control problem is the spectral factorization of an irrational transfer function. The basis for the spectral factorization algorithm is highlighted together with associated computational issues arising in optimal regulator design. Options for implementation of wide band vibration control for flexible structures based on the sampled-data frequency response models is also highlighted. A simple flexible structure control example is considered to demonstrate the combined frequency response modeling and control algorithms