On the Approximation of Functions on Locally Compact Abelian Groups

Questions of approximative nature are considered for a space of functions L ^p(G, ), 1 p , defined on a locally compact abelian Hausdorff group G with Haar measure . The approximating subspaces which are analogs of the space of exponential type entire functions are introduced.     

Coherence of a Chain of Chaotic Oscillators in a Nonlinear Gyrotropic Medium

We investigate the generalized Kuhn＇s model, namely, a chain of nonlinear chaotic oscillators describing a nonlinear gyrotropic medium. It is shown that despite the chaotic behavior of separate oscillators the chain preserves some coherency as a whole. The relation between the chain synchronization and the physical properties of a random mean field is established.     

Quantum chaos and its kinetic stage of evolution

Usually reason of irreversibility in open quantum-mechanical system is interaction with a thermal bath, consisting form infinite number of degrees of freedom. Irreversibility in the system appears due to the averaging over all possible realizations of the environment states. But, in case of open quantum-mechanical system with few degrees of freedom situation is even more complicated. Should one still expect irreversibility, if external perturbation is just an adiabatic force without any random features? Problem is not clear yet. This is the main question we address in this review article. We prove that the key point in the formation of irreversibility in chaotic quantum-mechanical systems with few degrees of freedom is the complicated structure of energy spectrum. We shall consider quantum-mechanical system with parametrically dependent energy spectrum. In particular, we study energy spectrum of the Mathieu–Schrodinger equation. Structure of the spectrum is quite non-trivial, consists from the domains of non-degenerated and degenerated states, separated from each other by branch points. Due to the modulation of the parameter, system will perform transitions from one domain to other one. For determination of eigenstates for each domain and transition probabilities between them, we utilize methods of abstract algebra. We shall show that peculiarity of parametrical dependence of energy terms, leads to the formation of mixed state and to the irreversibility, even for small number of levels involved in the process. This last statement is important. Meaning is that we are going to investigate quantum chaos in essentially quantum domain.In the second part of the article, we will introduce the concept of random quantum phase approximation. Then, along with the methods of random matrix theory, we will use this assumption for the derivation of muster equation in the formal and mathematically strict way.The content of this article is based on our previous studies. However, in this review article some original material is also included. This part mainly concerns the discussion about possible experimental realization of theoretical concepts in the field of organic chemistry.     

Coherence of a Chain of Chaotic Oscillators in a Nonlinear Gyrotropic Medium

We investigate the generalized Kuhn's model, namely, a chain of nonlinear chaotic oscillators describing a nonlinear gyrotropic medium. It is shown that despite the chaotic behavior of separate oscillators the chain preserves some coherency as a whole. The relation between the chain synchronization and the physical properties of a random mean field is established.     

ON AVOIDANCE ACTIVITIES IN FISHERY ENFORCEMENT MODELS

Compliance and enforcement in fisheries are important issues from an economic point of view since management measures are useless without a certain level of enforcement. These conclusions come from the well‐established theoretical literature on compliance and enforcement problems within fisheries and a common result is that, it is efficient to set fines as high as possible and monitoring as low as possible, when fines are costless and offenders are risk neutral. However, this result is sensitive to the assumption that fishermen cannot engage in avoidance activities, e.g., activities to reduce the likelihood of being detected when noncomplying. The paper presents a model of fisheries that allows the fishermen to engage in avoidance activities. The conclusions from the model are that, under certain circumstances, fines are costly transfers to society since they not only have a direct positive effect on the level of deterrence, but also an indirect negative effect in the form of increased avoidance activities to reduce the probability of detection. The paper contributes to the literature on avoidance activities by introducing the externality from the illegal behavior as an endogenous effect on other offenders. For an externality, that has an exogenous effect on other actors, Malik shows that fines are only costly transfers for conditional deterrence (when one actor is deterred while another actor is not). For fisheries, we show that fines are also costly transfers under no deterrence (when no agents are deterred).     

Distinctive features of nonlinear nuclear magnetic resonance

Nonlinear NMR modes are classified and the limits of realization are established for each of them. The unstable behavior of magnetization near the separatrix of relaxationless motion of nonlinear NMR is studied and ways of stabilizing this instability are considered.Tbilisi State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 731–737, July, 1991.     

Summability of Fourier series for almost-periodic functions on locally compact Abelian groups

Some results concerning the summability of Fourier series of continuous 2π-periodic functions are generalized for the case of almost-periodic functions defined on locally compact Abelian groups.     

Saturation of inhomogeneously broadened magnetic-resonance line under phonon-bottleneck conditions

Radiophysics and Quantum Electronics -     

Approximation of functions on an m-dimensional sphere by Cesàro means of Fourier-Laplace series

An investigation of the error in approximations of functions defined and continuous on the unit sphere of m-dimensional euclidean space by Ceskro sums of Fourier-Laplace series.Translated from Matematicheskie Zametki, Vol. 9, No. 3, pp. 343–353, March, 1971.