No 1 (2013)

We consider the problem of optimal recovery of function in Schwartz space from inaccurate data (in the mean square metric) on it’s Radon transform. We present explicit expressions for the error of optimal recovery and a set of optimal methods. As a consequence we prove one inequality for functions in Schwartz space.

The resource allocation problem in Orthogonal Frequency Division Multiple Access relay-enhanced heterogeneous cellular networks is studied. An analytical model of the downlink channel in discrete time is suggested. We derive and analyze various resource allocation algorithms. In order to evaluate the role of different resource allocation schemes we obtain blocking probabilities and other performance metrics of interest.

This paper investigates characteristics of the polling cycling models with exhaustive and gated service disciplines. We have derived mean queuing delays for suggested models and evaluated results.

In this paper we consider the equation of Fokkera-Planck for models of population dynamics and the method to obtain stochastic differential equation written as Langevin equations. And we received the Fokker-Planck equation for the model “predator-prey” and its variants and for models of symbiosis and competition.

In the present paper a concept of vector nodal finite element has been introduced, algorithms of construction of the vector nodal basis functions with high approximate properties from special functional spaces are presented. Examples of high-order interpolation of harmonic, irrotational vector fields by the developed finite elements illustrate their approximate advantage in comparison with the standard Lagrange elements.

Modern approaches to studying of freak waves at ocean by means of computing experiments are consi-dered. The description of computing experimental installation is given, used numerical methods are described, and the review of the received results is given too.

The paper analyzes the interaction of a Gaussian beam with a phase step structure (PSS). The shape of the spatial spectrum at the output of such a scheme is examined. The most detailed description was done for the case when the size of the PSS phase difference is 180 degrees. The effects that occur at the displacement of SPS in the plane perpendicular to the direction of incidence of the laser beam were considered. Discussions for the possible practical application of the scheme were carried out.

In the paper application of the beam propagation method (BPM) to investigation of wave processes in regular and nonregular graded-index waveguide structures with strongly asymmetric refractive index profile is analyzed. On purpose to match the BPM requirement to smoothness of the refractive index profile, the profile with strong asymmetry, at the problem solution, is approximately exchanged by a symmetrical one. For exponential and Gaussian profiles of the refractive index the BPM calculations are compared to the strict and WKB solution respectively. Calculation of a wave pattern of a mode field coupling into the substrate at the tapered edge of a waveguide with strongly asymmetric profile is demonstrated.

General relativistic theory of motion of the charged particles in the electromagnetic waves at the resonant conditions in the drift-eikonal approximation is presented. The motion of the particle in the vicinity of cyclotron, parametric and half-cyclotron resonances is considered.

The large-scale structure of the Universe is revealed to be characterized by a range of power-laws. The power-laws are evidences of fractality because they may be interpreted through a conception of the Universe as an assembly of self-similar space–time domains. We accept the hypothesis that the matter of the Universe is described by the scalar charged meson field possessing the rotary symmetry. On basis of the hypothesis, the fractal cosmological model with scale invariant Lagrange’s field equation and Einstein’s equation permitting physical explanation of these properties is constructed. The field energy densities (which are constant) and the space–time metrics of different domains differ in constant factors only. Therefore, the space–time domains are geometrically similar and evolve similarly. Fractal properties of initial cosmological density perturbations remain and lead to presence of the fractal properties of the Universe’s large-scale structure which formed from them. The nonsingular, compacted, pulsating and doubly-connected cosmological model as a partial solution for the homogeneous, isotropic and flat case is constructed. A background radiation power spectrum has been computed. The spectrum is shown to be close to the observable angular power spectrum of the SDSS-quasar distribution on the celestial sphere.

Early developed method of integrating the ballistic equations in dual-projective variables was applied for the gyroscopically stabilized projectile under action of relatively weak lift force L = γV 2 ≈ 0.1mg and the force of air drag R = αV 2 ≫ mg, both their coefficients α() and γ() being strongly dependent on angle of attack . Obtained are both exact and approximate expressions for the resolventa function f(b) = a bb′′(b) , with the a(b) and b = tg being an intercept and slope of trajectory respectively.

In the present paper we discuss the interrelation of the advanced interdisciplinary concepts of modern physics such as symmetry breaking, quantum protectorate, emergence and the Bogoliubov’s concept of quasiaverages in the context of modern theoretical physics, and, in particular, quantum and statistical physics. The main aim of this analysis was to demonstrate the connection and interrelation of these conceptual advances of the many-particle physics and to try to show explicitly that those concepts, though different in details, have certain common features. Some problems in the field of statistical physics of complex materials and systems e.g. foundation of the microscopic theory of magnetism and superconductivity were pointed in relation to these ideas. The main suggestion is that the emphasis of symmetry breaking concept is on the symmetry itself, whereas the method of quasiaverages emphasizes the degeneracy of a system. The concept of quantum protectorate reveals essential difference in the behavior of the complex many-body systems at the low-energy and high-energy scales. Thus the notion of quantum protectorate might provide distinctive signatures and good criteria for a hierarchy of energy scales and the appropriate emergent behavior.

The Einstein–Cartan theory as a natural generalization of the General Relativity is proposed. The cosmological term is connected with string additions for de Sitter world having Planck density before the Big Bang. Is proposed that this world was having the Lemaitre atom form with mass of modern Methagalaxy mass and the diameter 10 −13 cm. We propose that the Big Ban is the result of the transforming of the topological energetical string modes into oscillations one. The hypothesis of Fridmon particles as particles of dark matter with masses near one billion GeV and corresponding to dualized weak interaction symmetry group is proposed.

This review is concerned applications of matrix models in combinatorics. We will discuss counting of orientable and nonorientable gluings of regular 2n-gons using gaussian matrix integrals.