No 4 (2011)

Cover Page
Articles
Fiftieth anniversary of the Faculty of Science
Davydov V.V.
Abstract
Discrete and Continuous Models and Applied Computational Science. 2011;(4):5-6
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Rational Homotopy Type of Inverse Systems in T2 Category
Marchenko V.V.
Abstract
A connection between Rational homotopy theory of T2 category of 1-connected spaces and homotopy theory of certain algebraic categories is established. Quillens approach is mainlybased upon functoriality. This enables one to extend the theory to the category of inverse systems. In the present paper a notion of Rational homotopy type of inverse systems of 1-connectedspaces is introduced. Its equivalence to Rational homotopy theories of certain algebraic categories is proved.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):7-15
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On Saturation Problems for Riemann-Liouville Operators
Soroosh Mohammadi Farsani -.
Abstract
The problem of convergence almost everywhere and in weighted Lebesgue norms to the identity for the families of Riemann-Liouville operators is studied.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):16-22
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Two-Dimensional Binomial Distribution
Khokhlov Y.S., Shestakov I.P.
Abstract
We consider a model of two-dimensional random vector with dependent binomial marginals.The distribution for constructed model is determined.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):23-30
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On Asymptotic Unbiasedness of the Estimator for the Linear Functional of Spectral Density of Stationary Gaussian Process
Shomakhov A.Y.
Abstract
For the real-valued stationary Gaussian centered process X(t), t ? R, R = (- ?; + ? ), having a spectral density f(?), a problem of asymptotic unbiasedness is considered for the estimator (statistics) LT = ? ?(?)IT(?)d?, ? ?(- ?; + ? ), where is IT(?) a periodogram of a process, for the linear functional of the spectral density L(f) = ? ?(?)f(?)d? of the stationary Gaussian centered process based on the sample {X (t),0 ? t ? T }.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):31-37
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Analysis of Continuous Playback Probability in P2P Network
Adamu A., Gaidamaka Y.V.
Abstract
In this paper a discrete Markov chain for analyzing the process of content distribution inP2P streaming network was introduced, the steady state probabilities were derived and the probability of continuous playback was analyzed.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):38-46
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On the Stationary Probability Distribution for a Multi-Service Model of the Triple Play Network
Gudkova I.A.
Abstract
Modern multi-service networks are inseparably linked with the commercial concept "tripleplay" that implies simultaneous provisioning of telephony, television and data transmissionover a single broadband connection. These services generate traffics of three types - unicast streaming, multicast streaming and elastic traffics. In this paper, we propose a multi-servicemodel of a triple play single-link network; we obtained an approximate formula for the stationary probability for the model; and finally, we find an exact algorithm for calculating performance measures by reducing the dimension of the problem.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):47-54
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Hysteretic Overload Control in a SIP Signaling Network
Abaev P.O., Gaidamaka Y.V., Samouylov K.E.
Abstract
This review deals with the research of load control mechanisms in signaling networks that use three types of thresholds for congestion control. The main objective of this paper is toanalyze the congestion control mechanisms and mathematical models for SIP-servers. Thestudy is based on hysteresial techniques of flow control, which originally was developed forSignaling System 7. We propose general methods for describing hysteresis signaling flow control techniques. We study the current situation and problems of SIP built-in overloadcontrol mechanism, proposed by IETF. Our approaches to mathematical models constructionin the form of queuing systems with hysteresis control are presented.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):55-73
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Investigation of Solutions of Boundary Problems for the Quasipotential Equation Using the Shift Operator
Amirkhanov I.V., Muzafarov D.Z., Sarker N.R., Sarhadov I., Sharipov Z.A.
Abstract
The quasipotential equations are widely applied to the relativistic description of a system oftwo particles, for example, a quark and an antiquark. In the work, the solutions of boundary problems for the quasipotential equation with the Coulomb potential at various values of parameter .. are investigated with use of the shift operator. It is established that at .. > 0 there is a solution which aspires to the Schr.odinger equation solution. Besides, the so-called frontier layer solutions and transition of one type of the solution into another are found out.Investigations are carried out using the system of symbolical evaluations MAPLE.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):74-82
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On Modeling of Statistical Properties of Classical 3D Spin Glasses
Gevorkyan A.S., Abajyan H.G., Ayryan E.A.
Abstract
The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between spin-chains. It is proved that at the limit of Birkhoffs ergodic hypothesis performance 3D spin glasses can be generated by Hamiltonian of disordered 1D SSC with random environment. Disordered 1D SSC is defined on a regular lattice where one randomly oriented spin is put on each node of lattice. Also it is supposed that each spin randomly interacts with six nearest-neighboring spins (two spins on lattice and four in the environment). The recurrent transcendental equations are obtained on the nodes of spin-chain lattice. These equations combined with the Silvester conditions allow step by step construct spin-chain in the ground state of energy where all spins are in minimal energy of classical Hamiltonian. On the basis of these equations an original high-performance parallel algorithm is developed for 3D spin glasses simulation.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):83-95
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3D Mathematical Model for the Optimization of the Cyclotron Central Electrode Structure
Perepelkin E.E.
Abstract
In this paper the new optimization algorithm for the central region electrode structuredefinition for the cyclotron is considered. The 3D electrical field maps for various accelerating gaps are used for the central region electrode structure optimization. The accelerating gappositions and other parameters are defined by assuming maximal ion energy gain per turn.The best configuration for 4 basic acceleration regimes was constructed for VINCY cyclotron.The beam dynamics analysis for the new configuration was performed. It was shown that the new configuration has much less beam losses and better ion centering.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):96-106
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Numerical Description of the Fluid Pipe Motion with Multiscale Turbulence Model
Plokhotnikov K.E.
Abstract
A numerical description of turbulent motion of a pipe localized fluid is given in the paper. The description is based on multiscale turbulent fluid motion model developed by the author. Comparison of numerical results and experimental data is given.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):107-112
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Recording and Numerical Reconstruction of Digital Fresnel Holograms
Starikov S.N., Cheryomkhin P.A., Krasnov V.V.
Abstract
The scheme of digital Fresnel holograms recording with off-axis objective beam is considered, estimations of limiting parameters of registered objects are acquired. On the basis of the results experimental setup is created, digital Fresnel holograms in both modes of objectsillumination on transmission and on reflection are recorded. The obtained digital holograms are numerically reconstructed. Calculated and experimental values of the parameters are compared.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):113-123
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Optical Image Coding by Time Integration Using Commercial Camera and Liquid Crystal Display
Krasnov V.V., Starikov S.N., Cheryomkhin P.A.
Abstract
Experimental implementation of optical image coding method with time integration using commercial camera and liquid crystal display is described. Results of image optical coding andcoded images numerical restoration are presented. This method could be used for accessiblequality estimation of optical image coding using diffractive optical elements or as independentoptical coding method.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):124-134
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Calculated and Experimental Analysis of Characteristics of Spectrum Analyzer of Surface Roughness
Orazbayev B.D., Osovitskii A.N.
Abstract
The analysis of characteristics of surface roughness spectrum analyzer prototype whichuses a waveguide light scattering is performed. Calculated characteristics and layout optionsare compared with measurements. The experimental spectrum of the surface roughness ofthe gradient waveguide is presented.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):135-143
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On Solution of Diffraction Problem for Cylindrically Symmetric Inhomogeneity
Gorobets A.P., Polovinkin A.N., Ravin A.R.
Abstract
In this paper we consider the problem of diffraction of obliquely incident plane wave byan inhomogeneous cylinder. To simulate the two-dimensional inhomogeneities, we proposethe method of stepwise approximation of a radial dependence of the refractive index. This allows us to obtain expressions for the fields of diffraction, both inside and outside the areaof inhomogeneity, in the form of a series of the cylindrical harmonics.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):144-152
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Waveguide Optical Modulator in Silicon on Insulator
Masalsky N.V.
Abstract
The perspective approach for implementation of effective optical modulation on the basisof the waveguide structure fulfilled through standard technology in silicon on insulator is considered. On the basis of numerical calculations optimization tools of a unit constructionare defined.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):153-158
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The Development of Enterprise Modeling Instrument for Corporate Management Systems
Novikova G.M., Malyutina T.V.
Abstract
This article deals with the research of enterprise modeling instrument's disadvantages and its ways of possible development. There is an example of an integrated notation, containing such notions as "Event" and "Condition", and also an example of using the formal level of application domain to estimate the completeness and the consistency of the models mentioned.
Discrete and Continuous Models and Applied Computational Science. 2011;(4):159-168
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