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  7. 2012 год
  8. 34-5

Electronic Modeling

VOL 34, NO 5 (2012)

CONTENTS

Mathematical Methods and Models

  LITVIN O.N., NECHUIVITER O.P.
Exactness Substantiation of Cubature Formulas for Approximate Calculation of 3D Integrals of Fast-Oscillating Functions Using Interflatation
3-11
  BOGATYRYOV A.O., KRASNOSHLYK N.A.
Mathematical Model of Interphase Interaction in Metal Binary System
13-28
  KLEVTSOV Yu.A.
Simulation of Multidimensional Objects with Distributed Parameters
29-40

Informational Technologies

  KONDRASHCHENKO V.Ya.
Automatic Construction of Modeling Algorithms for Technical Systems of Network Topology by Logical Inference on the Functional Diagram
41-54

Computational Processes and Systems

  LEMEKHOV Yu.A.
Classification of Intercomponent Connections of High-Frequency Radioelectronic Products
55-68

Accuracy, Reliability, Diagnostics

  ZORIN V.V., ECKEL P.Ya., POPOV V.A., PETROV A.A., TKACHENKO V.V.
Model of Optimization Problems for Reliability of Electric Distribution Networks: Survey of Foreign Experience
69-90

Application of Modelling Methods and Facilities

  ZAKHARCHENKO S.N., SHIDLOVSKAYA N.A.
Modeling of Resistance of Granulated Current-Conducting Mediums by Parametric Dependences
91-102
  MELNIK I.V., TUGAY S.B.
Simulation of Volt-Ampere Characteristics of Non-Independent Additional Discharge in Triode Gas Discharge Electron Guns
103-105

 

 

Exactness Substantiation of Cubature Formulas for Approximate Calculation of 3D Integrals of Fast-Oscillating Functions Using Interflatation

LITVIN O.N., NECHUIVITER O.P.

ABSTRACT

Cubature formulas of the calculation of 3D highly oscillatory integrals are investigated by using operators of piece-polynomial spline-interflatation. These formulas are optimal by exactness. The estimations of error of approaching of the cubature formulas are presented on the class of differentiable functions.

KEYWORDS

integrals of rapidly oscillating functions of three variables, cubature formulas, interflatation functions.

REFERENCES

  1. Lytvyn, O.M. (2002), Interlinatsiya funktsiy ta deyaki yiyi zastosuvannya  [Interlineation  functions and some of its applications], Osnova, Kharkiv, Ukraine.
  2. Sergienko, I.V., Zadiraka, V.K., Lytvyn, O.M.  and  et al.  (2011),  Optymalni alhorytmy obchyslennya intehraliv vid shvydko ostsylyuyuchykh funktsiy ta yikh zastosuvannya. T. 1. Alhorytmy   [Optimal algorithms for calculating integrals of rapidly oscillating functions and their application. Vol. 1. Algorithms], Naukova Dumka, Kyiv, Ukraine.
  3. Lytvyn, О.N. and Nechuyviter, О.P. (2010), “Methods in the multivariate digital signal processing with using spline-interlineation”, Proc. of the IASTED International Conf. on Automation, Con­trol, and Information Technology (ASIT 2010), Novosibirsk, June 15-18, 2010, pp. 90-96.
  4. Lytvyn, O.M. and Udovychenko, V.M.  (2004), “Operators of finite three-dimensional Fourier transform”, Radioelektronika i informatyka, no. 4 (29), pp. 130-133.
  5. Lytvyn, O.M. and  Udovychenko, V.M. (2005), “Three-dimensional finite  Fourier and Hartley transforms  with use of  interflatation functions”, Vestnik Natsionalnogo tekhnicheskogo universiteta «KhPI», Vol. 38, pp. 90-130.
  6. Lytvyn, O.M. and  Nechuyviter, O.P. (2011),  “3D Fourier coefficients and operators piecewise constant spline interflatation”, Matematychne ta komp'yuterne modelyuvannya. Seriya: Fizyko-matematychni nauky [Mathematical and computer modeling. Series: physical and mathematical sciences. Scientific Papers], Zbirnyk naukovykh prats Kamyanets-Podilskyy natsionalnyy universytet im. Ivana Ohiyenka, Vol. 3, pp. 155-161.
  7. Lytvyn, O.M. and  Nechuyviter, O.P.  (2010), “On the lower bound for the optimal numerical integration error for class differentiated functions of two and three variables”, Postup v nauku: Zbirnyk naukovykh prats Buchatskoho instytutu menedzhmentu i audytu, no. 6, pp. 130-133.

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Mathematical Model of Interphase Interaction in Metal Binary System

BOGATYRYOV A.O., KRASNOSHLYK N.A.

ABSTRACT

A mathematical model of the interphase interaction in metal binary system with regard for the dif¬ference of partial molar volumes of components has been proposed and realized. Numerical sim¬ulation of growth (suppression) phases in a model system is performed. The effect of the partial molar volumes on the process of movement of interphase boundaries has been investigated.

KEYWORDS

mutual diffusion, intermediate phases, partial molar volume, Stefan problem.

REFERENCES

  1. Vasiliev, A.  (2007), “Kulicke & Soffa Industries: equipment and technologies for bonding wire leads”, Chip news,  no.  8 (121), pp. 67-71.
  2. Deryagina, I.L., Popova, E.N., Zakharevskaya, Ye.G. and  Romanov, Ye.P.  (2011), “Influence of the doping method  and the geometry of the composite on the structure of nanocrystalline layers Nb3Sn  in superconducting composites Nb/Cu-Sn”,  J. of Siberian Federal University. Mathematics & Physics,  no.  4 (2), pp. 149-161.
  3. Gurov, K.P. and  Gusak, A.M. (1982), “The description of the reaction diffusion”,  Fizika i khimiya obrabotki materialov, no.  6, pp. 109-114.
  4. Gurov, K.P. and  Gusak, A.M.  (1990), “About the incubation period of formation of intermediate phases, Izvestiya AN SSSR. Metally, no.  1, pp. 163-165.
  5. Gusak, A.M. and  Gurov, K.P.  (1982), “Kinetics of phase formation in the diffusion zone with mutual diffusion”, Fizika metallov i metallovedenie, Vol.  53, no.  5, pp. 842-851.
  6. Gusak, A.М.  (2010), Diffusion-Controlled Solid State Reactions: in Alloys, Thin-Films, and Nano Systems, Wiley-VCH.
  7. Sauer, F. and   Freise, V. (1962), “Diffusion in Binaren Gemischen Mit Volumenanderung, Z. Electro- chem., Vol. 66, pp. 353-363.
  8. Nakajima, H. (1997), “The Discovery and Acceptance of the Kirkendall Effect: The Result of a Short Research Career”,  JOM Journal of the Minerals, Vol. 49,  no. 6, pp. 15-19.
  9. Bogdanov, V.V. (2006),  Dyfuziya v krystalakh.  Navchalnyy posibnyk [Diffusion in crystals.  Textbook],  KHNU im. V.N. Karazina, Kharkiv, Ukraine.
  10. Mehrer, Н.  (2007), “Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-Controlled Processes”, Springer Series in Solid-State Sciences, Vol. 155, p. 654.
  11. Bogatyryov, A.O. and  Krasnoshlyk, N.A. (2010),  “Modeling of multiphase diffusion in binary metal system”, Vísnik Cherkaskogo uníversitetu. Seríya «Fíziko-matematichní nauki», Vol. 185, pp. 80-91.
  12. Krasnoshlyk, N.A. and  Bohatyryov, A.O.  (2010), “Numerical modeling of mutual diffusion of mobile interfaces”, Visnyk Cherkaskoho universytetu. Seriya «Prykladna matematyka. Informatyka», Vol. 173, pp. 48-57.

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Simulation of Multidimensional Objects with Distributed Parameters

KLEVTSOV Yu.A.

ABSTRACT

The algorithm of simulation of objects described by systems of differential partial equations has been designed on the basis of the spectral theory of non-stationary control systems. The rules set­ting the conformity between operations in time-space and spectral areas are stated. The transfer function of multidimensional object is entered. The example illustrates application of the method.

KEYWORDS

spectral characteristics, modeling, transfer function, the objects with distributed parameters.

REFERENCES

  1. Kraskevich, V.E. and  Klevtsov, Yu.A. (1983), “Spectral method for the description of multidimensional objects with distributed parameters. Adaptive ACS”, Tekhnіka, Issue  11,  pp. 11-16.
  2. Solodovnikov, V.V. and  Semenov, V.V.  (1974), Spektralnaya teoriya nestatsionarnykh sistem upravleniya [Spectral theory of nonstationary control systems], Nauka, Moscow, Russia.
  3. Kraskevich, V.Ye. and Klevtsov, Yu.A. (1981), “Spectral representation of linear objects with distributed parameters”,  Kibernetika na morskom transporte,  Issue 10,  pp. 87-94.
  4. Klevtsov, Yu.A. (1988), “Spectral description of objects with distributed parameters”,  Elektronnoe modelirovanie, Vol. 10, no. 3, pp. 27-31.
  5. Klevtsov, Yu.A.  (1998), “Algorithm for solving linear algebraic equation in spectral models of objects with distributed parameters”, Ibid., Vol.  20, no.  2, pp. 22-27.
  6. Klevtsov,  Yu.A. (2001),  “Simulation algorithm of the third kind boundary problem”, Ibid., Vol.  23, no. 3, pp. 40-46.

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Automatic Construction of Modeling Algorithms for Technical Systems of Network Topology by Logical Inference on the Functional Diagram

KONDRASHCHENKO V.Ya.

ABSTRACT

The author describes the general approaches and principles of automatic construction of modeling algorithms for solution of the problems at the project analysis stage of a certain class of technical systems based on the methods of artificial intelligence. The proposed method can be mathematically defined as the non-linear analogue method of defining\pard fs20 variables with their automatic choice.

KEYWORDS

structural modeling, automatic algorithmization.

REFERENCES

  1. Kondrashchenko, V.Ya., Vynnychuk, S.D. and  Fedorov, M.Yu.(1990),  Modelirovaniye gazovykh i zhidkostnykh raspredelitelnykh sistem [Modelling gas and liquid distribution systems], Naukova dumka,Kiev, Ukraine.
  2. Kondrashchenko, V.Ya. (2008), “Logic model as a mechanism for constructing modeling algorithms”, Sbornik trudov konferentsii «Modelirovanie-2008», Tom 1 [Proceedings of the Conference "Modelling of 2008"],  Kiev, Institute for  Modelling  in  Energy Engineering, May 14-16,   2008, Vol. 1, pp. 88-93.
  3. Adamenko, A.N. and Kuchukov, A.M. (2003), Logicheskoye programmirovaniye i Visual Prolog [Logic programming and Visual Prolog], BKHV-Petersburg, Saint-Petersburg, Russia.

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