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  5. VOL 40, NO 2 (2018)
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  7. 2014 год
  8. 36-1

Electronic Modeling

VOL 36, NO 1 (2014)

CONTENTS

Mathematical Methods and Models

  LISTROVOY S.V.
Method of Enumeration of Maximum Independent Sets in Arbitrary Unoriented Graphs
3-16
  BEREGUN V.S., GARMASH O.V., KRASILNIKOV A.I.
Mean-Root-Square Errors of Estimates for Cumulant Coefficients of the Fifth and Sixth Orders
17-28
  ZUBOK V.Yu.
Optimization of Relations between Internet Systems as a Particular Case of Steiner Problem
29-40

Informational Technologies

  VERLAN A.F., CHMYR I.A., FURTAT Yu.O.
Construction of a Formal Model of Question-Answer User-Automated System Interaction
41-48
  OGIR A.S., OGIR E.A., TARAPATA V.V.
New Information Technology of Formation of Holographic Acoustic Images of High Resolution in the Systems of Ultrasonic Visualization for Medical PurposesMedical Purposes
49-58

Accuracy, Reliability, Diagnostics

  SAPOZHNIKOV V.V., SAPOZHNIKOV Vl. V., YEFANOV D.V.
Weighted Codes with Summation for Organization of the Check of Logic Units
59-80

Application of modelling methods and facilities

  YEVDOKIMOV V.F., PETRUSHENKO E.I.
Integral Model of Three-Dimensional Distribution of Eddy Flows in Continuous Casting of Square Cross-Section under Electromagnetic Stirring in Vertical MCC. II
81-96
  ABRAMOVICH R.P., BALVA A.A., SAMOILOV V.D.
Construction of a Navigation Model for Computer Simulators and Parts of Scenario Type
97-106

Short notes

  MOROZOV D.I.
Use of p-Adic Model for Solving Finite-State Conjugacy of the Piecewise-Linear Spherical-Transitive Automorphism of the Binary Rooted Tree
107-112

Method of Enumeration of Maximum Independent Sets in Arbitrary Unoriented Graphs

LISTROVOY S.V.

ABSTRACT

A procedure of enumeration of only maximum independent sets in unoriented arbitrary graphs has been proposed; it allows reducing a temporary difficulty of the algorithm realization.

KEYWORDS

maximal independent sets, cliques.

REFERENCES

1. Kristofides, N. (1978), Teoriya grafov. Algoritmicheskiy podkhod  [Graph Theory. An algorithmic approach], Mir, Moscow, Russia.
2. Emelichev, V.A., Melnikov, O.I., Sarvanov, V.I. and  Tyshkevich, R.I. (1990), Lektsii po teorii grafov [Lectures on the theory of graphs],  Nauka, Moscow, Russia.
3. Listrovoy, S.V. and  Yablochkov, S.V. (2003), “The method of solving the problem of determining the minimal vertex coverings and maximal independent sets”, Elektronnoe modelirovanie, Vol.  25, no.  2, pp. 31-40.
4. Listrovoy, S.V. and  Gul,  A.Yu. (1999), “The method of solving the problem of minimal surfaces, based on the ranking approach”, Ibid., Vol.  21, no. 1, pp. 58-70.

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Mean-Root-Square Errors of Estimates for Cumulant Coefficients of the Fifth and Sixth Orders

BEREGUN V.S., GARMASH O.V., KRASILNIKOV A.I.

ABSTRACT

General expressions have been obtained for determining mathematical expectation and dispersion of estimates for cumulant coefficients of the fifth and sixth orders which permit calculating mean-root-square errors of estimates of these coefficients. Estimation errors of cumulant coefficients γs, s = 3,6, some type symmetric distributions at the fixed volume of a sample have been analyzed. Minimum volume of the sample is determined, when a preset relative error of estimates of cumulant coefficients of these distributions is provided.

KEYWORDS

estimate, cumulant coefficients, mean-root-square error, relative error. 

REFERENCES

1. Levin, B.R. and Shvarts, V. (1985), Veroyatnostnye modeli i metody v sistemakh svyazi i upravleniya [Probabilistic models and methods in communication systems and management],  Radio i svyaz, Moscow, Russia.
2. Novitskiy, P.V. and  Zograf, I.A. (1991), Otsenka pogreshnostey rezultatov izmereniy  [Evaluation of errors of measurement results],  Energoatomizdat, Leningrad, Russia.
3. Shelukhin, O.I. and  Belyakov, I.V. (1992), Negaussovskie protsessy [Non-Gaussian processes],  Politekhnika, St. Petersburg, Russia.
4. Kendall, M. and Styuart, A. (1966), Teoriya raspredeleniy. Per. s angl. Sazonova, V.V. and  Shiryaeva,  A.N.   ; pod red. Kolmogorova, A.N. [Theory of distributions. Transl. from English  Sazonov, V.V. and  Shiryaev, A.N. ; Ed. Kolmogorov, A.N.],  Nauka, Moscow, Russia.
5. Kramer, G. (1975), Matematicheskie metody statistiki. Per. s angl. Monina, A.S. and  Petrova, A.A.; pod red.  Kolmogorova, A.N. [Mathematical Methods of Statistics. Transl. from English. Monin, A.S. and Petrov, A.A.; Ed. Kolmogorov, A.N.], Mir, Moscow, Russia.
6. Mitropolskiy, A.K. (1971), Tekhnika statisticheskikh vychisleniy [Technique of statistical calculations], Nauka, Moscow, Russia.
7. Khan, G. and  Shapiro, S. (1969), Statisticheskie modeli v inzhenernykh zadachakh. Per. s angl. Kovalenko, Ye.G.; pod red. Nalimova, V.V. [Statistical models in engineering design. Transl. from English Kovalenko, E.G.; Ed. Nalimov, V.V.], Mir, Moscow, Russia.
8. Marchenko, B.G. and  Myslovich, M.V. (1992), Vibrodiagnostika podshipnikovykh uzlov elektricheskikh mashin [Vibration diagnostics of bearing units of electric cars], Naukova dumka, Kiev, Ukraine.
9. Beregun, V.S. and  Krasylnikov, O.I.(2010), “Research of areas of inseparable orthogonal representations of probability density”, Élektronika i svyaz, Vol. 56, no.  3, pp. 73-78.
10. Krasilnikov, A.I. and  Pilipenko, K.P. (2008),  “The use of two-component Gaussian mixture for identifying one vertex symmetric probability density”,  Ibid., Vol. 46,  no. 5, pp. 20-29.
11. Garmash, O.V. and  Krasilnikov. A.I. (2011), “Application of Pearson  functions  for Poisson  approximation for the spectral density of Kolmogorov linear stochastic processes”, Elektroníka ta sistemi upravlínnya, Vol. 29, no.  3, pp. 50-59.
12. Beregun, V.S.,  Gorovetska, T.A. and  Krasylnikov,  O.I. (2011), “Statistical analysis of the noise of the knee”,  Akustychnyy vísnyk, Vol. 14, no.  2, pp. 3-15.
13. Ayvazyan, S.A., Enyukov, I.S. and  Meshalkin, L.D. (1983), Prikladnaya statistika: Osnovy modelirovaniya i pervichnaya obrabotka dannykh  [Applied Statistics: Basics of modeling and primary data processing], Finansy i statistika, Moscow, Russia.
14. Kunchenko, Yu.P. (2001), Polinomialnye otsenki parametrov blizkikh k gaussovskim sluchaynykh velichin. Ch. I. Stokhasticheskie polinomy, ikh svoystva i primenenie dlya nakhozhdeniya otsenok parametrov [Polynomial parameter estimates close to the Gaussian random variables. Part I. Stochastic polynomials, their properties and applications to find the parameter estimates], ChITI,Cherkassy, Ukraine.
15. Bendat, Dzh. And  Pirsol, A. (1989), Prikladnoy analiz sluchaynykh dannykh. Per s angl. Privalskogo, V.E.  and Kochubinskogo, A.I.; pod red. Kovalenko, I.N. [Applied analysis of random data. Transl. from English. Privalskogo, V.E.  and Kochubinskogo, A.I.; Ed. Kovalenko, I.N.], Mir, Moscow, Russia.
16. Tikhonov, V.I. (1982), Statisticheskaya radiotekhnika [Statistical radio engineering], Radio i svyaz, Moscow, Russia.
17. Vadzinskiy, R.N. (2001), Spravochnik po veroyatnostnym raspredeleniyam [Handbook of probability distributions], Nauka, St. Petersburg, Russia. 

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Optimization of Relations between Internet Systems as a Particular Case of Steiner Problem

ZUBOK V.Yu.

ABSTRACT

The NP-complex Steiner Problem can be effectively solved in some particular cases. The article discusses approaches to the analysis and optimization of relations between Internet autonomous systems as a solution of a special case of Steiner Problem. Derived from the point of global Internet routing, restrictions on the placement of Steiner points and the organization of additional links are proposed.

KEYWORDS

complex networks, Steiner trees, optimization of relations.

REFERENCES

1. Newman, M.E.J. (2003), “The structure and function of complex networks”, SIAM Review, Vol. 45, pp. 167-256.
2. Fox, G. (2001), “Peer-to-Peer Networks”, Computing in science & engineering, Vol. 3, pp. 2-4.
3. Mahadevan, P.  and  Krioukov, D. (2006), “The Internet AS-Level Topology: Three Data Sources and One Definitive Metric”,  ACM SIGCOMM Computer Communications Review,  Vol. 36, pp. 17-26.
4. Kristofides, N. (1978), Teoriya grafov. Algoritmicheskiy podkhod  [Graph Theory. An algorithmic approach], Mir, Moscow, Russia.
5. Ilchenko, A.V. and  Blyshchik, V.F. (2012), “Minimum to include Steiner trees. An algorithm for constructing”, Tavriyskyy visnyk informatyky ta matematyky, Vol. 20, no. 1, pp. 35-44.
6. Panyukov, A.V. (2004), “Topological methods for solving the Steiner problem on the graph”, Avtomatika i telemekhanika, no. 3, pp. 89-99.
7. Fikhtengolts, G.M. (2001), Kurs differentsialnogo i integralnogo ischisleniya. T. 2. Izd. 7 [Course of differential and integral calculus. Vol.  2, Ed. 7],  Fizmatlit, Moscow, Russia.

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Construction of a Formal Model of Question-Answer User-Automated System Interaction

VERLAN A.F., CHMYR I.A., FURTAT Yu.O.

ABSTRACT

The article is dedicated to the problem of modeling the user dialogue interaction with the automated system in the process of training and work with the system. Logical model of the question and answer structure for their inclusion in the dialogue knowledge base, as well as the classification of question-answer interaction depending on the type of the question precondition are proposed.

KEYWORDS

dialogue interaction, structure of the question, question precondition, the machine dialogue.

REFERENCES

1. Belnap, N. and  Stil, S. (1981), Logika voprosov i otvetov [Logic of questions and answers],  Progress, Moscow, Russia.
2. Chen, Ch. and  Li, R. (1983),  Matematicheskaya logika i avtomaticheskoe dokazatelstvo teorem  [Mathematical logic and automatic theorem proving], Nauka, Moscow, Russia.
3. Khintikka, Ya. (1974), Voprosy o voprosakh. Sbornik statey «Filosofiya v sovremennom mire» [Questions about matters. Collection of articles "philosophy in the modern world"],  Nauka, pp. 303-362.
4. Sleygl, Dzh. (1973), Iskusstvennyy intellect [Artificial intelligence],  Mir, Moscow,  Russia.
5. Green, C.C. and  Bertram, R. (1968), “Research on intelligent question answering systems”,  Proc. Association for Computing Machinery 23rd Nat. Conf. Princeton, N.J., Brandon Systems Press, pp. 169-181.
6. Simmons, R.F. (1970), “Natural Language Question-Answering Systems: 1969”, Communication of the ACM, no. 1, pp. 15-30.
7. Rosenbaum, P.S. (1967), “A Grammar Base Question-Answering Procedure”, Ibid., no. 10, pp. 630-635.
8. Fiksel, J.R. and  Bower, G.H.(1976), “ Question-Answering by a Semantic Network of Parallel Automata”, Journal of Mathematical Psychology, no. 13, pp. 1-45.
9. Yanko, T.E. (1990), “Information model dialog. Scientific and technical information. Series 2”,  Informatsionnye protsessy i sistemy, no.  12, p. 30.
10. Klini, S. (1973), Matematicheskaya logika [Mathematical logic], Mir, Moscow, Russia.

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