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  8. 40-3

Electronic modeling

Vol 40, No 3 (2018)

https://doi.org/10.15407/emodel.40.03

CONTENTS

Mathematical Modeling and Computation Methods

  SAUKH S.Ye.
Methodology and Methods of Mathematical Modeling of Energy Engineering in Market Conditions
3-32
  LISTROVOY S.V., LISTROVAYA E.S.
Substantiation of the Hypothesis on Four Colors
33-40

Informational Technologies

  SAPOZHNIKOV V.V., SAPOZHNIKOV Vl.V., EFANOV D.V.
Modular-Modified Weighted Summation Codes Detecting Any Errors of Odd Multiplicities
41-62

Application of Modeling Methods and Facilities

  KRAVTSOV H.A., KOSHEL V.I., DOLGORUKOV A.V., TSURKAN V.V.
Trainable Model of the Calculus over Classifications
63-76
  MAKARICHEV A.V., KUD A.A., SHCHUKIN A.B.
Distribution of the Sums of Maximums for the Service Time of Applications for the Period of Employment in the Processes of Auction Trading
77-86
  KHYLCHENKO T.V.
Modeling of the Work of a New Dual-Channel Capacitive Mems Gravimeter of Aviation Gravimetric System
87-118
  LYSENKOV E.A., BOHVAN S.I., KLEPKO V.V.
Structural Models for Describing X-Ray Scattering from Carbon Nanotubes
105-117

METHODOLOGY AND METHODS OF MATHEMATICAL MODELING OF ENERGY ENGINEERING IN MARKET CONDITIONS

S.Ye. Saukh, Dr Sc. (Eng.),
Pukhov Institute for Problems of Modeling in Energy Engineering, NAS of Ukraine (15 General Naumov St, Kyiv, 03164, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.)

Èlektron. model. 2018, 40(3):03-32
https://doi.org/10.15407/emodel.40.03.003

ABSTRACT

Peculiarities of development of energy engineering modeling systems under conditions of market mechanisms of energy complex management have been analyzed. The requirements on ensuring the adequacy of energy modeling systems in market conditions have been formulated. The generalized mathematical model of the competitive equilibrium on the electricity market has been presented in the form of a system of problems of mathematical programming with complementarity constraints. The search for the solution of such a system of problems we reduce to finding a solu tion of large scale mixed nonlinear complementary problem in the form of a Karush-Kuhn-Tucker system. A collection of original methods is presented for solving individual subtasks arising from the application of the quasi-Newtonian method for solving complementary problems of large dimension. The benefits of our solver (ICRS) created on the original methodology in comparison with the worldwide PATH solver are shown. A model of equilibrium states of the electricity market of Ukraine is presented in the form of a detailed description of the system of tasks of mathematical programming with complementarity constraints. The computational experiments show the application of the methodology for constructing adequate mathematical models of energy markets and propose methods for solving a system of problems of mathematical programming with complementarity constraints.

KEYWORDS

energy market, equilibrium state, modeling methodology, mathematical programming, complementary problem, solver of large-scale complementary problems, computational experiment.

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SUBSTANTIATION OF THE HYPOTHESIS ON FOUR COLORS

S.V. Listrovoy, Dr Sc. (Eng.),
Ukrainian State University of Railway Transport, 7 Feuerbach Sq., Kharkov, 61050, Ukraine Е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.,
E.S. Listrovaya, Cand. Sc. (Eng.)
Zhukovsky National Aerospace University, 17 Chkalov St, Kharkov, 61070, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Èlektron. model. 2018, 40(3):33-40
https://doi.org/10.15407/emodel.40.03.033

ABSTRACT

The paper provides a substantiation of the machine proof of the hypothesis of four colors conducted by a group of mathematicians headed by K. Appel and V. Heiken [1].

KEYWORDS

chromatic number, triangulation, graph density

REFERENCES

1. Appel, K. and Haken, W. (1989), Every planar map four colorable contemporary mathematics, (R. I.): Amer. Math. Soc., Vol. 89.
https://doi.org/10.1090/conm/098
2. Berge, K. (1962), Teoriya grafov i yeyo primenenie [The theory of graphs and its application], IL, Moscow, USSR.
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MODULAR-MODIFIED WEIGHTED SUMMATION CODES DETECTING ANY ERRORS OF ODD MULTIPLICITIES

V.V. Sapozhnikov, Dr Sc. (Eng.), Vl.V. Sapozhnikov, Dr Sc. (Eng.), D.V. Efanov, Cand. Sc. (Eng.),
Emperor Alexande I St.Petersburg State Transport University, 9 Moskovsky Ave, Saint Petersburg, 190031, Russian Federation, e-mail:  This email address is being protected from spambots. You need JavaScript enabled to view it.

Èlektron. model. 2018, 40(3):41-62
https://doi.org/10.15407/emodel.40.03.041

ABSTRACT

The problem has been considered of constructing a class of codes with summation with the smallest total number of undetectable errors in data vectors for a given numbers of data and check bits. An algorithm is proposed for constructing modified modular codes with summation of weighted data bits with a sequence of weight coefficients that forms a natural series of numbers. Properties of a new class of codes are analyzed in comparison with known modular codes with summation of single indicators of digits. A classification and a detailed comparative analysis of modular codes with summation possessing the property of identifying any errors with odd multiplicities are given. The advantages and disadvantages of the new modified modular weighted codes with summation are shown.

KEYWORDS

technical diagnostics of discrete systems, summation code, Berger’s code, modular summation code, undetectable error, weighted summation codes, modified weighted summation code

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TRAINABLE MODEL OF THE CALCULUS OVER CLASSIFICATIONS

H.А. Kravtsov, Cand. Sc. (Eng.), V.I. Koshel, Post-graduate, A. V. Dolgorukov, Post-graduate
Pukhov Institute for Problems in Electrical Engineering, 15 General Naumov St, Kyiv, 03164, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.   This email address is being protected from spambots. You need JavaScript enabled to view it. This email address is being protected from spambots. You need JavaScript enabled to view it.
V.V. Tsurkan, Sc. (Eng.),
National Technical Institute of Ukraine “Ihor Sikorsky Kyiv Polytechnic Institute” (22, Bldg, 37 Pobeda St, Kyiv, 03056, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Èlektron. model. 2018, 40(3):63-76
https://doi.org/10.15407/emodel.40.03.063

ABSTRACT

The authors investigate the classical concept of measure in accordance with symmetry conditions, reflexivity and triangle inequality. The requirements to the measure have been formulated for its further use in the theory of the calculus over classification. Some features of the distance function, correlation coefficient, cosine measure of similarity are signification restrictions for applying them for the theory. All measures used in practice have been studied. The results of research have shown that new measure should be introduced that has been proposed. The authors have given formal definition of the trainable model of calculus over classification.

KEYWORDS

similarity measure, difference measure, distance function, calculation model, model trainability, continuum of equivalent measures

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