ARISTOV V.V.

ABSTRACT

An augmented mathematical model of multistage difference-differential formulas of numerical integration for the analysis of the effect of speed-up regions on solution of the system of homogeneous differential equations has been proposed. The algorithm of their transformation into equivalent in behavior one-stage numerical formulas has been developed. Methods of transformation of the extended block matrix into the system matrix of the general analytical model have been
proposed.

KEYWORDS

numerical integration, multi-step formula for integration, transfer functions, the site acceleration, extended matrix, eigenvalues, loopback test. 

REFERENCES

1. Khemming, R.R. (1968), Chislennye metody analiza [Numerical methods of analysis],  Nauka, Moscow, Russia. 
2. Aristov, V.V. (1992), Funktsionalnye makrooperatsii: Osnovy iteratsionnykh algoritmov Functional macro operation: Basic iterative algorithms], Nauk. dumka, Kiev, Ukraine.
3. Aristov, V.V. (2011), “Mathematical models of iterative relations generalized CORDIC-algorithm”, Elektronnoe modelirovanie, Vol.  33, no.  1, pp. 3-29.
4. Gantmakher, F.R. (1988), Teoriya matrits  [Matrix theory], Nauka, Moscow, Russia.
5. Culver, W.J. (1966), “On the existence and uniqueness of the real logarithm of a matrix”, Proc. of the American Mathematical Society, Vol. 17, no. 5, pp. 1146-1151.
6. Higham, N. (2012), “The Matrix Logarithm: from Theory to Computation”, 6-th European Congress of Mathematics, July 2012, available at: http://www.ma.man.ac.uk/~higham
7. Aristov, V.V. (1996), “Application of canonical transfer functions for analysis, synthesis and transformation of iterative algorithms”, Elektronnoe modelirovanie, Vol. 18, no. 4, pp. 74-81.

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KOSTYAN N.L., NAKONECHNAYA O.A.

ABSTRACT

The paper deals with method to obtain analytical expressions for the functions of time by representation of experimentally obtained data in a form of solution of a homogeneous linear differential equation with constant coefficients. The increase of the approximation accuracy was achieved by using the method of finding the pseudoinverse matrix.

KEYWORDS

approximation, z-transform homogeneous linear differential equation,  pseudo inverse matrix. 

REFERENCES

1. Neymark, Yu.I. (2010), Dinamicheskie sistemy i upravlyaemye protsessy [Dynamical systems and controlled processes], Librokom, Moscow, Russia.
2. Stepanyants, G.A. (2010), Teoriya dinamicheskikh system [The theory of dynamical systems], Librokom, Moscow, Russia.
3. Gantmakher, F.R. (2004), Teoriya matrits [Matrix theory], Fizmatlit, Moscow, Russia.

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DOLGIN V.P., BARMINA M.V., DOLGIN D.I.

ABSTRACT

The method for solution of the problem of correcting the intensities of flows providing the preset features of queueing system has been stated. The authors demonstrate a possibility to solve the inverse queueing problem for the linear system of equations by direct and compensation methods.

KEYWORDS

flow of events, probability, state graph, inverse problem, adaptation.

REFERENCES

1.Gerchikova, I.N. (2001), Menedzhment. 3-e izd.  [Management. 3rd ed], YuNITI, Moscow, Russia. 

2. Meskon, M.Kh., Albert, M. and  Khedouri, F. (2000), Osnovy menedzhmenta: Perevod s angl. [Fundamentals of Management], Translated from English, Delo, Moscow, Russia.

3. Venttsel, E.S. and  Ovcharov, L.A.  (2000), Teoriya sluchaynykh protsessov i yeye inzhenernyye prilozheniya [Theory of random processes and its engineering applications], Vysshaya shkola,  Moscow, Russia.  

4. Dolgin, D.I., Barmina, M.V. and  Dolgin, V.P. (2013), “A correction method of a decentralized system of queuing”,  Progressivnye napravleniya razvitiya mashino-priborostroeniya, transporta i ekologii. Materialy mezhdunar. nauch.-tekhn. konf. studentov, aspirantov i molodykh uchenykh  [The progressive directions  of development of the machine device construction, transport and the environment. Materials of   intern. scientific  and tech. conf. of students, graduate students and young scientists], Sevastopol, SevNTU, May 20-23, 2013,  pp. 16-17.

5. Ilin, V.A. and  Kim, G.D. (2007), Lineynaya algebra i analiticheskaya geometriya   Linear algebra and analytic geometry], TK Velbi, izd-vo Prospekt, Moscow, Russia.

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YEVDOKIMOV V.F., PETRUSHENKO E.I.

ABSTRACT

An auxiliary problem has been solved to simplify the solution of the basic problem: the integral model of three-dimensional distribution of eddy flows in the continuous casting has been constructed making no allowance for eddy flows in a mould; the model is based on the vector system of integral equations, equivalent to Maxwell equations in the conducting medium.

KEYWORDS

integral model,  three-dimensional distribution, eddy currents,  continuous casting,  square cross-section,  vector system of integral equations, scalar system of integral equations, complex form,  algebraic form, electromagnetic stirring, vertical MCC. 

REFERENCES

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