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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 6, Pages 1291–1312
DOI: https://doi.org/10.17377/smzh.2016.57.608
(Mi smj2824)
 

Euler–Dirac integrals and monotone functions in models of cyclic synthesis

V. V. Ivanov

Sobolev Institute of Mathematics, Novosibirsk, Russia
References:
Abstract: We study the limit behavior of sequences of cyclic systems of ordinary differential equations that were invented for the mathematical description of multistage synthesis. The main construction of the article is the distribution function of initial data. It enables us to indicate necessary and sufficient existence conditions as well as completely describe the structure and all typical properties of the limits of solutions to the integro-differential equations of “convolution” type to which the systems of cyclic synthesis are easily reduced. All notions, methods, and problems under discussion belong to such classical areas as real function theory, Euler integrals, and asymptotic analysis.
Keywords: multistage synthesis, Dirac bells, incomplete Euler gamma-function, Laplace asymptotics, Abel sums, distribution of initial data, Stieltjes integral, Helly selection principle, two-dimensional Heaviside step function, Lebesgue point, Chebyshev inequality.
Received: 16.06.2015
Revised: 20.09.2016
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 6, Pages 1011–1028
DOI: https://doi.org/10.1134/S0037446616060082
Bibliographic databases:
Document Type: Article
UDC: 517.925+517.5
Language: Russian
Citation: V. V. Ivanov, “Euler–Dirac integrals and monotone functions in models of cyclic synthesis”, Sibirsk. Mat. Zh., 57:6 (2016), 1291–1312; Siberian Math. J., 57:6 (2016), 1011–1028
Citation in format AMSBIB
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\paper Euler--Dirac integrals and monotone functions in models of cyclic synthesis
\jour Sibirsk. Mat. Zh.
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\vol 57
\issue 6
\pages 1291--1312
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\crossref{https://doi.org/10.17377/smzh.2016.57.608}
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\transl
\jour Siberian Math. J.
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\issue 6
\pages 1011--1028
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    Сибирский математический журнал Siberian Mathematical Journal
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