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Euler–Dirac integrals and monotone functions in models of cyclic synthesis
V. V. Ivanov Sobolev Institute of Mathematics, Novosibirsk, Russia
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
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
Linking options:
https://www.mathnet.ru/eng/smj2824 https://www.mathnet.ru/eng/smj/v57/i6/p1291
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Abstract page: | 245 | Full-text PDF : | 138 | References: | 40 | First page: | 5 |
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