Search academic texts

Registration Number

0222U004616, 0116U005558 , R & D reports

Title

Embeddings of functional and operator spaces and mathematical models

Head

Korenovskyi Anatolii O, Доктор фізико-математичних наук

Registration Date

19-09-2022

Organization

Odessa I. I. Mechnikov National University

Description

 For monotone functions, which satisfy the Gurov—Reshetnyak condition, it are found the sharp positive and negative powers of summability on the semiaxis. Estimates of equimeasurable rearrangements of functions from the specified classes are established. Obtained estimates of equimeasurable rearrangements of functions from classes satisfying Hölder's and Jensen's inverse inequalities. The rate of decrease of integral averages was found and the properties of monotonic functions from the classes satisfying the reverse Hölder and Jensen inequalities were obtained and examples showing the accuracy of the obtained results were constructed. Bernstein-type inequalities for fractional derivatives and fractional integrals of arbitrary algebraic polynomials in the space L0 and estimates for constants in Segé and Turan-type inequalities for algebraic polynomials on the unit circle and on the segment [0, 2π] are obtained. The structure of the Bergman space in the Siegel domain is established with up to isomorphism; the commutativity of the Toeplitz algebra of operators in weighted Bergman spaces is proved. For three industrial species (turtle, sprat and rapana) a general database was formed and the parameters necessary for stock assessment were found, the corresponding mathematical methods were finalized. Mathematical models were developed for the studied species in the Stock Synthesis (SS3) package, which were applied by the Black Sea group of experts of the National Research Council of Ukraine. The obtained results and built models can be used to estimate stocks in the waters of the Black Sea and manage the fishing industry of Ukraine.

Product Description

popup.authors

Adamov Aleksey M.
Vartanyan Grigoriy M.
Kovalenko Larisa G.
Leonchyk Evgeniy Y.
Lysenko Zoya M.
Shanin Ruslan V.