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Information × Registration Number 0222U004414, 0118U003669 , R & D reports Title The application of the mathematical methods in the study of integral characteristics of deterministic and stochastic complex systems popup.stage_title Head Bogdanskii Yurii V., Доктор фізико-математичних наук Registration Date 01-08-2022 Organization Public organization organization of veterans and graduates of the Institute of Energy Conservation and Energy Management of the National Technical University of Ukraine "Kyiv Polytechnic Institute named after Igor Sikorsky" popup.description2 Scientific Research Work: 97 pages, 1 part, 8 add., 15 references. STOKES FORMULA, GAUSS-OSTROGRADSKY FORMULA, FRIEDRICH'S INEQUALITY, SPACE PICTURE; MAHALANOBIS DISTANCE, FUZZY NUMBER, ZHEGALKIN POLYNOMIAL, PARABOLIC EQUATION, NON-LINEAR POTENTIAL, PERIODIC SOLUTION. Research objects: Stokes formula on Banach manifold. L_2-version of Gauss-Ostrogradsky formula. Friedrichs inequality on a Hilbert space. Object recognition on a space picture of Earth. Trotter-Daletsky formula for elliptic operator. Convergence of functional sequences with a fuzzy argument. Triangle method for obtaining of Zhegalkin polynomial. Periodic solution of differential equations. Research aims: To extend Stokes formula on Banach manifold. To obtain L_2-version of Gauss-Ostrogradsky formula. To generalize Friedrichs inequality on a Hilbert space. To improve pixels classification of a space picture of Earth To extend Trotter-Daletsky formula for elliptic operator. To get conditions for convergence of functional sequences with a fuzzy argument. To obtain another justification for triangle method for obtaining of Zhegalkin polynomial To get conditions for existence of periodic solution of differential equations. Results obtained: Divergent version of Stokes formula is extended on Banach manifold with uniform atlas. L_2-version of Gauss-Ostrogradsky formula is obtained. Two version of generalization of Friedrichs inequality on a Hilbert space are derived. Using Mahalanobis distance, pixels classification of a space picture of Earth is improved. Trotter-Daletsky formula is extended for elliptic operator. Conditions for convergence of functional sequences with a fuzzy argument are obtained. Another justification for triangle method for obtaining of Zhegalkin polynomial are obtained. Conditions for existence of periodic solution of differential equations of the second order and equation with delay are obtained. Product Description popup.authors Bogdansky Yuriy V. Bondarenko Vikor G. Bokhonov Yuriy Ye. Kalyuzhnyi Oleksandr O. Kaniovska Iryna Yu. Maltsev Anton Yu. Podkolzin Glib B. Spektors'kyj Igor Ya. Stus' Oleksandr V. Chapovsky Yuriy A. popup.nrat_date 2022-08-01 Close