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Aleksei Fedorovich Filippov ((ロシア語:Алексей Фёдорович Филиппов); 29 September 1923 – 10 October 2006) was a Russian mathematician, who worked on differential equations, differential inclusions, diffraction theory, and numerical methods. A. F. Filippov was born in Moscow in 1923. After serving in the Red Army during the Second World War he attended Moscow State University (Faculty of Mechanics and Mathematics). After graduating from the university in 1950, he worked there until his death in 2006 (a professor since 1978). He got his Ph.D. under the supervision of I. G. Petrovsky. Filippov showed interest in continuous loops in 1950 when he constructed a proof that they divide a plane into interior and exterior parts.〔A.F. Filippov (1950) (An elementary proof of Jordan's theorem ), ''Uspekhi Matematischeskikh Nauk'' 5(39):173–6, link from All-Russian Mathematical Portal〕 Known as the Jordan curve theorem, it exemplifies a mathematical proposition easily stated but difficult to prove. In 1955 Filippov and V. S. Ryaben'kii became interested in difference equations and wrote ''On the Stability of Difference Equations''.〔Review by W.J. Trjitzinsky: 〕 The work was developed into a textbook in 1961 which was used in Moscow State University and many other Russian universities for several decades.〔 U.W. Hochstrasser review: 〕 In 1959 he published a paper containing a lemma about implicit functions designed for use in optimal control theory which is named after him (''Filippov's lemma'').〔A.F. Filippov (1959) "On certain questions in the theory of optimal control", Journal of the Society for Industrial and Applied Mathematics Control, Series A, 1:76–84〕〔E.J. McShane & R.B. Warfield Jr. (1967) (On Filippov's Implicit Functions Lemma ), ''Proceedings of the American Mathematical Society''〕〔S. Nababan (1979) "A Filippov-type lemma for functions involving delays and its application to time-delayed optimal control problems", ''Journal of Optimization Theory and Applications'' 27(3):357–76〕 Filippov made an important contribution in the theory of discontinuous ordinary differential equations with his monograph ''Differential Equations with Discontinuous Righthand Sides'' (1985).〔A.F. Filippov (1985) (Differential Equations with Discontinuous Righthand Sides ), Kluwer Academic Publishers, link from Google Books, review by J. Jarník: 〕 Such set-valued dynamical systems arise in sliding mode control, an important class of feedback control systems demonstrating robust control. Such systems model some mechanical systems with Coulomb friction, and more recently genetic networks. A. F. Filippov was awarded the Moscow State University's Lomonosov Award in 1993. ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Aleksei Fedorovich Filippov」の詳細全文を読む スポンサード リンク
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