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Bernard Osgood Koopman (1900 – August 18, 1981) was a French-born American mathematician, known for his work in ergodic theory, the foundations of probability, statistical theory and operations research. ==Education and work== After living in France and Italy, the Koopmans immigrated to the United States in 1915. Koopman was a student of George David Birkhoff and his initial work concentrated on dynamical systems and mathematical physics. In 1931/1932, Koopman and John von Neumann proposed a Hilbert space formulation of classical mechanics, known as the Koopman–von Neumann classical mechanics. During World War II, he joined the Anti-Submarine Warfare Operations Research Group (ASWORG, later ORG) in Washington, D.C., directed by Philip M. Morse, to work for the U.S. Navy.〔Philip M. Morse: ''In memoriam: Bernard Osgood Koopman, 1900–1981'', Operations Research, Vol. 30, No. 3 (May - Jun., 1982), pp. viii+417-427. Published by: Institute for Operations Research and the Management Sciences (INFORMS), DOI: 10.2307/170181 ((jstor 170181 ))〕 The work of Koopman and his colleagues at ASWORG concerned the development of techniques for the US Navy to hunt U-boats.〔Gary Kinder: ''Ship of Gold in the Deep Blue Sea'' Grove/Atlantic Inc., 2009, ISBN 978-0802144256, (p. 215 )〕 The theoretical work laid the foundations for search theory which subsequently became a field of its own within operations research.〔"Search theory () came to being during World War II with the work of B. O. Koopman and his colleagues in the Antisubmarine Warfare Operations Research Group (ASWORG)." Cited from: Henry R. Richardson, ''Search theory'', Professional Paper 449, April 1986〕 Their results remained classified ''Confidential'' for many years after the war; after 1955 Koopman set out to publish three articles on easily declassifiable portions of the work in the Journal of the Operations Research Society of America. He wrote down the results in detailed form in the book ''Search and Screening'' which was declassified in 1958.〔Laura H. Nunn, (An introduction to the literature on search theory ), Professional Paper 305, June 1981, Center for Naval Analyses (CNA) Corporation (accessed 31.01.2012)〕 A large part of his work is a systematization of the work performed by his group at ASWORG; the portions on optimum allocation of search effort and on probabilistic aspects of search theory were developed by Koopman himself.〔 The Pitman–Koopman–Darmois theorem states that the only families of probability distributions that admit a sufficient statistic whose dimension remains bounded as the sample size increases are exponential families. 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「Bernard Koopman」の詳細全文を読む スポンサード リンク
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