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Bernard Koopman
Bernard Osgood Koopman (January 19, 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, Koopman emigrated 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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
7th Arrondissement Of Paris
The 7th arrondissement of Paris (''VIIe arrondissement'') is one of the 20 Arrondissements of Paris, arrondissements of the capital city of France. In spoken French, this arrondissement is referred to as ''le septième''. The arrondissement, called Palais-Bourbon in a reference to the seat of the National Assembly (France), National Assembly, includes some of the major and well-known tourist attractions of Paris, such as the Eiffel Tower, the Les Invalides, Hôtel des Invalides (Napoleon's resting place), the Chapel of Our Lady of the Miraculous Medal, as well as a concentration of museums such as the Musée d'Orsay, Musée Rodin and the Musée du Quai Branly – Jacques Chirac. Situated on the Rive Gauche—the "Left" bank of the Seine, River Seine—this central arrondissement, which includes the historical aristocratic neighbourhood of Faubourg Saint-Germain, contains a number of French national institutions, among them the National Assembly and numerous Ministry (government ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies and the Axis powers. World War II was a total war that directly involved more than 100 million personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the only two nuclear weapons ever used in war. World War II was by far the deadliest conflict in human history; it resulted in 70 to 85 million fatalities, mostly among civilians. Tens of millions died due to genocides (including the Holocaust), starvation, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pitman–Koopman Theorem
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family. The terms "distribution" and "family" are often used loosely: specifically, ''an'' exponential family is a ''set'' of distributions, where the specific distribution varies with the parameter; however, a parametric ''family'' of distributions is often referred to as "''a'' distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families is sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Fogg Osgood
William Fogg Osgood (March 10, 1864, Boston – July 22, 1943, Belmont, Massachusetts) was an American mathematician. Education and career In 1886, he graduated from Harvard, where, after studying at the universities of Göttingen (1887–1889) and Erlangen (Ph.D., 1890), he was instructor (1890–1893), assistant professor (1893–1903), and thenceforth professor of mathematics. From 1918 to 1922, he was chairman of the department of mathematics at Harvard. He became professor emeritus in 1933. From 1934 to 1936, he was visiting professor of mathematics at Peking University. From 1899 to 1902, he served as editor of the ''Annals of Mathematics'', and in 1905–1906 was president of the American Mathematical Society, whose ''Transactions'' he edited in 1909–1910. Contributions The works of Osgood dealt with complex analysis, in particular conformal mapping and uniformization of analytic functions, and calculus of variations. He was invited by Felix Klein to write an article ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percy Williams Bridgman
Percy Williams Bridgman (April 21, 1882 – August 20, 1961) was an American physicist who received the 1946 Nobel Prize in Physics for his work on the physics of high pressures. He also wrote extensively on the scientific method and on other aspects of the philosophy of science. The Bridgman effect, the Bridgman–Stockbarger technique, and the high-pressure mineral bridgmanite are named after him. Biography Early life Bridgman was born in Cambridge, Massachusetts, and grew up in nearby Auburndale. Bridgman's parents were both born in New England. His father, Raymond Landon Bridgman, was "profoundly religious and idealistic" and worked as a newspaper reporter assigned to state politics. His mother, Mary Ann Maria Williams, was described as "more conventional, sprightly, and competitive". Bridgman attended both elementary and high school in Auburndale, where he excelled at competitions in the classroom, on the playground, and while playing chess. Described as both shy and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Family
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family. The terms "distribution" and "family" are often used loosely: specifically, ''an'' exponential family is a ''set'' of distributions, where the specific distribution varies with the parameter; however, a parametric ''family'' of distributions is often referred to as "''a'' distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families is sometimes l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sufficient Statistic
In statistics, a statistic is ''sufficient'' with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter". In particular, a statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than the statistic, as to which of those probability distributions is the sampling distribution. A related concept is that of linear sufficiency, which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic. The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pitman–Koopman–Darmois Theorem
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family. The terms "distribution" and "family" are often used loosely: specifically, ''an'' exponential family is a ''set'' of distributions, where the specific distribution varies with the parameter; however, a parametric ''family'' of distributions is often referred to as "''a'' distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families is sometimes lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research Society Of America
The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger of the Operations Research Society of America (ORSA) and The Institute of Management Sciences (TIMS). Overview INFORMS promotes greater public awareness, interest, and understanding about the benefits of operations research (O.R.) and analytics and provides a variety of programs and services that support lifelong learning and networking for O.R. and analytics professionals. This includes publishing 16 peer-reviewed journals, hosting numerous conferences and meetings, providing continuing education courses and professional certification, and administering dozens of special-interest communities that help professionals network and collaborate with colleagues from around the world. INFORMS is a member of the International Federation of Operatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Search Theory
In microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting. Search theory clarifies how buyers and sellers choose when to acknowledge a coordinating offer for a transaction. Search theory also provides an explanation for why frictional unemployment happens as people look for jobs and corporations look for new employees. Search theory has been used primarily to explain labor market inefficiencies, but also for all forms of "buyers" and "sellers", whether products, homes or even spouses/partners. It can be applied. The clearing price will be met quickly as supply and demand react freely. However, this does not happen in the real world. Search theory tries to explain how. Search theory has been applied in labor economics to analyze frictional unemployment resulting from job hunting by workers. In consumer theory, it has been applied to analyze purchasing decisions. From a wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
U-boat
U-boats were naval submarines operated by Germany, particularly in the First and Second World Wars. Although at times they were efficient fleet weapons against enemy naval warships, they were most effectively used in an economic warfare role (commerce raiding) and enforcing a naval blockade against enemy shipping. The primary targets of the U-boat campaigns in both wars were the merchant convoys bringing supplies from Canada and other parts of the British Empire, and from the United States, to the United Kingdom and (during the Second World War) to the Soviet Union and the Allied territories in the Mediterranean. German submarines also destroyed Brazilian merchant ships during World War II, causing Brazil to declare war on both Germany and Italy on 22 August 1942. The term is an anglicised version of the German word ''U-Boot'' , a shortening of ''Unterseeboot'' ('under-sea-boat'), though the German term refers to any submarine. Austro-Hungarian Navy submarines were also kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
US Navy
The United States Navy (USN) is the maritime service branch of the United States Armed Forces and one of the eight uniformed services of the United States. It is the largest and most powerful navy in the world, with the estimated tonnage of its active battle fleet alone exceeding the next 13 navies combined, including 11 allies or partner nations of the United States as of 2015. It has the highest combined battle fleet tonnage (4,635,628 tonnes as of 2019) and the world's largest aircraft carrier fleet, with eleven in service, two new carriers under construction, and five other carriers planned. With 336,978 personnel on active duty and 101,583 in the Ready Reserve, the United States Navy is the third largest of the United States military service branches in terms of personnel. It has 290 deployable combat vessels and more than 2,623 operational aircraft . The United States Navy traces its origins to the Continental Navy, which was established during the American Revolut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
