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The Shapiro reaction or tosylhydrazone decomposition is an organic reaction in which a ketone or aldehyde is converted to an alkene through an intermediate hydrazone in the presence of 2 equivalents of organolithium reagent. [1] [2] [3] The reaction was discovered by Robert H. Shapiro in 1967. [4] The Shapiro reaction was used in the Nicolaou ...
Coupon collector's problem. In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: If each box of a brand of cereals contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be ...
Arthur K. Shapiro, M.D., (January 11, 1923 – June 3, 1995) was an American psychiatrist and expert on Tourette syndrome. His "contributions to the understanding of Tourette syndrome completely changed the prevailing view of this disorder"; [2] he has been described as "the father of modern tic disorder research" [3] and is "revered by his ...
Ascher Herman Shapiro (May 20, 1916 – November 26, 2004) was a professor of Mechanical Engineering at MIT. He grew up in New York City. He grew up in New York City. Early life and education [ edit ]
Philip James DeFranco [3] (born Philip James Franchini Jr.; [4] born December 1, 1985), commonly known by his online nickname PhillyD, and formerly known as sxephil, is an American media host and YouTube personality. He is best known for The Philip DeFranco Show, a news commentary show centered on current events in politics and pop culture .
Zone 5 uses eight 2-digit codes (51–58) and two sets of 3-digit codes (50x, 59x) to serve South and Central America. Zone 6 uses seven 2-digit codes (60–66) and three sets of 3-digit codes (67x–69x) to serve Southeast Asia and Oceania. Zone 7 uses an integrated numbering plan; two digits (7x) determine the area served: Russia or Kazakhstan.
Joel H. Shapiro is an American mathematician, active in the field of composition operators. He is the author of the book Composition Operators and Classical Function Theory ( ISBN 3540940677 ), and the American Mathematical Society memoir "Cyclic Phenomena for Composition Operators" (Memoirs of the American Math.
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