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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 ...
Statement of the inequality. Suppose is a natural number and are positive numbers and: Then the Shapiro inequality states that. where and . For greater values of the inequality does not hold, and the strict lower bound is with . The initial proofs of the inequality in the pivotal cases [2] and [3] rely on numerical computations.
On paper, the job market looks like it’s hardly ever been better. But the unemployment rate for bachelor’s degree recipients aged 20 to 29 is above 12%.
Jack Shapiro. Jack Emanuel "Soupy" Shapiro (March 22, 1907 – February 5, 2001) was an American gridiron football player who played in one game with the Staten Island Stapletons of the National Football League (NFL) in 1929. Shapiro is most famous for being the shortest player in NFL history at about 5 ft 1 in (1.55 m).
Children. 2. Joanna Cassidy (born Joanna Virginia Caskey; August 2, 1944 [1]) is an American actress and former model. She began working as a model in the 1960s and made her professional acting debut in 1973, appearing in the thriller films The Laughing Policeman and The Outfit. She later starred in films Bank Shot (1974), The Late Show (1977 ...
David Shapiro (born November 25, 1946) is an American economist at the Pennsylvania State University. He joined the Penn State faculty [1] in 1980. He is a leading academic in the field of Economic Demography , specializing in fertility transition in sub-Saharan Africa and in the study of children's schooling in Africa.