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Paul Robert Shapiro is an American astrophysicist. Shapiro earned a bachelor's degree and doctorate from Harvard University , in 1974 and 1978, respectively, [1] and began teaching at the University of Texas at Austin in 1981, after completing postdoctoral research at the Institute for Advanced Study . [2]
Senator Shapiro may refer to: David C. Shapiro (1925–1981), Illinois State Senate. Florence Shapiro (born 1948), Texas State Senate. Categories: Disambiguation pages. Title and name disambiguation pages.
Laura Shapiro (born June 20, 1946) is an American food journalist and historian. Shapiro was a dance critic for The Boston Globe in the 1970s and joined Newsweek magazine in 1984. She shifted to food writing during her 15-year tenure at Newsweek , and in 1995, she won a James Beard Foundation Award for one of her magazine features.
Aaron Shapiro is an American entrepreneur, marketing executive, and investor based in New York City. Shapiro co-founded the email marketing software company Silverpop in 1999. [1] In 2005 he joined the experience design and digital marketing agency Huge as one of four co-founders, becoming CEO in 2010. [2]
Gerald M. Shapiro (born 1942 in Philadelphia) is an American composer of acoustic and electronic music. Shapiro studied first at the Eastman School of Music, where he received a Bachelor of Music degree with distinction in 1964. He then did graduate work at Mills College, where he received an M.A. in 1967, the University of California, Davis ...
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.
Ralph Shapiro (November 27, 1908 – April 8, 1974) was an American businessman and politician from New York. Life [ edit ] He was born on November 27, 1908, [1] the son of Jacob Shapiro and Fanny (Rosenthal) Shapiro.
Sumner Shapiro (January 13, 1926 – November 14, 2006) was a United States Navy rear admiral who served as Director of the Office of Naval Intelligence from 1978 to 1982. [4] Early life and education [ edit ]