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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.
Allen J. Shapiro (February 7, 1932—May 30, 1987), better known as Al Shapiro and by his pen name A. Jay, was a gay Jewish American artist active from the 1960s through 1980s. [4] [5] He is credited with the creation of the first-ever gay comic strip, The Adventures of Harry Chess : The Man from A.U.N.T.I.E .
28 U.S.C. § 2284. Shapiro v. McManus, 577 U.S. ___ (2015), was a case in which the Supreme Court of the United States clarified when United States District Court judges must refer cases to three-judge panels. In a unanimous opinion written by Justice Antonin Scalia, the Court ruled that federal district courts are required to refer cases to a ...
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]
Charlie Rubin. Susan Shapiro is the American author of 17 books, including The Byline Bible, Five Men Who Broke My Heart, Only as Good as Your Word, Lighting Up, Speed Shrinking, and What's Never Said, and coauthor of The Bosnia List and the New York Times bestseller Unhooked .
Los Angeles, California, U.S. Occupation (s) Television producer, writer. Arnold Joel Shapiro [1] (born February 1, 1941) is an American television producer and writer. His best known work is the 1978 Oscar and Emmy-winning documentary, Scared Straight! [2] [3] His other productions include the CBS reality series, Rescue 911, hosted by William ...
Zalman Mordecai Shapiro (12 May 1920 – 16 July 2016) was an American chemist and inventor. He received 15 patents , including a 2009 patent on a process to make commercial production of diamonds cheaper, [1] and played a key role in the development of the reactor that powered the world's first nuclear powered submarine , the Nautilus .
Career. Shapiro was an assistant professor of mathematics at University of Minnesota from 1969 to 1976 and was a visiting professor of economics from 1976 to 1977. He was the chairman of the division of mathematical sciences at North Dakota State University from 1977 to 1985. Shapiro was a visiting scholar at the computer science department at ...