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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.
Doug Shapiro (born September 15, 1959) is a former American professional cyclist who became a bicycle accident consultant. He was a member of two American Olympic teams and was only the third ever American to compete in and finish the Tour de France. For over the last twenty years, he has served as a consultant and expert witness to attorneys ...
Harold Seymour Shapiro (2 April 1928 [1] – 5 March 2021) was a professor of mathematics at the Royal Institute of Technology in Stockholm, Sweden, best known for inventing the so-called Shapiro polynomials (also known as Golay–Shapiro polynomials or Rudin–Shapiro polynomials) and for work on quadrature domains. [citation needed] His main ...
Raymond M. Durkin. Raymond M. " Ray " Durkin (1936 – December 23, 2014) was an American Democratic party politician from New Jersey who has served as chairman of the New Jersey Democratic State Committee as well as the Essex County Democratic Committee. Durkin grew up in the Vailsburg neighborhood in the West Ward of Newark, New Jersey. [1]
Robert Leslie Shapiro (born September 2, 1942) is an American attorney and entrepreneur. He is best known for being the short-term defense lawyer of Erik Menéndez in 1990, and a member of the "Dream Team" of O. J. Simpson's attorneys that successfully defended him from the charges that he murdered his ex-wife, Nicole Brown Simpson, and Ron Goldman, in 1994.
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.