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Fred Richard Shapiro is an American legal scholar and academic working as the editor of The Yale Book of Quotations, The Oxford Dictionary of American Legal Quotations, and several other books. Education [ edit ]
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.
Thus u 108 = u 13 + 1 = u 3 + 1 = u 1 + 2 = u 0 + 2 = 2, which can be verified by observing that the binary representation of 108, which is 1101100, contains two sub-strings 11. And so r 108 = (−1) 2 = +1. A 2-uniform morphism that requires a coding to generate the Rudin-Shapiro sequence is the following:
Robert H. Shapiro (July 18, 1935 – August 21, 2004) was an American chemist and the first provost of the United States Naval Academy. Education and career [ edit ] After serving with both the United States Navy and the United States Marine Corps , Shapiro earned degrees in chemistry and pharmacy at the University of Connecticut , and then ...
From 1972 to 1974, Shapiro served as Maryland State Securities Commissioner. In 1972, he founded a Baltimore law firm now known as Shapiro Sher. [3] Subsequently, in 1976, Shapiro founded Shapiro, Robinson & Associates, [4] a sports management firm. In 1995, he founded Shapiro Negotiations Institute, [5] a negotiation seminar and consulting firm.
Paul Shapiro (born 1939) is an American Abstract Expressionist and landscape painter. [1] New Mexican author Jon Carver writes of Shapiro's work: "Paul's interest in art and his commitment to painting is unassailable and extends to the depths of his being."
Rationing is the controlled distribution of scarce resources, goods, or services, or an artificial restriction of demand. Rationing controls the size of the ration, which is one person's allotted portion of the resources being distributed on a particular day or at a particular time. Rationing in the United States was introduced in stages during ...
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.