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Coupon. In marketing, a coupon is a ticket or document that can be redeemed for a financial discount or rebate when purchasing a product . Customarily, coupons are issued by manufacturers of consumer packaged goods [1] or by retailers, to be used in retail stores as a part of sales promotions. They are often widely distributed through mail ...
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:
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 ...
In 2012, Shapiro earned $979,000, with $721,000 as his retirement. Shapiro taught executive programs at Arthur Andersen, Ciba-Geigy, General Electric, IBM, Johnson & Johnson, the Sara Lee Corporation, Schneider Electric and Unilever, and he was a consultant for Barilla, Eastman Kodak, Italtel, Frito-Lay and Perkin Elmer.
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.
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.