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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 ...
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.
Front cover of the manual. The Freedom Fighter's Manual is a fifteen-page propaganda booklet that was manufactured by the United States Central Intelligence Agency and airdropped over Nicaragua in 1983, with the stated goal of providing a "Practical guide to liberating Nicaragua from oppression and misery by paralyzing the military-industrial complex of the traitorous marxist state".
Beginning Monday, a California law will require credit card networks like Visa and Mastercard to provide banks with special retail codes that can be assigned to gun stores in order to track their ...
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 ...
Shapiro's lemma. In mathematics, especially in the areas of abstract algebra dealing with group cohomology or relative homological algebra, Shapiro's lemma, also known as the Eckmann–Shapiro lemma, relates extensions of modules over one ring to extensions over another, especially the group ring of a group and of a subgroup.
Rankin–Selberg method. In mathematics, the Rankin–Selberg method, introduced by ( Rankin 1939) and Selberg ( 1940 ), also known as the theory of integral representations of L -functions, is a technique for directly constructing and analytically continuing several important examples of automorphic L -functions.
The PGA Championship offered an $18.5 million purse last month, which gave Xander Schauffele $3.3 million for his win. While the top four finishers will all take home seven figures, everyone ...