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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.
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. The reaction was discovered by Robert H. Shapiro in 1967.
The Sharpless catalog is a list of 313 H II regions (emission nebulae) intended to be comprehensive north of declination −27°. (It does include some nebulae south of that declination as well.) The first edition was published in 1953 with 142 objects (Sh1), and the second and final version was published by US astronomer Stewart Sharpless in ...
Edward S. Shapiro (born 1938) [1] is a historian of American history and American Jewish history. He received his BA at Georgetown University and his PhD at Harvard University. His doctoral dissertation was The American Distributists and the New Deal.
Extreme couponing is an activity that combines shopping skills with couponing in an attempt to save as much money as possible while accumulating the most groceries.
Far-right commentator Candace Owens and conservative news outlet The Daily Wire have parted ways. “The rumors are true— I am finally free,” Owens wrote Friday on X.