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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. [1] [2] [3] The reaction was discovered by Robert H. Shapiro in 1967. [4] The Shapiro reaction was used in the Nicolaou ...
Victor L. Shapiro. Victor Lenard Shapiro (16 October 1924, Chicago – 1 March 2013, Riverside, California) was an American mathematician, specializing in trigonometric series and differential equations. [1] He is known for his two theorems (published in 1957) on the uniqueness of multiple Fourier series. [2] [3]
Shapiro polynomials. In mathematics, the Shapiro polynomials are a sequence of polynomials which were first studied by Harold S. Shapiro in 1951 when considering the magnitude of specific trigonometric sums. [1] In signal processing, the Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. [2]
ATSF 3000 class 2-10-10-2. The forward section of the boiler is a primitive superheater and feedwater heater. In 1911 and 1912, the Atchison, Topeka and Santa Fe Railway modified ten 2-10-2 Baldwin -built locomotives into a new 2-10-10-2 configuration dubbed the 3000 class. They were the largest locomotives in the world from their introduction ...
Sen. Bob Menendez’s trial enters a new phase this week as prosecutors and defense lawyers test the boundaries of the court, the law and the judge running the show.