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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.
The Shapiro–Wilk test tests the null hypothesis that a sample x1, ..., xn came from a normally distributed population. The test statistic is. where. with parentheses enclosing the subscript index i is the i th order statistic, i.e., the i th-smallest number in the sample (not to be confused with ). is the sample mean.
Samples used for radiocarbon dating must be handled carefully to avoid contamination. Not all material can be dated by this method; only samples containing organic matter can be tested: the date found will be the date of death of the plants or animals from which the sample originally came. C content; this can mean conversion to gaseous, liquid ...
A group of newspapers, including the New York Daily News and Chicago Tribune, sued Microsoft and OpenAI in New York federal court on Tuesday, accusing them of misusing reporters' work to train ...
President Joe Biden on Wednesday called close US ally Japan “xenophobic” at a Washington, D.C., fundraiser, just weeks after lauding the US-Japan alliance at a state dinner.