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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 ...
Deepfakes are just the latest threat in a growing wave of cyber threats, but placing security above convenience can help keep you safe.
The Talk may soon be coming to a close, but cohosts Amanda Kloots, Sheryl Underwood and Natalie Morales couldn’t be happier with how the show will end. “It has been 15 years. You know, we’re ...
The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic Solar System tests of general relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than they would if the mass of the object were not present. The time delay is caused by time dilation ...
Signature. Tupac Amaru Shakur ( / ˈtuːpɑːk ʃəˈkʊər / TOO-pahk shə-KOOR; born Lesane Parish Crooks; June 16, 1971 – September 13, 1996), also known by his stage names 2Pac and Makaveli, was an American rapper and songwriter. Considered to be one of the most influential and successful rappers of all time, [1] [2] academics regard him ...
Jesse Grant/Getty Images Ryan Phillippe took a walk down memory lane with a photo of ex-wife Reese Witherspoon. “We were hot and drenched in late 90’s angst @reesewitherpoon (such a cooler ...
Kohl's shares plunged as much as 25% on Thursday after the retailer reported a surprise first-quarter loss and lowered its forecast for the year.. The department store chain saw a 5.3% drop in net ...
“Back to Black,” the Amy Winehouse biopic directed by Sam Taylor-Johnson, brings the life of the neo-soul icon to the big screen nearly 13 years after her death.
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.
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]