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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 ...
In 2011, Dollar Tree achieved total sales of $6.63 billion, opened 278 new stores, and completed a 400,000 square feet (37,000 m 2) expansion of its distribution center in Savannah, Georgia. In 2012, Dollar Tree opened another 345 new stores and exceeded $7 billion in sales, with an end-of-the-year market cap at $9.13 billion.
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]
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y , the distribution of the random variable Z that is formed as the product Z = X Y {\displaystyle Z=XY} is a product distribution .
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May 1, 2024 at 9:20 PM. May 1—WILKES-BARRE — If Gov. Josh Shapiro and Lieutenant Governor Austin Davis are to be successful in getting more funding approved for fighting gun violence, stories ...
Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
But the rate of participation in that program appears to be low: Only 2.3% of its 7 million active listings have received carbon monoxide detectors through the program, according to a statement ...
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