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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.
Yehuda Meir Shapiro ( Polish: Majer Jehuda Szapira; 3 March 1887 – 27 October 1933) was a prominent Polish Hasidic rabbi and rosh yeshiva, also known as the Lubliner Rav. He is noted for his promotion of the Daf Yomi study program in 1923, and establishing the Chachmei Lublin Yeshiva in 1930. During the years 1922 to 1927 Shapiro was the ...
As of 2010, 90.2% (10,710,239) of Pennsylvania residents age five and older spoke English at home as a primary language while 4.1% (486,058) spoke Spanish, 0.9% (103,502) spoke German including Pennsylvania Dutch, and 0.5% (56,052) spoke Chinese, which includes Mandarin of the population over the age of five.
Shapiro syndrome is an extremely rare disorder consisting of paroxysmal hypothermia (due to hypothalamic dysfunction of thermoregulation ), hyperhydrosis (sweating), and agenesis of the corpus callosum with onset typically on adulthood. The disease affects about 50 people worldwide. The duration and frequency of the episodes vary from person to ...
Fred Richard Shapiro is an American legal scholar and academic working as the editor of The Yale Book of Quotations, The Oxford Dictionary of American Legal Quotations, and several other books. Education [ edit ]
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]
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Harold Seymour Shapiro (2 April 1928 [1] – 5 March 2021) was a professor of mathematics at the Royal Institute of Technology in Stockholm, Sweden, best known for inventing the so-called Shapiro polynomials (also known as Golay–Shapiro polynomials or Rudin–Shapiro polynomials) and for work on quadrature domains. [citation needed] His main ...
Zorya Yakovlevna Shapiro (Russian: Зоря Яковлевна Шапиро; 7 December 1914 – 4 July 2013) was a Soviet mathematician, educator and translator.She is known for her contributions to representation theory and functional analysis in her collaboration with Israel Gelfand, and the Shapiro-Lobatinski condition in elliptical boundary value problems.