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[1] [2] In the following year, both authors improved their results and published them independently. [3] [4] [5] Nonetheless, a complete proof of the inequality went missing in the literature for a long time. Indeed, to some extent, both original works of Gagliardo and Nirenberg do not contain a full and rigorous argument proving the result.
CHSH stands for John Clauser, Michael Horne, Abner Shimony, and Richard Holt, who described it in a much-cited paper published in 1969. [1] They derived the CHSH inequality, which, as with John Stewart Bell's original inequality, [2] is a constraint—on the statistical occurrence of "coincidences" in a Bell test—which is necessarily true if ...
Tris (pentafluorophenyl)borane, sometimes referred to as "BCF", is the chemical compound (C6F5)3B. It is a white, volatile solid. The molecule consists of three pentafluorophenyl groups attached in a "paddle-wheel" manner to a central boron atom; the BC3 core is planar. It has been described as the “ideal Lewis acid ” because of its high ...
Cauchy–Schwarz inequality. The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) [1][2][3][4] is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is considered one of the most important and widely used inequalities in mathematics.
Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of income and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general. While different theories may try to explain how income inequality comes about, income ...
Hoeffding's inequality was proven by Wassily Hoeffding in 1963. [1] Hoeffding's inequality is a special case of the Azuma–Hoeffding inequality and McDiarmid's inequality. It is similar to the Chernoff bound, but tends to be less sharp, in particular when the variance of the random variables is small. [2]
QM-AM-GM-HM inequalities. In mathematics, the QM-AM-GM-HM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean square). Suppose that are positive real numbers.
Social inequality is linked to economic inequality, usually described on the basis of the unequal distribution of income or wealth. Although the disciplines of economics and sociology generally use different theoretical approaches to examine and explain economic inequality, both fields are actively involved in researching this inequality.
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