# inequality

• 61Ky Fan inequality — In mathematics, the Ky Fan inequality is an inequality involving the geometric mean and arithmetic mean of two sets of real numbers of the unit interval. The result was published on page 5 of the book Inequalities by Beckenbach and Bellman (1961) …

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• 62Ascriptive inequality — Ascription occurs when social class or stratum placement is primarily hereditary. In other words, people are placed in positions in a stratification system because of qualities beyond their control. Race, sex, age, class at birth, religion,&#8230; …

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• 63Clausius–Duhem inequality — Continuum mechanics …

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• 64Sobolev inequality — In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the&#8230; …

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• 65Minkowski's first inequality for convex bodies — In mathematics, Minkowski s first inequality for convex bodies is a geometrical result due to the German mathematician Hermann Minkowski. The inequality is closely related to the Brunn–Minkowski inequality and the isoperimetric inequality.&#8230; …

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• 66Gromov's systolic inequality for essential manifolds — In Riemannian geometry, M. Gromov s systolic inequality for essential n manifolds M dates from 1983. It is a lower bound for the volume of an arbitrary metric on M, in terms of its homotopy 1 systole. The homotopy 1 systole is the least length of …

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• 67Brascamp-Lieb inequality — In mathematics, the Brascamp Lieb inequality is a result in geometry concerning integrable functions on n dimensional Euclidean space R n . It generalizes the Loomis Whitney inequality, the Prékopa Leindler inequality and Hölder s inequality, and …

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• 68Social inequality — refers to a lack of social equality, where individuals in a society do not have equal social status. Areas of potential social inequality include voting rights, freedom of speech and assembly, the extent of property rights and access to education …

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• 69Gaussian isoperimetric inequality — The Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov and independently by Christer Borell, states that among all sets of given Gaussian measure in the n dimensional Euclidean space, half spaces have the minimal&#8230; …

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• 70Triangle inequality — In mathematics, the triangle inequality states that for any triangle, the length of a given side must be less than or equal to the sum of the other two sides but greater than or equal to the difference between the two sides.In Euclidean geometry&#8230; …

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• 71Nesbitt's inequality — In mathematics, Nesbitt s inequality is a special case of the Shapiro inequality. It states that for positive real numbers a, b and c we have: Contents 1 Proof 1.1 First proof …

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• 72IQ and Global Inequality — is a controversial 2006 book by psychologist Richard Lynn and political scientist Tatu Vanhanen. IQ and Global Inequality is follow up to their 2002 book IQ and the Wealth of Nations,[ …

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• 73Prékopa-Leindler inequality — In mathematics, the Prékopa Leindler inequality is an integral inequality closely related to the reverse Young s inequality, the Brunn Minkowski inequality and a number of other important and classical inequalities in analysis. The result is&#8230; …

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• 74Wirtinger's inequality for functions — For other inequalities named after Wirtinger, see Wirtinger s inequality. In mathematics, historically Wirtinger s inequality for real functions was an inequality used in Fourier analysis. It was named after Wilhelm Wirtinger. It was used in 1904 …

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• 75Loewner's torus inequality — In differential geometry, Loewner s torus inequality is an inequality due to Charles Loewner for the systole of an arbitrary Riemannian metric on the 2 torus.tatementIn 1949 Charles Loewner proved that every metric on the 2 torus mathbb T^2&#8230; …

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• 76Pu's inequality — [ Roman Surface representing RP2 in R3] In differential geometry, Pu s inequality is an inequality proved by P. M. Pu for the systole of an arbitrary Riemannian metric on the real projective plane RP2.tatementA student of Charles Loewner s, P.M.&#8230; …

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• 77Muirhead's inequality — In mathematics, Muirhead s inequality, named after Robert Franklin Muirhead, also known as the bunching method, generalizes the inequality of arithmetic and geometric means. Contents 1 Preliminary definitions 1.1 The a mean 1.2 Doubly stochastic&#8230; …

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• 78Doob's martingale inequality — In mathematics, Doob s martingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a stochastic process exceeds any given value over a given interval of time. As the name suggests, the result&#8230; …

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• 79Weitzenböck's inequality — In mathematics, Weitzenböck s inequality states that for a triangle of side lengths a, b, c, and area Delta, the following inequality holds:: a^2 + b^2 + c^2 geq 4sqrt{3}, Delta. Equality occurs if and only if the triangle is equilateral. Pedoe s …

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• 80Gromov's inequality for complex projective space — In Riemannian geometry, Gromov s optimal stable 2 systolic inequality is the inequality: mathrm{stsys} 2{}^n leq n!;mathrm{vol} {2n}(mathbb{CP}^n),valid for an arbitrary Riemannian metric on the complex projective space, where the optimal bound&#8230; …

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