# inequality

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**Bernstein inequality**— In mathematics, Bernstein inequality may refer to:* Bernstein s inequality (mathematical analysis) * Bernstein inequalities (probability theory)disambig …162

**Weierstrass product inequality**— In mathematics, the Weierstrass product inequality states that given real numbers 0 le; a , b , c , d le; 1, it follows that:(1 a)(1 b)(1 c)(1 d)+a+b+c+d geq 1.The inequality is named after the German mathematician Karl Weierstrass …163

**Barrow's inequality**— In geometry, Barrow s inequality states the following: Let P be a point inside the triangle ABC , U , V , and W be the points where the angle bisectors of BPC , CPA , and APB intersect the sides BC , CA , AB , respectively. Then: PA+PB+PCgeq… …164

**Participation inequality**— An expression coined by Will Hill of AT T Laboratories and later cited by Jakob Nielsen [http://www.useit.com/alertbox/9708b.html Community is Dead; Long Live Mega Collaboration , Jakob Nielsen s Alertbox for August 15, 1997] The earliest known… …165

**Spatial inequality**— of the unequal distribution in income or services depending on the area or location. The services such as medical or welfare will have even more skills and more range of services. The space within the different locations is the clustering of… …166

**Ventilation-perfusion inequality**— (also known as Ventilation Perfusion Mismatch) is when certain groups of alveoli experience a decrease in ventilation which causes a higher concentration of carbon dioxide (CO2) and a lower concentration of oxygen (O2). The inequality refers to… …167

**Steffensen's inequality**— In mathematics, Steffensen s inequality, named after Johan Frederik Steffensen, is an integral inequality in real analysis. It states that if fnof; : [ a , b ] rarr; R is a non negative, monotonically decreasing, integrable function and g : [ a …168

**Berger's inequality for Einstein manifolds**— In mathematics mdash; specifically, in differential topology mdash; Berger s inequality for Einstein manifolds is the statement that any 4 dimensional Einstein manifold ( M , g ) has non negative Euler characteristic chi; ( M ) ge; 0. The… …169

**Berger inequality**— In mathematics, Berger inequality may refer to* Berger s inequality for Einstein manifolds;* the Berger Kazdan comparison theorem …170

**Askey–Gasper inequality**— In mathematics, the Askey–Gasper inequality, named after Richard Askey and George Gasper, is an inequality for Jacobi polynomials proved by harvtxt|Askey|Gasper|1976. It states that if beta; ge; 0, α + beta; ge; −2, and −1 le; x le; 1 then:sum {k …171

**Lebedev–Milin inequality**— In mathematics, the Lebedev–Milin inequality is any of several inequalities for the coefficients of the exponential of a power series, found by Lebedev and Milin (1965) and Isaak Moiseevich Milin (1977). It was used in the proof of the… …172

**Schwarz inequality**— Math. 1. Also called Cauchy s inequality. the theorem that the inner product of two vectors is less than or equal to the product of the magnitudes of the vectors. 2. Also called Cauchy Schwarz inequality. the theorem that the square of the… …173

**triangle inequality**— noun The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors, or any equivalent inequality in other spaces …174

**Componentwise inequality**— In mathematics, a componentwise inequality is an expression of the form: [1][2][3] The vectors do not have to be real, they can be from any space in which the inequality relation is defined. See also …175

**Income Inequality**— The unequal distribution of household or individual income across the various participants in an economy. Income inequality is often presented as the percentage of income to a percentage of population. For example, a statistic may indicate that… …176

**Schwarz inequality**— Math. 1. Also called Cauchy s inequality. the theorem that the inner product of two vectors is less than or equal to the product of the magnitudes of the vectors. 2. Also called Cauchy Schwarz inequality. the theorem that the square of the… …177

**triangle inequality**— noun Etymology: from its application to the distances between three points in a coordinate system Date: 1941 an inequality stating that the absolute value of a sum is less than or equal to the sum of the absolute values of the terms …178

**Hadamard's inequality**— In mathematics, Hadamard s inequality, named after Jacques Hadamard, bounds above the volume in Euclidean space of n dimensions marked out by n vectors: vi for 1 le; i le; n .It states, in geometric terms, that this is at a maximum when the… …179

**Golden–Thompson inequality**— In mathematics, the Golden–Thompson inequality is as follows. Suppose A and B are Hermitian matrices. Then: operatorname{tr}, e^{A+B} le operatorname{tr} left(e^A e^B ight)where tr is the trace, and e A is the matrix exponential.References* J.E.… …180

**Grothendieck inequality**— In mathematics, the Grothendieck inequality relates :max { 1 leq s i leq 1, 1 leq t j leq 1 } left| sum {i,j} a {ij} s i t j ight| to :max {S i,T j in B(H)} left| sum {i,j} a {ij} langle S i , T j angle ight|,where B(H) is the unit ball of a… …