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Templates that present a particular chart, diagram or graph (or particular charts, diagrams or graphs). For templates that present / format / amend one or more charts / diagrams / graphs supplied to them, see Chart, diagram and graph formatting and function templates .
Two-dimensional linear inequalities are expressions in two variables of the form: + < +, where the inequalities may either be strict or not. The solution set of such an inequality can be graphically represented by a half-plane (all the points on one "side" of a fixed line) in the Euclidean plane. [2]
In the context of metric measure spaces, the definition of a Poincaré inequality is slightly different.One definition is: a metric measure space supports a (q,p)-Poincare inequality for some , < if there are constants C and λ ≥ 1 so that for each ball B in the space, ‖ ‖ () ‖ ‖ ().
The quantile is the unique function satisfying the Galois inequalities Q ( p ) ≤ x {\displaystyle Q(p)\leq x} if and only if p ≤ F ( x ) . {\displaystyle p\leq F(x).} If the function F is continuous and strictly monotonically increasing, then the inequalities can be replaced by equalities, and we have
In the economic literature on inequality four properties are generally postulated that any measure of inequality should satisfy: Anonymity or symmetry This assumption states that an inequality metric does not depend on the "labeling" of individuals in an economy and all that matters is the distribution of income.
Markov's inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a random variable. Markov's inequality can also be used to upper bound the expectation of a non-negative random variable in terms of its distribution function.
In convex optimization, a linear matrix inequality (LMI) is an expression of the form ():= + + + + where = [, =, …,] is a real vector,,,, …, are symmetric matrices, is a generalized inequality meaning is a positive semidefinite matrix belonging to the positive semidefinite cone + in the subspace of symmetric matrices .
In mathematical analysis, the Minkowski inequality establishes that the L p spaces are normed vector spaces.Let be a measure space, let < and let and be elements of (). Then + is in (), and we have the triangle inequality