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For example, the approach based on "upper gradients" leads to Newtonian-Sobolev space of functions. Thus, it makes sense to say that a space "supports a Poincare inequality". It turns out that whether a space supports any Poincare inequality and if so, the critical exponent for which it does, is tied closely to the geometry of the space.
The Cramér–Rao bound is stated in this section for several increasingly general cases, beginning with the case in which the parameter is a scalar and its estimator is unbiased.
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 mathematics, Grönwall's inequality (also called Grönwall's lemma or the Grönwall–Bellman inequality) allows one to bound a function that is known to satisfy a certain differential or integral inequality by the solution of the corresponding differential or integral equation. There are two forms of the lemma, a differential form and an ...
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations.CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods.
The Frobenius norm defined by ‖ ‖ = = = | | = = = {,} is self-dual, i.e., its dual norm is ‖ ‖ ′ = ‖ ‖.. The spectral norm, a special case of the induced norm when =, is defined by the maximum singular values of a matrix, that is, ‖ ‖ = (), has the nuclear norm as its dual norm, which is defined by ‖ ‖ ′ = (), for any matrix where () denote the singular values ...