Search Results for ""

A financial measure of a fund's sensitivity to market movements which measures the relationship between a fund's excess return over Treasury Bills and the excess return of a ...

A map is called bijective if it is both injective and surjective. A bijective map is also called a bijection. A function f admits an inverse f^(-1) (i.e., "f is invertible") ...

If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f degreesg is differentiable at x. Furthermore, let y=f(g(x)) and u=g(x), then ...

For three consecutive orders of an orthonormal polynomial, the following relationship holds for n=2, 3, ...: p_n(x)=(A_nx+B_n)p_(n-1)(x)-C_np_(n-2)(x), (1) where A_n>0, B_n, ...

A monoid that is commutative i.e., a monoid M such that for every two elements a and b in M, ab=ba. This means that commutative monoids are commutative, associative, and have ...

In machine learning theory and artificial intelligence, a concept c over a domain X is a Boolean function c:X->{0,1}. A collection of concepts is called a concept class. In ...

There are several meanings of the word content in mathematics. The content of a polytope or other n-dimensional object is its generalized volume (i.e., its "hypervolume"). ...

Let f be a finite real-valued function defined on an interval [a,b]. Then at every point in [a,b] except on a set of Lebesgue measure zero, either: 1. There is a finite ...

A metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation, supremum must be replaced by infimum, ...

A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...