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Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...

A linear ordinary differential equation of order n is said to be homogeneous if it is of the form a_n(x)y^((n))+a_(n-1)(x)y^((n-1))+...+a_1(x)y^'+a_0(x)y=0, (1) where ...

An axiom proposed by Huntington (1933) as part of his definition of a Boolean algebra, H(x,y)=!(!x v y) v !(!x v !y)=x, (1) where !x denotes NOT and x v y denotes OR. Taken ...

The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...

An infinitesimal which is not the differential of an actual function and which cannot be expressed as dz=((partialz)/(partialx))_ydx+((partialz)/(partialy))_xdy, the way an ...

Integer division is division in which the fractional part (remainder) is discarded is called integer division and is sometimes denoted \. Integer division can be defined as ...

Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...

The intensity measure mu of a point process X relative to a Borel set B subset R^d is defined to be the expected number of points of X falling in B. Symbolically, ...

A bijective map between two metric spaces that preserves distances, i.e., d(f(x),f(y))=d(x,y), where f is the map and d(a,b) is the distance function. Isometries are ...