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An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

A multiway system that generates causal networks which are all isomorphic as acyclic digraphs is said to exhibit causal invariance, and the causal network itself is also said ...

There are several different definitions of conical coordinates defined by Morse and Feshbach (1953), Byerly (1959), Arfken (1970), and Moon and Spencer (1988). The ...

Darboux's formula is a theorem on the expansion of functions in infinite series and essentially consists of integration by parts on a specific integrand product of functions. ...

The surface of revolution given by the parametric equations x(u,v) = cosusin(2v) (1) y(u,v) = sinusin(2v) (2) z(u,v) = sinv (3) for u in [0,2pi) and v in [-pi/2,pi/2]. It is ...

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 ...

The group of an elliptic curve which has been transformed to the form y^2=x^3+ax+b is the set of K-rational points, including the single point at infinity. The group law ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

A handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in opposite ...

Throughout abstract algebra, the term "magma" is most often used as a synonym of the more antiquated term "groupoid," referring to a set equipped with a binary operator. The ...