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A functor is said to be faithful if it is injective on maps. This does not necessarily imply injectivity on objects. For example, the forgetful functor from the category of ...

A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

A graph is a forbidden subgraph if its presence as a subgraph of a given graph means it is not a member of some family of graphs. For example, a bipartite graph is a graph ...

The frame bundle on a Riemannian manifold M is a principal bundle. Over every point p in M, the Riemannian metric determines the set of orthonormal frames, i.e., the possible ...

The tabulation of raw data obtained by dividing it into classes of some size and computing the number of data elements (or their fraction out of the total) falling within ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

The modular group Gamma is the set of all transformations w of the form w(t)=(at+b)/(ct+d), where a, b, c, and d are integers and ad-bc=1. A Gamma-modular function is then ...

Let C=C^+ union C^- (where C^+ intersection C^-=emptyset) be the disjoint union of two finite components C^+ and C^-. Let alpha and beta be two involutions on C, each of ...

Green's identities are a set of three vector derivative/integral identities which can be derived starting with the vector derivative identities del ·(psidel phi)=psidel ...

The group theoretical term for what is known to physicists, by way of its connection with matrix traces, as the trace. The powerful group orthogonality theorem gives a number ...