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The essential supremum is the proper generalization to measurable functions of the maximum. The technical difference is that the values of a function on a set of measure zero ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...

An exterior angle beta of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to 2pi-alpha, where alpha is the corresponding internal ...

The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

A forgetful functor (also called underlying functor) is defined from a category of algebraic gadgets (groups, Abelian groups, modules, rings, vector spaces, etc.) to the ...

A set of algebraic invariants for a quantic such that any invariant of the quantic is expressible as a polynomial in members of the set. Gordan (1868) proved the existence of ...

For a general two-player zero-sum game, max_(i<=m)min_(j<=n)a_(ij)<=min_(j<=n)max_(i<=m)a_(ij). If the two are equal, then write ...

Let I(x,y) denote the set of all vertices lying on an (x,y)-graph geodesic in G, then a set S with I(S)=V(G) is called a geodetic set in G and is denoted g(G).

Analytic continuation gives an equivalence relation between function elements, and the equivalence classes induced by this relation are called global analytic functions.

For all n, there exists a k such that the kth term of the Goodstein sequence G_k(n)=0. In other words, every Goodstein sequence converges to 0. The secret underlying ...