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Quantifier elimination is the removal of all quantifiers (the universal quantifier forall and existential quantifier exists ) from a quantified system. A first-order theory ...

Rule 110 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

The 57-cell, also called the pentacontaheptachoron, is a regular self-dual locally projective polytope with 57 hemidodecahedral facets described by Coxeter (1982) and also ...

Let K be a class of topological spaces that is closed under homeomorphism, and let X be a topological space. If X in K and for every Y in K such that X subset= Y, X is a ...

A catastrophe which can occur for four control factors and one behavior axis. The butterfly catastrophe is the universal unfolding of the singularity f(x)=x^6 of codimension ...

A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on ...

Given a set S with a subset E, the complement (denoted E^' or E^_) of E with respect to S is defined as E^'={F:F in S,F not in E}. (1) Using set difference notation, the ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

A family gamma of nonempty subsets of X whose union contains the given set X (and which contains no duplicated subsets) is called a cover (or covering) of X. For example, ...

A cusp catastrophe is a catastrophe which can occur for two control factors and one behavior axis. The cusp catastrophe is the universal unfolding of the singularity f(x)=x^4 ...