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A catastrophe which can occur for three control factors and two behavior axes. The elliptical umbilic is catastrophe of codimension 3 that has the equation ...

A class of processes which attempt to round off a domain and simplify its theory by adjoining elements.

If P(x,y) and P(x^',y^') are two points on an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1, (1) with eccentric angles phi and phi^' such that tanphitanphi^'=b/a (2) and A=P(a,0) and ...

In population studies, the direct offspring of a reference population (roughly) constitutes a single generation. For a cellular automaton, the fundamental unit of time during ...

Consider a clause (disjunction of literals) obtained from those of a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then a literal obtained from ...

If G is a group, then the torsion elements Tor(G) of G (also called the torsion of G) are defined to be the set of elements g in G such that g^n=e for some natural number n, ...

y^(n/m)+c|x/a|^(n/m)-c=0, with n/m>2. If n/m<2, the curve is a hypoellipse.

The term "ice fractal" refers to a fractal (square, triangle, etc.) that is based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, ...

The number of elements greater than i to the left of i in a permutation gives the ith element of the inversion vector (Skiena 1990, p. 27).

A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...