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A catastrophe which can occur for one control factor and one behavior axis. It is the universal unfolding of the singularity f(x)=x^3 and has the equation F(x,u)=x^3+ux.

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

By analogy with the geometric centroid, the centroid of an arbitrary function f(x) is defined as <x>=(intxf(x)dx)/(intf(x)dx), (1) where the integrals are taken over the ...

Bracewell's term for the rectangle function.

Let f be an integer polynomial. The f can be factored into a product of two polynomials of lower degree with rational coefficients iff it can be factored into a product of ...

A perspective collineation in which the center and axis are not incident. The term was first used by Poncelet (Cremona 1960, p. ix).

The interesting function defined by the definite integral G(x)=int_0^xsin(tsint)dt, illustrated above (Glasser 1990). The integral cannot be done in closed form, but has a ...

The dual of the great truncated icosahedron U_(55) and Wenninger dual W_(95).

Let Gamma be a representation for a group of group order h, then sum_(R)Gamma_i(R)_(mn)Gamma_j(R)_(m^'n^')^*=h/(sqrt(l_il_j))delta_(ij)delta_(mm^')delta_(nn^'). The proof is ...

The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996): 1. Orientability, 2. Number of boundary components, 3. Euler ...