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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 closed embedded smooth plane curve has at least four vertices, where a vertex is defined as an extremum of curvature.

If f(x) is an even function, then b_n=0 and the Fourier series collapses to f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx), (1) where a_0 = 1/piint_(-pi)^pif(x)dx (2) = ...

If f(x) is an odd function, then a_n=0 and the Fourier series collapses to f(x)=sum_(n=1)^inftyb_nsin(nx), (1) where b_n = 1/piint_(-pi)^pif(x)sin(nx)dx (2) = ...

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 ...

The curvature and torsion functions along a space curve determine it up to an orientation-preserving isometry.

Let t be an infinite word over a finite alphabet Sigma. Then there exists a uniformly recurrent infinite word r such that Sub(r) subset= Sub(t), where Sub(w) is the set of ...

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...

Bracewell's term for the rectangle function.