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A flow line for a map on a vector field F is a path sigma(t) such that sigma^'(t)=F(sigma(t)).

There are seven frieze groups, which can be written in orbifold notation as *22infty, 2*infty, 22infty, *inftyinfty, infty*, inftyx, inftyinfty.

A map x|->x^p where p is a prime.

If the average number of envelopes per pigeonhole is a, then some pigeonhole will have at least a envelopes. Similarly, there must be a pigeonhole with at most a envelopes.

If M is continuous and int_a^bM(x)h(x)dx=0 for all infinitely differentiable h(x), then M(x)=0 on the open interval (a,b).

A mathematical object invented to solve irreducible congruences of the form F(x)=0 (mod p), where p is prime.

For n players, n-1 games are needed to fairly determine first place, and n-1+lg(n-1) are needed to fairly determine first and second place.

gamma_r=(kappa_r)/(sigma^(r+2)), where kappa_r are cumulants and sigma is the standard deviation.

year winner 2010 Yves Meyer

The geodesics on a general cylinder generated by lines parallel to a line l with which the tangent makes a constant angle.