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A function periodic with period 2pi such that p(theta+pi)=-p(theta) for all theta is said to be Möbius periodic.

Always increasing; never remaining constant or decreasing. Also called strictly increasing.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A system of parameter chain complexes used for multiplication on differential graded algebras up to homotopy.

pi may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the ...

The metric ds^2=(dx^2+dy^2)/((1-|z|^2)^2) of the Poincaré hyperbolic disk.

j_n(z)=(z^n)/(2^(n+1)n!)int_0^picos(zcostheta)sin^(2n+1)thetadtheta, where j_n(z) is a spherical Bessel function of the first kind.

An n-manifold which cannot be "nontrivially" decomposed into other n-manifolds.

p^~=|phi_i(x)><phi_i(t)| (1) p^~sum_(j)c_j|phi_j(t)>=c_i|phi_i(x)> (2) sum_(i)|phi_i(x)><phi_i(x)|=1. (3)

A superset which is not the entire set.