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

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

The map x^' = x+1 (1) y^' = 2x+y+1, (2) which leaves the parabola x^('2)-y^'=(x+1)^2-(2x+y+1)=x^2-y (3) invariant.

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.

A homogeneous polynomial in two or more variables.

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.

A ruled semicircle used for measuring and drawing angles.