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A class of area-preserving maps of the form theta_(i+1) = theta_i+2pialpha(r_i) (1) r_(i+1) = r_i, (2) which maps circles into circles but with a twist resulting from the ...

f(x)=1-2x^2 for x in [-1,1]. Fixed points occur at x=-1, 1/2, and order 2 fixed points at x=(1+/-sqrt(5))/4. The natural invariant of the map is rho(y)=1/(pisqrt(1-y^2)).

An ungula is a portion of a solid of revolution obtained by cutting via a plane oblique to its base. The term derives from the Latin word ungula for the hoof of a horse. ...

A unilateral shift is a weighted shift T for which alpha_n=1 for all n.

The number 1. There are n nth roots of unity, known as the de Moivre numbers.

Involving one variable, as opposed to two (bivariate) or many (multivariate).

The quantifier "for all" ( forall ), sometimes also known as the "general quantifier."

For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...

int_0^(pi/2)cos^nxdx = int_0^(pi/2)sin^nxdx (1) = (sqrt(pi)Gamma(1/2(n+1)))/(nGamma(1/2n)) (2) = ((n-1)!!)/(n!!){1/2pi for n=2, 4, ...; 1 for n=3, 5, ..., (3) where Gamma(n) ...

If each of two curves meets the line at infinity in distinct, nonsingular points, and if all their intersections are finite, then if to each common point there is attached a ...