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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)).

A unar is an algebra A=(A,f), where f is a single unary operation.

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) ...