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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)).

The Ulam sequence {a_i}=(u,v) is defined by a_1=u, a_2=v, with the general term a_n for n>2 given by the least integer expressible uniquely as the sum of two distinct earlier ...

Let graph G have p points v_i and graph H have p points u_i, where p>=3. Then if for each i, the subgraphs G_i=G-v_i and H_i=H-u_i are isomorphic, then the graphs G and H are ...

The function defined by U(n)=(n!)^(n!). The values for n=0, 1, ..., are 1, 1, 4, 46656, 1333735776850284124449081472843776, ... (OEIS A046882).

Let S be a nonempty set, then an ultrafilter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F. 2. If A,B in F, then A ...

The ultraradical symbol is a notation thet can be used to express solutions not obtainable by finite root extraction. The solution to the irreducible quintic equation x^5+x=a ...

An umbilic point, also called simply an umbilic, is a point on a surface at which the curvature is the same in any direction.

An operator T which maps some basic polynomial sequence p_n(x) into another basic polynomial sequence q_n(x).

In set theory, a unary operation on set A is a function A->A. More generally, a unary operation is a function with exactly one operand, such as the factorial, square root, or ...

A quantity which does not exhibit estimator bias. An estimator theta^^ is an unbiased estimator of theta if <theta^^>=theta.