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An irreducible representation of a group is a group representation that has no nontrivial invariant subspaces. For example, the orthogonal group O(n) has an irreducible ...

Let x_0 be a rational number in the closed interval [0,1], and generate a sequence using the map x_(n+1)=2x_n (mod 1). (1) Then the number of periodic map orbits of period p ...

Consider the process of taking a number, adding its digits, then adding the digits of the number derived from it, etc., until the remaining number has only one digit. The ...

A flow defined analogously to the Anosov diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

An attractor is a set of states (points in the phase space), invariant under the dynamics, towards which neighboring states in a given basin of attraction asymptotically ...

An automorphic function f(z) of a complex variable z is one which is analytic (except for poles) in a domain D and which is invariant under a countably infinite group of ...

A 1-variable unoriented knot polynomial Q(x). It satisfies Q_(unknot)=1 (1) and the skein relationship Q_(L_+)+Q_(L_-)=x(Q_(L_0)+Q_(L_infty)). (2) It also satisfies ...

The Barth decic is a decic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 345. It is given by the ...

The bigyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(79). The unit bigyrate diminished rhombicosidodecahedron has volume ...

A binary quadratic form is a quadratic form in two variables having the form Q(x,y)=ax^2+2bxy+cy^2, (1) commonly denoted <a,b,c>. Consider a binary quadratic form with real ...