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Numbers 1, alpha_1, ..., alpha_L are rationally independent iff under the action of rotation rho_(alpha_1)×...×rho_(alpha_L) on the L-dimensional torus, every orbit is ...

A spectrum formed by the Lagrange numbers. The only ones less than three are the Lagrange numbers, but the last gaps end at Freiman's constant. Real numbers larger than ...

The smallest n for which a point x_0 is a periodic point of a function f so that f^n(x_0)=x_0. For example, for the function f(x)=-x, all points x have period 2 (including ...

Suppose that {f_n} is a sequence of measurable functions, that f_n->f pointwise almost everywhere as n->infty, and that |f_n|<=g for all n, where g is integrable. Then f is ...

A prime factorization algorithm in which a sequence of trial divisors is chosen using a quadratic sieve. By using quadratic residues of N, the quadratic residues of the ...

A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

Let K be a field of field characteristic 0 (e.g., the rationals Q) and let {u_n} be a sequence of elements of K which satisfies a difference equation of the form ...

Polynomials s_n(x) which form the Sheffer sequence for f^(-1)(t)=1+t-e^t, (1) where f^(-1)(t) is the inverse function of f(t), and have generating function ...

An n-cycle is a finite sequence of points Y_0, ..., Y_(n-1) such that, under a map G, Y_1 = G(Y_0) (1) Y_2 = G(Y_1) (2) Y_(n-1) = G(Y_(n-2)) (3) Y_0 = G(Y_(n-1)). (4) In ...

A spectrum containing the real numbers larger than Freiman's constant.