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Let F be a field of field characteristic p. Then the Frobenius automorphism on F is the map phi:F->F which maps alpha to alpha^p for each element alpha of F.

The number of nodes in a graph is called its order.

Consider a one-dimensional Hamiltonian map of the form H(p,q)=1/2p^2+V(q), (1) which satisfies Hamilton's equations q^. = (partialH)/(partialp) (2) p^. = ...

A knot that secures a rope to a post, ring, another rope, etc., but does not keep its shape by itself.

The branch of algebraic topology which deals with homotopy groups. Homotopy methods can be used to solve systems of polynomials by embedding the polynomials in a family of ...

Using Clebsch-Aronhold notation, an algebraic curve satisfies xi_1^na_y^n+xi_1^(n-1)xi_2a_y^(n-1)a_x+1/2n(n-1)xi_1^(n-2)xi_2^2a_y^(n-2)a_x^2+... ...

For 0<=x<=pi/2, 2/pix<=sinx<=x.

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 ...

In abstract topology, a machine is method for producing infinite loop spaces and spectra. In automata theory, an abstract machine that is implemented in hardware is simply ...

An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.