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Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

Discrepancy is a measure of the deviation of a point set from a uniform distribution. In general, the computation of the discrepancy of a point set is computationally ...

A symbol used to distinguish a third quantity x^('') ("x double prime") from two other related quantities x and x^' ("x prime). Double primes are most commonly used to denote ...

For any two ergodic measure-preserving transformations on nonatomic probability spaces, there is an isomorphism between the two probability spaces carrying orbits onto orbits.

A cylindrical algebraic decomposition that omits sets of measure zero. Generic cylindrical algebraic decompositions are generally much quicker to compute than are normal ...

A unit of angular measure in which the angle of an entire circle is 400 gradians. A right angle is therefore 100 gradians. A gradian is sometimes also called a gon or a grade.

The condition for isoenergetic nondegeneracy for a Hamiltonian H=H_0(I)+epsilonH_1(I,theta) is |(partial^2H_0)/(partialI_ipartialI_j) (partialH_0)/(partialI_i); ...

A set of plane measure 0 that contains a circle of every radius.

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 major arc (right figure) is an arc of a circle having measure greater than or equal to 180 degrees (pi radians).