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Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

Given a sequence S_i as input to stage i, form sequence S_(i+1) as follows: 1. For k in [1,...,i], write term i+k and then term i-k. 2. Discard the ith term. 3. Write the ...

Mann's theorem is a theorem widely circulated as the "alpha-beta conjecture" that was subsequently proven by Mann (1942). It states that if A and B are sets of integers each ...

The Montgomery-Odlyzko law (which is a law in the sense of empirical observation instead of through mathematical proof) states that the distribution of the spacing between ...

A predicate in logic equivalent to the composition NOT OR that yields false if any condition is true, and true if all conditions are false. A NOR B is equivalent to !(A v B), ...

The regularized gamma functions are defined by P(a,z) = (gamma(a,z))/(Gamma(a)) (1) Q(a,z) = (Gamma(a,z))/(Gamma(a)), (2) where gamma(a,z) and Gamma(a,z) are incomplete gamma ...

Resolution is a widely used word with many different meanings. It can refer to resolution of equations, resolution of singularities (in algebraic geometry), resolution of ...

There exists a positive integer s such that every sufficiently large integer is the sum of at most s primes. It follows that there exists a positive integer s_0>=s such that ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then every even function h(rho) analytic in ...

The sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... (OEIS A002024) consisting of 1 copy of 1, 2 copies of 2, 3 copies of 3, and so on. Surprisingly, there exist simple formulas ...