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A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...

The approximation of a piecewise monotonic function f by a polynomial with the same monotonicity. Such comonotonic approximations can always be accomplished with nth degree ...

A statistical distribution for which the variables may take on a continuous range of values. Abramowitz and Stegun (1972, p. 930) give a table of the parameters of most ...

The cubeplex graph is the cubic Hamiltonian graph on 12 nodes illustrated above in several embeddings and corresponding to the graph Gamma_1 in Fischer and Little (2001). It ...

A cyclotomic field Q(zeta) is obtained by adjoining a primitive root of unity zeta, say zeta^n=1, to the rational numbers Q. Since zeta is primitive, zeta^k is also an nth ...

The third singular value k_3, corresponding to K^'(k_3)=sqrt(3)K(k_3), (1) is given by k_3=sin(pi/(12))=1/4(sqrt(6)-sqrt(2)). (2) As shown by Legendre, ...

Let Q(x)=Q(x_1,x_2,...,x_n) be an integer-valued n-ary quadratic form, i.e., a polynomial with integer coefficients which satisfies Q(x)>0 for real x!=0. Then Q(x) can be ...

The Kreisel conjecture is a conjecture in proof theory that postulates that, if phi(x) is a formula in the language of arithmetic for which there exists a nonnegative integer ...

Let P(N) denote the number of primes of the form n^2+1 for 1<=n<=N, then P(N)∼0.68641li(N), (1) where li(N) is the logarithmic integral (Shanks 1960, pp. 321-332). Let Q(N) ...

The problem of finding the strategy to guarantee reaching the boundary of a given region ("forest") in the shortest distance (i.e., a strategy having the best worst-case ...