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The Hermite constant is defined for dimension n as the value gamma_n=(sup_(f)min_(x_i)f(x_1,x_2,...,x_n))/([discriminant(f)]^(1/n)) (1) (Le Lionnais 1983). In other words, ...

As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

A relation connecting the values of a meromorphic function inside a disk with its boundary values on the circumference and with its zeros and poles (Jensen 1899, Levin 1980). ...

The expected number of real zeros E_n of a random polynomial of degree n if the coefficients are independent and distributed normally is given by E_n = ...

Find the minimum number f(n) of subsets in a separating family for a set of n elements, where a separating family is a set of subsets in which each pair of adjacent elements ...

To fit a functional form y=Ae^(Bx), (1) take the logarithm of both sides lny=lnA+Bx. (2) The best-fit values are then a = ...

The term "left factorial" is sometimes used to refer to the subfactorial !n, the first few values for n=1, 2, ... are 1, 3, 9, 33, 153, 873, 5913, ... (OEIS A007489). ...

Given an integer e>=2, the Payam number E_+/-(e) is the smallest positive odd integer k such that for every positive integer n, the number k·2^n+/-1 is not divisible by any ...

The prime distance pd(n) of a nonnegative integer n is the absolute difference between n and the nearest prime. It is therefore true that pd(p)=0 for primes p. The first few ...

A qubit (or quantum bit) is the analog of a bit for quantum computation. Unlike an ordinary bit, which may only assume two possible values (usually called 0 and 1), a qubit ...