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There are at least three theorems known as Jensen's theorem. The first states that, for a fixed vector v=(v_1,...,v_m), the function |v|_p=(sum_(i=1)^m|v_i|^p)^(1/p) is a ...

Let V(r) be the volume of a ball of radius r in a complete n-dimensional Riemannian manifold with Ricci curvature tensor >=(n-1)kappa. Then V(r)<=V_kappa(r), where V_kappa is ...

Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U such that |f(z_0)|>=|f(z)| for all z in U, then f is constant. The ...

A geometric series sum_(k)a_k is a series for which the ratio of each two consecutive terms a_(k+1)/a_k is a constant function of the summation index k. The more general case ...

A set n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). If the sum of ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...

Newton's iteration is an algorithm for computing the square root sqrt(n) of a number n via the recurrence equation x_(k+1)=1/2(x_k+n/(x_k)), (1) where x_0=1. This recurrence ...

A surface (or "space") of section, also called a Poincaré section (Rasband 1990, pp. 7 and 93-94), is a way of presenting a trajectory in n-dimensional phase space in an ...

Defining p_0=2, p_n as the nth odd prime, and the nth prime gap as g_n=p_(n+1)-p_n, then the Cramér-Granville conjecture states that g_n<M(lnp_n)^2 for some constant M>1.

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...