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Li's criterion states that the Riemann hypothesis is equivalent to the statement that, for lambda_n=1/((n-1)!)(d^n)/(ds^n)[s^(n-1)lnxi(s)]|_(s=1), (1) where xi(s) is the ...

Also called Radau quadrature (Chandrasekhar 1960). A Gaussian quadrature with weighting function W(x)=1 in which the endpoints of the interval [-1,1] are included in a total ...

A Lyapunov function is a scalar function V(y) defined on a region D that is continuous, positive definite, V(y)>0 for all y!=0), and has continuous first-order partial ...

The five Mathieu groups M_(11), M_(12), M_(22), M_(23), and M_(24) were the first sporadic groups discovered, having been found in 1861 and 1873 by Mathieu. Frobenius showed ...

A deconvolution algorithm (sometimes abbreviated MEM) which functions by minimizing a smoothness function ("entropy") in an image. Maximum entropy is also called the ...

There are two definitions of a metacyclic group. 1. A metacyclic group is a group G such that both its commutator subgroup G^' and the quotient group G/G^' are cyclic (Rose ...

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 osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

An oval is a curve resembling a squashed circle but, unlike the ellipse, without a precise mathematical definition. The word oval derived from the Latin word "ovus" for egg. ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...