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Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...

An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

Ramanujan calculated mu=1.45136380... (Hardy 1999, Le Lionnais 1983, Berndt 1994), while the correct value is mu=1.45136923488... (OEIS A070769; Derbyshire 2004, p. 114). The ...

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, ...

The sporadic groups are the 26 finite simple groups that do not fit into any of the four infinite families of finite simple groups (i.e., the cyclic groups of prime order, ...

A real polynomial P is said to be stable if all its roots lie in the left half-plane. The term "stable" is used to describe such a polynomial because, in the theory of linear ...

An attracting set that has zero measure in the embedding phase space and has fractal dimension. Trajectories within a strange attractor appear to skip around randomly. A ...

The Struve function, denoted H_n(z) or occasionally H_n(z), is defined as H_nu(z)=(1/2z)^(nu+1)sum_(k=0)^infty((-1)^k(1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2)), (1) where ...