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Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

An abundant number, sometimes also called an excessive number, is a positive integer n for which s(n)=sigma(n)-n>n, (1) where sigma(n) is the divisor function and s(n) is the ...

There are four varieties of Airy functions: Ai(z), Bi(z), Gi(z), and Hi(z). Of these, Ai(z) and Bi(z) are by far the most common, with Gi(z) and Hi(z) being encountered much ...

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. ...

A formal extension of the hypergeometric function to two variables, resulting in four kinds of functions (Appell 1925; Picard 1880ab, 1881; Goursat 1882; Whittaker and Watson ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

A 4-cusped hypocycloid which is sometimes also called a tetracuspid, cubocycloid, or paracycle. The parametric equations of the astroid can be obtained by plugging in n=a/b=4 ...

An (n,k)-banana tree, as defined by Chen et al. (1997), is a graph obtained by connecting one leaf of each of n copies of an k-star graph with a single root vertex that is ...