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An operator A:f^((n))(I)|->f(I) assigns to every function f in f^((n))(I) a function A(f) in f(I). It is therefore a mapping between two function spaces. If the range is on ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

Given a set of ordered quantities, a list of the fractions of values at or below each quantity is know as a plotting position. A quantile-quantile plot compares observed ...

Consider the sequence {x_n}_(n=0)^infty defined by x_0=1 and x_(n+1)=[3/2x_n], where [z] is the ceiling function. For n=0, 1, ..., the first few terms are 1, 2, 3, 5, 8, 12, ...

Given an integer sequence {a_n}_(n=1)^infty, a prime number p is said to be a primitive prime factor of the term a_n if p divides a_n but does not divide any a_m for m<n. It ...

Let a sequence be defined by A_(-1) = s (1) A_0 = 3 (2) A_1 = r (3) A_n = rA_(n-1)-sA_(n-2)+A_(n-3). (4) Also define the associated polynomial f(x)=x^3-rx^2+sx+1, (5) and let ...

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

The notion of weak amenability was first introduced by Bade et al. (1987), who termed a commutative Banach algebra A "weakly amenable" if every continuous derivation from A ...

The Yff circles are the two triplets of congruent circle in which each circle is tangent to two sides of a reference triangle. In each case, the triplets intersect pairwise ...

Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...