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Let f(x) be a nonnegative and monotonic decreasing function in [a,b] and g(x) such that 0<=g(x)<=1 in [a,b], then int_(b-k)^bf(x)dx<=int_a^bf(x)g(x)dx<=int_a^(a+k)f(x)dx, ...

A map phi:M->M where M is a manifold is C^r structurally stable if any C^r perturbation is topologically conjugate to phi. Here, C^r perturbation means a function psi such ...

The tail of a vector AB^-> is the initial point A, i.e., the point at which the vector originates. The tails of a statistical distribution with probability density function ...

The depth of a vertex v in a rooted tree as the number of edges from v to the root vertex. A function to return the depth of a vertex v in a tree g may be implemented in a ...

Dawson's integral (Abramowitz and Stegun 1972, pp. 295 and 319), also sometimes called Dawson's function, is the entire function given by the integral F(x) = ...

Wavelets are a class of a functions used to localize a given function in both space and scaling. A family of wavelets can be constructed from a function psi(x), sometimes ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...

Kobon Fujimura asked for the largest number N(n) of nonoverlapping triangles that can be constructed using n lines (Gardner 1983, p. 170). A Kobon triangle is therefore ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

Pronic numbers are figurate numbers of the form P_n=2T_n=n(n+1), where T_n is the nth triangular number. The first few are 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, ... (OEIS ...