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An apodization function, also called the Hann function, frequently used to reduce leakage in discrete Fourier transforms. The illustrations above show the Hanning function, ...

A point in a weighted tree that has minimum weight for the tree. The set of all centroid points is called a tree centroid (Harary 1994, p. 36). The largest possible values ...

The digraph union of two digraphs is the digraph whose vertex set (respectively, edge set) is the union of their vertex sets (respectively, edge sets). Given a positive ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

The north pole is the point on a sphere with maximum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

For n points in the plane, there are at least N_1=sqrt(n-3/4)-1/2 different distances. The minimum distance can occur only <=3n-6 times, and the maximum distance can occur ...

The Trott curve is a simple example of a quartic curve having 28 real bitangents-the maximum possible for a quartic-given by the equation ...

The function psi(x)={x(1-(x^2)/(c^2))^2 for |x|<c; 0 for |x|>c (1) sometimes used in robust estimation. It has a minimum at x=-c/sqrt(5) and a maximum at x=c/sqrt(5), where ...

A metric space X is boundedly compact if all closed bounded subsets of X are compact. Every boundedly compact metric space is complete. (This is a generalization of the ...

Landau's function g(n) is the maximum order of an element in the symmetric group S_n. The value g(n) is given by the largest least common multiple of all partitions of the ...