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Solving the wave equation on a disk gives a solution in terms of Bessel functions.

A point B is said to lie between points A and C (where A, B, and C are distinct collinear points) if AB+BC=AC. A number of Euclid's proofs depend on the idea of betweenness ...

Catalan's triangle is the number triangle 1 ; 1 1 ; 1 2 2 ; 1 3 5 5 ; 1 4 9 14 14 ; 1 5 14 28 42 42 ; 1 6 20 48 90 132 132 (1) (OEIS A009766) with entries given by ...

A partially ordered set (or ordered set or poset for short) (L,<=) is called a complete lattice if every subset M of L has a least upper bound (supremum, supM) and a greatest ...

The dominance relation on a set of points in Euclidean n-space is the intersection of the n coordinate-wise orderings. A point p dominates a point q provided that every ...

A metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation, supremum must be replaced by infimum, ...

A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point ...

To solve the heat conduction equation on a two-dimensional disk of radius a=1, try to separate the equation using U(r,theta,t)=R(r)Theta(theta)T(t). (1) Writing the theta and ...

On the surface of a sphere, attempt separation of variables in spherical coordinates by writing F(theta,phi)=Theta(theta)Phi(phi), (1) then the Helmholtz differential ...

A theorem, also called the iteration theorem, that makes use of the lambda notation introduced by Church. Let phi_x^((k)) denote the recursive function of k variables with ...