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Let a hotel have a denumerable set of rooms numbered 1, 2, 3, .... Then any finite number n of guests can be accommodated without evicting the current guests by moving the ...

A determinant which arises in the solution of the second-order ordinary differential equation x^2(d^2psi)/(dx^2)+x(dpsi)/(dx)+(1/4h^2x^2+1/2h^2-b+(h^2)/(4x^2))psi=0. (1) ...

Suppose that A is a Banach algebra and X is a Banach A-bimodule. For n=0, 1, 2, ..., let C^n(A,X) be the Banach space of all bounded n-linear mappings from A×...×A into X ...

A function phi(t) satisfies the Hölder condition on two points t_1 and t_2 on an arc L when |phi(t_2)-phi(t_1)|<=A|t_2-t_1|^mu, with A and mu positive real constants. In some ...

Let a chord of constant length be slid around a smooth, closed, convex curve C, and choose a point on the chord which divides it into segments of lengths p and q. This point ...

A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a ...

Homogeneous barycentric coordinates are barycentric coordinates normalized such that they become the actual areas of the subtriangles. Barycentric coordinates normalized so ...

Let M be a Riemannian manifold, and let the topological metric on M be defined by letting the distance between two points be the infimum of the lengths of curves joining the ...

The solid cut from a horizontal cylinder of length L and radius R by a single plane oriented parallel to the cylinder's axis of symmetry (i.e., a portion of a horizontal ...

A (presumably autobiographical) character in one of astrophysicist Fred Hoyle's novels opined the following. "I figure that if to be totally known and totally loved is worth ...