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The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

For any two nonzero p-adic numbers a and b, the Hilbert symbol is defined as (a,b)={1 if z^2=ax^2+by^2 has a nonzero solution; -1 otherwise. (1) If the p-adic field is not ...

If f:[a,b]->[a,b] (where [a,b] denotes the closed interval from a to b on the real line) satisfies a Lipschitz condition with constant K, i.e., if |f(x)-f(y)|<=K|x-y| for all ...

A composite number defined analogously to a Smith number except that the sum of the number's digits equals the sum of the digits of its distinct prime factors (excluding 1). ...

Two topological spaces X and Y are homotopy equivalent if there exist continuous maps f:X->Y and g:Y->X, such that the composition f degreesg is homotopic to the identity ...

The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then ...

An exponential growth law of the form y=ar^x characterizing a quantity which increases at a fixed rate proportionally to itself.

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

Little's law states that, under steady state conditions, the average number of items in a queuing system equals the average rate at which the items arrive multiplied by the ...