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An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...

A Cunningham number is a binomial number of the form C^+/-(b,n)=b^n+/-1 with b>1 and n positive integers. Bases b^k which are themselves powers need not be considered since ...

An ambiguous figure in which the brain switches between seeing a rabbit and a duck. The duck-rabbit was "originally noted" by American psychologist Joseph Jastrow (Jastrow ...

Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...

Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

Find consecutive powers, i.e., solutions to x^p-y^q=+/-1, excluding 0 and 1. Catalan's conjecture states that the only solution is 3^2-2^3=1, so 8 and 9 (2^3 and 3^2) are the ...

A metric characterizing the difference between two knots K and K^' in S^3.

The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).