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Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

A multiplicative factor (usually indexed) such as one of the constants a_i in the polynomial a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0. In this polynomial, the monomials are ...

A generalization of the product rule for expressing arbitrary-order derivatives of products of functions, where (n; k) is a binomial coefficient. This can also be written ...

The Mangoldt function is the function defined by Lambda(n)={lnp if n=p^k for p a prime; 0 otherwise, (1) sometimes also called the lambda function. exp(Lambda(n)) has the ...

Given vectors u and v, the vector direct product, also known as a dyadic, is uv=u tensor v^(T), where tensor is the Kronecker product and v^(T) is the matrix transpose. For ...

Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it ...

Mills (1947) proved the existence of a real constant A such that |_A^(3^n)_| (1) is prime for all integers n>=1, where |_x_| is the floor function. Mills (1947) did not, ...

In the technical combinatorial sense, an a-ary necklace of length n is a string of n characters, each of a possible types. Rotation is ignored, in the sense that b_1b_2...b_n ...

A connective in logic known as the "exclusive or," or exclusive disjunction. It yields true if exactly one (but not both) of two conditions is true. The XOR operation does ...