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The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X. For example, in the ...

In general, a remainder is a quantity "left over" after performing a particular algorithm. The term is most commonly used to refer to the number left over when two integers ...

Rényi entropy is defined as: H_alpha(p_1,p_2,...,p_n)=1/(1-alpha)ln(sum_(i=1)^np_i^alpha), where alpha>0, alpha!=1. As alpha->1, H_alpha(p_1,p_2,...,p_n) converges to ...

Rényi's polynomial is the polynomial (Rényi 1947, Coppersmith and Davenport 1991) that has 29 terms and whose square has 28, making it a sparse polynomial square.

Given a function f specified by parametric variables u_1, ..., u_n, a reparameterization f^^ of f over domain U is a change of variables u_i in U->v_i->V via a function phi ...

An expression describing a form in which a quantity can be written. For example, all primes p>3 can be "represented as" 6n+/-1.

In a complete metric space, a countable union of nowhere dense sets is said to be meager; the complement of such a set is a residual set.

A plot of y_i versus the estimator e_i=y^^_i-y_i. Random scatter indicates the model is probably good. A pattern indicates a problem with the model. If the spread in e_i ...

In a local ring R, there is only one maximal ideal m. Hence, R has only one quotient ring R/m which is a field. This field is called the residue field.

For a given monic quartic equation f(x)=x^4+a_3x^3+a_2x^2+a_1x+a_0, (1) the resolvent cubic is the monic cubic polynomial g(x)=x^3+b_2x^2+b_1x+b_0, (2) where the coefficients ...