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A Hilbert space is a vector space H with an inner product <f,g> such that the norm defined by |f|=sqrt(<f,f>) turns H into a complete metric space. If the metric defined by ...

The Jacobi symbol, written (n/m) or (n/m) is defined for positive odd m as (n/m)=(n/(p_1))^(a_1)(n/(p_2))^(a_2)...(n/(p_k))^(a_k), (1) where m=p_1^(a_1)p_2^(a_2)...p_k^(a_k) ...

The appearance of nontrivial zeros (i.e., those along the critical strip with R[z]=1/2) of the Riemann zeta function zeta(z) very close together. An example is the pair of ...

The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst (1845, 1847). The ...

The Lotka-Volterra equations describe an ecological predator-prey (or parasite-host) model which assumes that, for a set of fixed positive constants A (the growth rate of ...

The norm of a mathematical object is a quantity that in some (possibly abstract) sense describes the length, size, or extent of the object. Norms exist for complex numbers ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

A sequent is an expression Gamma|-Lambda, where Gamma and Lambda are (possibly empty) sequences of formulas. Here, Gamma is called the antecedent and Lambda is called the ...