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An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

If an analytic function has a single simple pole at the radius of convergence of its power series, then the ratio of the coefficients of its power series converges to that ...

A function giving the distribution of the interpoint distances of a curve. It is defined by p(r)=1/Nsum_(ij)delta_(r_(ij)=r).

If the random variates X_1, X_2, ... satisfy the Lindeberg condition, then for all a<b, lim_(n->infty)P(a<(S_n)/(s_n)<b)=Phi(b)-Phi(a), where Phi is the normal distribution ...

A linear approximation to a function f(x) at a point x_0 can be computed by taking the first term in the Taylor series f(x_0+Deltax)=f(x_0)+f^'(x_0)Deltax+....

The log-likelihood function F(theta) is defined to be the natural logarithm of the likelihood function L(theta). More precisely, F(theta)=lnL(theta), and so in particular, ...

A maximum likelihood estimator is a value of the parameter a such that the likelihood function is a maximum (Harris and Stocket 1998, p. 824).

Let f be a nonnegative and continuous function on the closed interval [a,b], then the solid of revolution obtained by rotating the curve f(x) about the x-axis from x=a to x=b ...

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A Müntz space is a technically defined space M(Lambda)=span{x^(lambda_0),x^(lambda_1),...} which arises in the study of function approximations.