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Let A be a closed convex subset of a Banach space and assume there exists a continuous map T sending A to a countably compact subset T(A) of A. Then T has fixed points.

A Taylor series remainder formula that gives after n terms of the series R_n=(f^((n+1))(x^*))/(n!p)(x-x^*)^(n+1-p)(x-x_0)^p for x^* in (x_0,x) and any p>0 (Blumenthal 1926, ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then the Selberg zeta function is defined as ...

Serret's integral is given by int_0^1(ln(x+1))/(x^2+1)dx = 1/8piln2 (1) = 0.272198... (2) (OEIS A102886; Serret 1844; Gradshteyn and Ryzhik 2000, eqn. 4.291.8; Boros and Moll ...

Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential ...

A singular integral is an integral whose integrand reaches an infinite value at one or more points in the domain of integration. Even so, such integrals can converge, in ...

Let K be a T2-topological space and let F be the space of all bounded complex-valued continuous functions defined on K. The supremum norm is the norm defined on F by ...

A tesseral harmonic is a spherical harmonic of the form cos; sin(mphi)P_l^m(costheta). These harmonics are so named because the curves on which they vanish are l-m parallels ...

Let L be a language of first-order predicate logic, let I be an indexing set, and for each i in I, let A_i be a structure of the language L. Let u be an ultrafilter in the ...

A zonal harmonic is a spherical harmonic of the form P_l(costheta), i.e., one which reduces to a Legendre polynomial (Whittaker and Watson 1990, p. 302). These harmonics are ...