In this article normalization of a Hamiltonian system with reflection symmetry is performed by means of Lie transforms. The periodic solutions are computed by means of inverse transformation and they ...

Abstract: There is often a need to approximate integrals of highly oscillatory functions when studying scattering and diffraction of electromagnetic waves. This paper presents a method of estimating ...

Variational lower bounds are a simple and efficient way to approximate Bayesian integrals. By bounding the integrand at every point, we obtain a bound on the integral value. Variational Bayes (Attias ...

A line drawing of the Internet Archive headquarters building façade. An illustration of a magnifying glass. An illustration of a magnifying glass.

Calculating the area under a curve has been a long-time problem in mathematics. Curves that can be represented by a formula, such as a parabola, can be integrated using mathematical resources, such as ...

The Calculus class provides methods which calculate numerical approximations for the derivative and integral at certain points similar to the programs on many graphing calculators. There are two ...

P.S.—I thank Mr. C. F. Merchant for pointing out in NATURE of June 3 that the four-ordinate rule is already in use, and for giving a reference to Tchebycheff's rules, with which I was unacquainted.

ABSTRACT: We study the ability of three different projection methods to solve high-dimensional state space problems: Galerkin, collocation, and least squares projection. The curse of dimensionality ...