Sinc-Galerkin method for solving nonlinear boundary-value problems

AbstractThe sinc-Galerkin method is used to approximate solutions of nonlinear problems involving nonlinear second-, fourth-, and sixth-order differential equations with homogeneous and nonhomogeneous boundary conditions. The scheme is tested on four nonlinear problems. The results demonstrate the reliability and efficiency of the algorithm developed

On Fields with Finite Information Density

The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication. Here, we prove the mathematical conjectures that were made in this Letter.Comment: 31 pages, to appear in Phys.Rev.

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros

Special functions

CIRCULAR FUNCTIONS Consider the rectangular coordinate system shown in Figure 6.1. The coordinate is positive to the right of the origin and the coordinate is positive above the origin. The radius vector r shown terminating on the point is shown rotated by the angle up from the axis. The radius vector r has component values and