The orbital dynamics of most planetary satellites is governed by the quadrupole moment from the equatorial bulge of the host planet and the tidal field from the Sun. On the Laplace surface, the long-term orbital evolution driven by the combined effects of these forces is zero, so that orbits have a fixed orientation and shape. The “classical” Laplace surface is defined for circular orbits, and ...

In this paper we investigate and compare a number of real inversion formulas for the Laplace transform. The focus is on the accuracy and applicability of the formulas for numerical inversion. In this contribution, we study the performance of the formulas for measures concentrated on a positive half-line to continue with measures on an arbitrary half-line.

An efficient transient analysis of lossy lines with nonlinear loads requires the ability to compute and represent a suitable set of line impulse responses. In this paper, we propose the evaluation of the matched-line impulse responses by means of an algorithm for the numerical inversion of the Laplace Transform. Based on a discussion of the structure of the impulse responses, we demonstrate how...

A time scale is any closed subset of the real line. Continuous time and discrete time are special cases. The unilateral Laplace transform of a signal on a time scale subsumes the continuous-time unilateral Laplace transform, and the discretetime unilateral z-transform as special cases. The regions of convergence (ROCs) time scale Laplace transforms are determined by the time scale’s graininess....

We define a notion of determining sets for the discrete Laplacian in a domain Ω. A set D is called determining if harmonic functions are uniquely determined by providing their values on D, and if D has the same size as the boundary of Ω. It is shown that there exist determining sets that are fairly evenly distributed in Ω. A number of basic properties of determining sets are derived.

OF THE DISSERTATION Chip-Firing Games with Dirichlet Eigenvalues and Discrete Green’s Functions

We study spectrum inclusion regions for complex Jacobi matrices that are compact perturbations of the discrete laplacian. The condition sufficient for the lack of discrete spectrum for such matrices is given.

The paper presents an innovative way of a simulation of multiconductor transmission line (MTL) circuits which combines the Laplace transformations in one and in two variables. This approach enables to compute both nodal voltages (branch currents) in lumped-element parts of a circuit and voltage (current) waves distributions along MTLs’ wires effectively. The first one is performed by the numeri...

The aim of this article is to present and reformulate systematically what is known about surfaces in the projective 3-space, in view of transformations of surfaces, and to complement with some new results. Special emphasis will be laid on line congruences and Laplace transformations. A line congruence can be regarded as a transformation connecting one focal surface with the other focal surface....