Numerical propagation of partially coherent laser beams through optical systems

The propagation of partially coherent beams through optical systems is computed numerically in one transverse dimension. The optical system is divided into different elementary segments, through which the propagation of light can be calculated by appropriate operators, working on the coherence function or the Wigner distribution function respectively. For the necessary changes between these two functions describing the partially coherent beams, the use of the remarkable z-transform seems to be an advantage. With this algorithm the grid and the resolution in the spatial frequency domain can be arbitrarily chosen in contrast to the usual Fourier transform, the influence of phase aberrations on the focusability of Gauss-Schell model beams is discussed as an application example of the numerical model. With the help of this tool, practical beam guiding systems can be simulated for use with multimode laser radiation.     

Lebesgue constants for periodic Hermite spline interpolation operators on uniform lattices

We derive a complex line integral representation for the ebyshev norm of periodic spline interpolation operators of odd degree on uniform lattices. Several generalizations are indicated.     

About the Linear Stability of the Spherically Symmetric Solution for the Equations of a Barotropic Viscous Fluid under the Influence of Self-Gravitation

This paper is concerned with the question of linear stability of motionless, spherically symmetric equilibrium states of viscous, barotropic, self-gravitating fluids. We prove the linear asymptotic stability of such equilibria with respect to perturbations which leave the angular momentum, momentum, mass and the position of the center of gravity unchanged. We also give some decay estimates for such perturbations, which we derive from resolvent estimates by means of analytic semigroup theory.     

Eliminating graphs by means of parallel knock-out schemes

In 1997 Lampert and Slater introduced parallel knock-out schemes, an iterative process on graphs that goes through several rounds. In each round of this process, every vertex eliminates exactly one of its neighbors. The parallel knock-out number of a graph is the minimum number of rounds after which all vertices have been eliminated (if possible). The parallel knock-out number is related to well-known concepts like perfect matchings, hamiltonian cycles, and 2-factors.We derive a number of combinatorial and algorithmic results on parallel knock-out numbers: for families of sparse graphs (like planar graphs or graphs of bounded tree-width), the parallel knock-out number grows at most logarithmically with the number n of vertices; this bound is basically tight for trees. Furthermore, there is a family of bipartite graphs for which the parallel knock-out number grows proportionally to the square root of n. We characterize trees with parallel knock-out number at most 2, and we show that the parallel knock-out number for trees can be computed in polynomial time via a dynamic programming approach (whereas in general graphs this problem is known to be NP-hard). Finally, we prove that the parallel knock-out number of a claw-free graph is either infinite or less than or equal to 2.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Origins and structures of background ions produced by fast-atom bombardment of glycerol

Accurate mass measurements were used to assign elemental compositions and tandem mass spectrometry was used to characterize the peak-at-every-mass background ions produced by kiloelectron-volt-particle bombardment of neat fast-atom bombardment matrices. The majority of the background ions observed in the mass spectrum of neat glycerol was identified. On the basis of the experiments with glycerol, a theory for the formation of background ions is presented. Results are discussed according to the chemical and physical changes that ygoe;on-volt-particle bombardment produces in the matrix.