On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

A remark on the moduli field of a curve

We give a purely algebro-geometric proof of the fact that every nonsingular projective curve can be defined over a finite extension of its moduli field. This extends a result byWolfart [7] to curves over fields of arbitrary characteristic. Received: 30 November 2001     

Asymptotic densities of Maass newforms

We define the counting function for Maass newforms of Hecke congruence groups and calculate the three main terms of this counting function. We then give necessary and sufficient conditions for this expansion to have the same shape as if it were counting eigenvalues related to cocompact surfaces. We relate the result to classical instances of the Jacquet-Langlands correspondence.     

Multi-Wavelength Optical Packet Routing Technologies Based on Superstructured Fiber Bragg Gratings

A WDM compatible Edge-to-Edge Self-Routed optical packet switched network that simplifies the optical processing is proposed. The system employs all-optical packet label generation and recognition using coded superstructured Fiber Bragg gratings.     

Preperfect graphs

We say that a vertexx of a graph is predominant if there exists another vertexy ofG such that either every maximum clique ofG containingy containsx or every maximum stable set containingx containsy. A graph is then called preperfect if every induced subgraph has a predominant vertex. We show that preperfect graphs are perfect, and that several well-known classes of perfect graphs are preperfect. We also derive a new characterization of perfect graphs.     

Spectroscopic investigation of the ionization kinetics in XeCl laser discharges by Xe* density measurements

Time and spatially resolved absorption measurements of Xe^* particle number densities performed at an X-ray preionized self-sustained XeCl^*-laser discharge were used to investigate the reaction kinetics of such discharges and to test the validity of the commonly-made assumption that they are fit well by spatially homogeneous numerical models. It turned out that the Xe^* density distribution over the discharge cross section remains homogeneous for less than 100 ns only. Comparing the experimental results of the homogeneous discharge phase with zero-dimensional model calculations, we conclude that induced emission modeled using two excited xenon levels must be taken into account for the quantitative interpretation of the absorption measurements. For the interpretation of the Xe 6s-6p absorption measurements even a multilevel model will be necessary. Further we conclude from the relative courses and the absolute values of the Xe^* particle number densities that realistic HCl kinetics should contain three vibrationally excited levels and stepwise excitation processes as proposed by Dem'yanov et al. [8].