5,396 research outputs found
Cyclic coverings of the -adic projective line by Mumford curves
Exact bounds for the positions of the branch points for cyclic coverings of
the -adic projective line by Mumford curves are calculated in two ways.
Firstly, by using Fumiharu Kato's *-trees, and secondly by giving explicit
matrix representations of the Schottky groups corresponding to the Mumford
curves above the projective line through combinatorial group theory.Comment: 17 pages, 3 eps-figures. To appear in manuscripta mathematic
Efficient wideband electromagnetic scattering computation for frequency dependent lossy dielectrics using WCAWE
This paper presents a model order reduction algorithm for the volume electric field integral equation (EFIE) formulation, that achieves fast and accurate frequency sweep calculations of electromagnetic wave scattering. An inhomogeneous, two-dimensional, lossy dielectric object whose material is characterized by a complex permittivity which varies with frequency is considered. The variation in the dielectric properties of the ceramic BaxLa4Ti 2+xO 12+3x in the <1 GHz frequency range is investigated for various values of x in a frequency sweep analysis. We apply the well-conditioned asymptotic waveform evaluation (WCAWE) method to circumvent the computational complexity associated with the numerical solution of such formulations. A multipoint automatic WCAWE method is also demonstrated which can produce an accurate solution over a much broader bandwidth. Several numerical examples are given on order to illustrate the accuracy and robustness of the proposed methods
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