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Preprint
Computation of locally free class groups
(2006)
We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the
locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.
Preprint
Solution properties of the de Branges differential recurrence equation
(2005)
In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of ...
Preprint
Numerical simulation of tunnel fires using preconditioned finite volume schemes
(2006)
This article is concerned with the numerical simulation of flows at low Mach numbers which are subject to the gravitational force and strong heat sources. As a specific example for such flows, a fire event in a car tunnel will be considered in detail. The low Mach flow is treated with a preconditioning technique allowing the computation of unsteady flows, while the source terms for gravitation and heat are incorporated via operator splitting. It is shown that a first order discretization in space is not able to compute ...
Preprint
Duplication coefficients via generating functions
(2006)
In this paper, we solve the duplication problem P_n(ax) = sum_{m=0}^{n}C_m(n,a)P_m(x) where {P_n}_{n>=0} belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give closed-form expressions as well as recurrence relations satisfied by the duplication coefficients.
Preprint
On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field
(Universität Kassel, FB 17, Mathematik/Informatik, 2005)
Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).
Preprint
Shrinking restarting automata
(Universität Kassel, FB 17, Mathematik/Informatik, 2005)
Restarting automata are a restricted model of computation that was introduced by Jancar et.al. to model the so-called analysis by reduction. A computation of a restarting automaton consists of a sequence of cycles such that in each cycle the automaton performs exactly one rewrite step, which replaces a small part of the tape content by another, even shorter word. Thus, each language accepted by a restarting automaton belongs to the complexity class $CSL cap NP$. Here we consider a natural generalization of this model, ...
Preprint
5. Krypto-Tag - Workshop über Kryptographie
(2006)
Dieser Tagungsband enthält die gesammelten Zusammenfassungen der acht eingereichten Vorträge des 5. Krypto-Tags. Der Kryptotag ist eine zentrale Aktivität der Fachgruppe "Angewandte Kryptologie" der Gesellschaft für Informatik e.V. Er ist eine wissenschaftliche Veranstaltung im Bereich der Kryptologie und von der organisatorischen Arbeit der Fachgruppe getrennt.
Preprint
Learning analysis by reduction from positive data
(Universität Kassel, FB 17, Mathematik/Informatik, 2005)
Analysis by reduction is a linguistically motivated method for checking correctness of a sentence. It can be modelled by restarting automata. In this paper we propose a method for learning restarting automata which are strictly locally testable (SLT-R-automata). The method is based on the concept of identification in the limit from positive examples only. Also we characterize the class of languages accepted by SLT-R-automata with respect to the Chomsky hierarchy.
Preprint
Construction of recurrent fractal interpolation surfaces(RFISs) on rectangular grids
(2008)
A recurrent iterated function system (RIFS) is a genaralization of an IFS and provides
nonself-affine fractal sets which are closer to natural objects. In general, it's attractor
is not a continuous surface in R3. A recurrent fractal interpolation surface (RFIS) is an
attractor of RIFS which is a graph of bivariate continuous interpolation function. We
introduce a general method of generating recurrent interpolation surface which are at-
tractors of RIFSs about any data set on a grid.