Computing residue class rings and Picard groups of orders - Klüners, Jürgen; Pauli, Sebastian (Journal of Algebra)
Let K be a global field and O be an order of K. We develop algorithms for the computation of the unit group of residue class rings for ideals O in . As an application we show how to compute the unit group and the Picard group of O provided that we are able to compute the unit group and class group of the maximal order O of K.
Keywords: Algebra and Number Theory

Robust speaker direction estimation with particle filtering - Warsitz, Ernst; Haeb-Umbach, Reinhold (IEEE Workshop on Multimedia Signal Processing (MMSP 2004))
The paper is concerned with binaural signal processing for a bimodal human-robot interface with hearing and vision. The two microphone signals are processed to obtain an enhanced single-channel input signal for the subsequent speech recognizer and to localize the acoustic source, an important information for establishing a natural human-robot communication. We utilize a robust adaptive algorithm for filter-and-sum beamforming (FSB) and extract speaker direction information from the resulting FIR filter coefficients. Further, particle filtering is applied which conducts a nonlinear Bayesian tracking of speaker movement. Good location accuracy can be achieved even in highly reverberant environments. The results obtained outperform the conventional generalized cross correlation (GCC) method.
Keywords: bimodal human-robot interface; binaural signal processing; enhanced single-channel input signal; filter-and-sum beamforming; filtering theory; FIR filter coefficient; generalized cross correlation method; microphones; microphone signal; nonlinear Bayesian tracking; particle filtering; robust adaptive algorithm; robust speaker direction estimation; signal processing; speech enhancement; speech recognition; speech recognizer; user interfaces

Formal Refinement and Model Checking of An Echo Cancellation Unit - Krupp, Alexander; Müller, Wolfgang; Oliver, Ian (Proceedings of DATE’04 Designers' Forum)
This article presents an approach, which combines theorem proving-based refinement with model checking for state based real-time systems. Our verification flow starts from UML state diagrams, which are translated to the formal B language and are model checked for real-time properties. By means of the B language and a B theorem prover, refined state diagrams are verified against their abstract representation. The approach is presented by means of the refinement of a digital echo cancellation unit.
Keywords: Echo cancellers; Logic; Unified modeling language; Automata; Data structures; Boolean functions; Electronic design automation and methodology; Prototypes; Specification languages; Constraint theory

Minimal discriminants for fields with small Frobenius groups as Galois groups - Fieker, Claus; Klüners, Jürgen (Journal of Number Theory)
We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield.
Keywords: Algebra and Number Theory

Improved implementation of an algorithm for non-linear isotropic/kinematic hardening in elastoplasticity - Mahnken, Rolf (Communications in Numerical Methods in Engineering)
Keywords: Applied Mathematics; Computational Theory and Mathematics; General Engineering; Modeling and Simulation; Software

Numerical simulation of interface debonding with a combined damage/friction constitutive model - Döbert, C.; Mahnken, Rolf; Stein, E. (Computational Mechanics)
Keywords: Applied Mathematics; Computational Mathematics; Computational Theory and Mathematics; Mechanical Engineering; Ocean Engineering; Computational Mechanics

Parameter estimation for a viscoplastic damage model using a gradient‐based optimization algorithm - Mahnken, Rolf; Johansson, Magnus; Runesson, Kenneth (Engineering Computations)
In this work a gradient‐based optimization method is applied in order to determine material parameters for a viscoplastic model with dynamic yield surface coupled to damage as presented in 1997. To this end a sensitivity analysis consistent with the integration scheme presented previously is performed in a systematic manner, both for strain and stress controlled experiments. The algorithm is tested in two numerical examples: first, simulated data are used, in order to re‐obtain parameters for the case of damage under monotonic loading. In the second example material parameters are obtained based on experimental data for lcf‐testing of an austenetic stainless steel, thus showing a very good agreement with respect to hardening, rate and damage effects.
Keywords: Computational Theory and Mathematics; Computer Science Applications; General Engineering; Software

A Database for Field Extensions of the Rationals - Klüners, Jürgen; Malle, Gunter (LMS Journal of Computation and Mathematics)
This paper announces the creation of a database for number fields. It describes the contents and the methods of access, indicates the origin of the polynomials, and formulates the aims of this collection of fields.
Keywords: Computational Theory and Mathematics; General Mathematics

Galois Group Computation for Rational Polynomials - Geissler, Katharina; Klüners, Jürgen (Journal of Symbolic Computation)
We describe methods for the computation of Galois groups of univariate polynomials over the rationals which we have implemented up to degree 15. These methods are based on Stauduhar’s algorithm. All computations are done in unramified p -adic extensions. For imprimitive groups we give an improvement using subfields. In the primitive case we use known subgroups of the Galois group together with a combination of Stauduhar’s method and the absolute resolvent method.
Keywords: Computational Mathematics; Algebra and Number Theory

Computing Local Artin Maps, and Solvability of Norm Equations - Acciaro, Vincenzo; Klüners, Jürgen (Journal of Symbolic Computation)
Let L = K(α) be an Abelian extension of degree n of a number field K, given by the minimal polynomial of α over K. We describe an algorithm for computing the local Artin map associated with the extension L / K at a finite or infinite prime v of K. We apply this algorithm to decide if a nonzero a ∈ K is a norm from L, assuming that L / K is cyclic.
Keywords: Computational Mathematics; Algebra and Number Theory

Explicit Galois Realization of Transitive Groups of Degree up to 15 - Klüners, Jürgen; Malle, Gunter (Journal of Symbolic Computation)
We describe methods for the construction of polynomials with certain types of Galois groups. As an application we deduce that all transitive groups G up to degree 15 occur as Galois groups of regular extensions of ℚ (t), and in each case compute a polynomial f ∈ ℚ [ x ] with Gal(f) = G.
Keywords: Computational Mathematics; Algebra and Number Theory

A Polynomial with Galois GroupSL2(11) - Klüners, Jürgen (Journal of Symbolic Computation)
We compute a polynomial with Galois group SL₂(11) over ℚ. Furthermore we prove that SL₂(11) is the Galois group of a regular extension of ℚ (t).
Keywords: Computational Mathematics; Algebra and Number Theory

On Polynomial Decompositions - Klüners, Jürgen (Journal of Symbolic Computation)
We present a new polynomial decomposition which generalizes the functional and homogeneous bivariate decomposition of irreducible monic polynomials in one variable over the rationals. With these decompositions it is possible to calculate the roots of an imprimitive polynomial by solving polynomial equations of lower degree.
Keywords: Computational Mathematics; Algebra and Number Theory

KANT V4 - DABERKOW, M.; FIEKER, C.; Klüners, Jürgen; POHST, M.; ROEGNER, K.; SCHÖRNIG, M.; WILDANGER, K. (Journal of Symbolic Computation)
The software packageKANT V4for computations in algebraic number fields is now available in version 4. In addition a new user interface has been released. We will outline the features of this new software package.
Keywords: Computational Mathematics; Algebra and Number Theory

On Computing Subfields - Klüners, Jürgen; Pohst, Michael (Journal of Symbolic Computation)
The purpose of this article is to determine all subfields ℚ(β) of fixed degree of a given algebraic number field ℚ(α). It is convenient to describe each subfield by a pair (h,g) of polynomials in ℚ[t] resp. Z[t] such thatgis the minimal polynomial of β = h(α). The computations are done in unramifiedp-adic extensions and use information concerning subgroups of the Galois group of the normal closure of ℚ(α) obtained from the van der Waerden criterion.
Keywords: Computational Mathematics; Algebra and Number Theory