@inproceedings{39061, abstract = {{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.}}, author = {{Krupp, Alexander and Müller, Wolfgang and Oliver, Ian}}, booktitle = {{Proceedings of DATE’04 Designers' Forum}}, isbn = {{0-7695-2085-5}}, keywords = {{Echo cancellers, Logic, Unified modeling language, Automata, Data structures, Boolean functions, Electronic design automation and methodology, Prototypes, Specification languages, Constraint theory}}, title = {{{Formal Refinement and Model Checking of An Echo Cancellation Unit}}}, doi = {{10.1109/DATE.2004.1269214}}, year = {{2004}}, } @article{34896, abstract = {{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.}}, author = {{Fieker, Claus and Klüners, Jürgen}}, issn = {{0022-314X}}, journal = {{Journal of Number Theory}}, keywords = {{Algebra and Number Theory}}, number = {{2}}, pages = {{318--337}}, publisher = {{Elsevier BV}}, title = {{{Minimal discriminants for fields with small Frobenius groups as Galois groups}}}, doi = {{10.1016/s0022-314x(02)00071-9}}, volume = {{99}}, year = {{2003}}, } @article{45423, author = {{Mahnken, Rolf}}, issn = {{1069-8299}}, journal = {{Communications in Numerical Methods in Engineering}}, keywords = {{Applied Mathematics, Computational Theory and Mathematics, General Engineering, Modeling and Simulation, Software}}, number = {{10}}, pages = {{745--754}}, publisher = {{Wiley}}, title = {{{Improved implementation of an algorithm for non-linear isotropic/kinematic hardening in elastoplasticity}}}, doi = {{10.1002/(sici)1099-0887(199910)15:10<745::aid-cnm288>3.0.co;2-r}}, volume = {{15}}, year = {{2002}}, } @article{45417, author = {{Döbert, C. and Mahnken, Rolf and Stein, E.}}, issn = {{0178-7675}}, journal = {{Computational Mechanics}}, keywords = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}}, number = {{5}}, pages = {{456--467}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Numerical simulation of interface debonding with a combined damage/friction constitutive model}}}, doi = {{10.1007/s004660050493}}, volume = {{25}}, year = {{2002}}, } @article{45427, abstract = {{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.}}, author = {{Mahnken, Rolf and Johansson, Magnus and Runesson, Kenneth}}, issn = {{0264-4401}}, journal = {{Engineering Computations}}, keywords = {{Computational Theory and Mathematics, Computer Science Applications, General Engineering, Software}}, number = {{7}}, pages = {{925--955}}, publisher = {{Emerald}}, title = {{{Parameter estimation for a viscoplastic damage model using a gradient‐based optimization algorithm}}}, doi = {{10.1108/02644409810236920}}, volume = {{15}}, year = {{2002}}, } @article{34897, abstract = {{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.}}, author = {{Klüners, Jürgen and Malle, Gunter}}, issn = {{1461-1570}}, journal = {{LMS Journal of Computation and Mathematics}}, keywords = {{Computational Theory and Mathematics, General Mathematics}}, pages = {{182--196}}, publisher = {{Wiley}}, title = {{{A Database for Field Extensions of the Rationals}}}, doi = {{10.1112/s1461157000000851}}, volume = {{4}}, year = {{2001}}, } @article{34900, abstract = {{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.}}, author = {{Geissler, Katharina and Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{6}}, pages = {{653--674}}, publisher = {{Elsevier BV}}, title = {{{Galois Group Computation for Rational Polynomials}}}, doi = {{10.1006/jsco.2000.0377}}, volume = {{30}}, year = {{2000}}, } @article{34901, abstract = {{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.}}, author = {{Acciaro, Vincenzo and Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{3}}, pages = {{239--252}}, publisher = {{Elsevier BV}}, title = {{{Computing Local Artin Maps, and Solvability of Norm Equations}}}, doi = {{10.1006/jsco.2000.0361}}, volume = {{30}}, year = {{2000}}, } @article{34899, abstract = {{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.}}, author = {{Klüners, Jürgen and Malle, Gunter}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{6}}, pages = {{675--716}}, publisher = {{Elsevier BV}}, title = {{{Explicit Galois Realization of Transitive Groups of Degree up to 15}}}, doi = {{10.1006/jsco.2000.0378}}, volume = {{30}}, year = {{2000}}, } @article{34898, abstract = {{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).}}, author = {{Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{6}}, pages = {{733--737}}, publisher = {{Elsevier BV}}, title = {{{A Polynomial with Galois GroupSL2(11)}}}, doi = {{10.1006/jsco.2000.0380}}, volume = {{30}}, year = {{2000}}, } @article{34902, abstract = {{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.}}, author = {{Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{3}}, pages = {{261--269}}, publisher = {{Elsevier BV}}, title = {{{On Polynomial Decompositions}}}, doi = {{10.1006/jsco.1998.0252}}, volume = {{27}}, year = {{1999}}, } @article{34903, abstract = {{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.}}, author = {{DABERKOW, M. and FIEKER, C. and Klüners, Jürgen and POHST, M. and ROEGNER, K. and SCHÖRNIG, M. and WILDANGER, K.}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{3-4}}, pages = {{267--283}}, publisher = {{Elsevier BV}}, title = {{{KANT V4}}}, doi = {{10.1006/jsco.1996.0126}}, volume = {{24}}, year = {{1997}}, } @article{34904, abstract = {{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.}}, author = {{Klüners, Jürgen and Pohst, Michael}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, number = {{3-4}}, pages = {{385--397}}, publisher = {{Elsevier BV}}, title = {{{On Computing Subfields}}}, doi = {{10.1006/jsco.1996.0140}}, volume = {{24}}, year = {{1997}}, }