@techreport{16967, author = {{Hochmuth, Reinhard and Biehler, Rolf and Schaper, Niclas and Kuklinski, Christiane and Lankeit, Elisa and Leis, Elena and Liebendörfer, Michael and Schürmann, Mirko}}, title = {{{Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathmatikbezogenes Lernen in der Studieneingangsphase : Schlussbericht: Teilprojekt A der Leibniz Universität Hannover, Teilprojekte B und C der Universität Paderborn: Berichtszeitraum: 01.03.2015-31.08.2018}}}, doi = {{10.2314/KXP:1689534117}}, year = {{2018}}, } @article{37661, author = {{Rösler, Margit and Voit, Michael}}, issn = {{0022-2526}}, journal = {{Studies in Applied Mathematics}}, keywords = {{Applied Mathematics}}, number = {{4}}, pages = {{474--500}}, publisher = {{Wiley}}, title = {{{Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones}}}, doi = {{10.1111/sapm.12217}}, volume = {{141}}, year = {{2018}}, } @article{37662, author = {{Rösler, Margit and Graczyk, Piotr and Luks, Tomasz}}, issn = {{0926-2601}}, journal = {{Potential Analysis}}, keywords = {{Analysis}}, number = {{3}}, pages = {{337--360}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{On the Green Function and Poisson Integrals of the Dunkl Laplacian}}}, doi = {{10.1007/s11118-017-9638-6}}, volume = {{48}}, year = {{2018}}, } @article{40050, author = {{Baeumer, Boris and Luks, Tomasz and Meerschaert, Mark M.}}, issn = {{0025-584X}}, journal = {{Mathematische Nachrichten}}, keywords = {{General Mathematics}}, number = {{17-18}}, pages = {{2516--2535}}, publisher = {{Wiley}}, title = {{{Space‐time fractional Dirichlet problems}}}, doi = {{10.1002/mana.201700111}}, volume = {{291}}, year = {{2018}}, } @article{34843, abstract = {{A polynomial time algorithm to find generators of the lattice of all subfields of a given number field was given in van Hoeij et al. (2013). This article reports on a massive speedup of this algorithm. This is primary achieved by our new concept of Galois-generating subfields. In general this is a very small set of subfields that determine all other subfields in a group-theoretic way. We compute them by targeted calls to the method from van Hoeij et al. (2013). For an early termination of these calls, we give a list of criteria that imply that further calls will not result in additional subfields. Finally, we explain how we use subfields to get a good starting group for the computation of Galois groups.}}, author = {{Elsenhans, Andreas-Stephan and Klüners, Jürgen}}, issn = {{0747-7171}}, journal = {{Journal of Symbolic Computation}}, keywords = {{Computational Mathematics, Algebra and Number Theory}}, pages = {{1--20}}, publisher = {{Elsevier BV}}, title = {{{Computing subfields of number fields and applications to Galois group computations}}}, doi = {{10.1016/j.jsc.2018.04.013}}, volume = {{93}}, year = {{2018}}, } @inbook{42788, abstract = {{We classify all one-class genera of admissible lattice chains of length at least 2 in hermitian spaces over number fields. If L is a lattice in the chain and p the prime ideal dividing the index of the lattices in the chain, then the {p}-arithmetic group Aut(L{p}) acts chamber transitively on the corresponding Bruhat-Tits building. So our classification provides a step forward to a complete classification of these chamber transitive groups which has been announced 1987 (without a detailed proof) by Kantor, Liebler and Tits. In fact we find all their groups over number fields and one additional building with a discrete chamber transitive group.}}, author = {{Kirschmer, Markus and Nebe, Gabriele}}, booktitle = {{Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory}}, isbn = {{9783319705651}}, publisher = {{Springer International Publishing}}, title = {{{One Class Genera of Lattice Chains Over Number Fields}}}, doi = {{10.1007/978-3-319-70566-8_22}}, year = {{2018}}, } @article{42790, abstract = {{We show that exceptional algebraic groups over number fields do not admit one-class genera of parahoric groups, except in the case G₂ . For the group G₂, we enumerate all such one-class genera for the usual seven-dimensional representation.}}, author = {{Kirschmer, Markus}}, issn = {{1246-7405}}, journal = {{Journal de Théorie des Nombres de Bordeaux}}, keywords = {{Algebra and Number Theory}}, number = {{3}}, pages = {{847--857}}, publisher = {{Cellule MathDoc/CEDRAM}}, title = {{{One-class genera of exceptional groups over number fields}}}, doi = {{10.5802/jtnb.1052}}, volume = {{30}}, year = {{2018}}, } @article{44333, abstract = {{This work deals with an algebro–geometric theory of solutions of the classical Yang–Baxter equation based on torsion free coherent sheaves of Lie algebras on Weierstraß cubic curves.}}, author = {{Burban, Igor and Galinat, L.}}, journal = {{Communications in Mathematical Physics}}, number = {{1}}, pages = {{123–169}}, title = {{{Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation}}}, doi = {{10.1007/s00220-018-3172-2}}, volume = {{364}}, year = {{2018}}, } @unpublished{44538, author = {{Burban, Igor and Drozd, Yu.}}, title = {{{Non-commutative nodal curves and derived tame algebras}}}, year = {{2018}}, } @article{44332, author = {{Burban, Igor and Zheglov, A.}}, journal = {{International Journal of Mathematics}}, number = {{10}}, title = {{{Fourier-Mukai transform on Weierstraß cubics and commuting differential operators}}}, volume = {{29}}, year = {{2018}}, } @misc{45394, author = {{Dröse, Jennifer and Prediger, Susanne and Marcus, A.}}, title = {{{Strategien zum Verstehen von Textaufgaben – Fach- und sprachintegriertes Unterrichtsmaterial in Basis- und Regelfassung}}}, year = {{2018}}, } @article{6571, author = {{Jurgelucks, Benjamin and Claes, Leander and Walther, Andrea and Henning, Bernd}}, issn = {{1055-6788}}, journal = {{Optimization Methods and Software}}, number = {{4-6}}, pages = {{868----888}}, publisher = {{Taylor and Francis Ltd.}}, title = {{{Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation}}}, doi = {{10.1080/10556788.2018.1435652}}, volume = {{33}}, year = {{2018}}, } @inproceedings{45680, author = {{Bruns, Julia and Unterhauser, E. and Gasteiger, H.}}, booktitle = {{Beiträge zum Mathematikunterricht}}, pages = {{377–380}}, publisher = {{WTM-Verlag}}, title = {{{Entwicklung des Begriffsverständnisses zu Vierecksfiguren in der Grundschule – Erste Ergebnisse aus dem Projekt BegriV}}}, year = {{2018}}, } @article{45690, author = {{Bruns, Julia and Gasteiger, H.}}, journal = {{mathematik lehren}}, pages = {{10–13}}, title = {{{Gemeinsame Arbeitsphasen produktiv nutzen – verschiedene Methoden kooperativen Lernens im Mathematikunterricht der Grundschule}}}, volume = {{205}}, year = {{2018}}, } @inbook{36485, abstract = {{This chapter presents an overview of the contributions in TSG 1: Early Childhood Mathematics Education at ICME-13 which focused on issues from the perspective of early childhood educators. A basic assumption of this chapter is that the opportunities for young children to develop mathematical understandings and skills are influenced by several conditions at a macro, meso and micro level. First, curricula provide a framework for early mathematics teaching and learning with varying expectations (by teachers) about what can occur in the pre-school environment—informal learning (such as through play), content to learn and activities to experience. Second, early childhood educators’ mathematical knowledge, pedagogical knowledge, understandings, beliefs, and perceptions influence how they enact these expectations. These competencies can be developed and supported by professional learning. Third, educational programs, resources and activities used in the pre-school environment impact on the mathematical opportunities children engage in at the micro level.}}, author = {{Cooke, Audrey and Bruns, Julia}}, booktitle = {{Contemporary Research and Perspectives on Early Childhood Mathematics Education}}, editor = {{Elia, Iliada and Mulligan, Joanne and Anderson, Ann and Baccaglini-Frank, Anna and Benz, Christiane}}, isbn = {{978-3-319-73432-3}}, pages = {{267–289}}, publisher = {{Springer International Publishing}}, title = {{{Early Childhood Educators’ Issues and Perspectives in Mathematics Education}}}, doi = {{10.1007/978-3-319-73432-3_14}}, year = {{2018}}, } @inbook{36480, abstract = {{Im vorangegangenen Kapitel wurde die Vorgeschichte beschrieben, wie es durch Initiative der Deutsche Telekom Stiftung zur Gründung des DZLM gekommen ist. In diesem zweiten Kapitel werden die Tätigkeitsfelder und Konzepte des DZLM in seiner ersten Förderphase vom 01.10.2011 bis 30.09.2016 beschrieben.}}, author = {{Barzel, Bärbel and Biehler, Rolf and Blömeke, Sigrid and Brandtner, Regine and Bruns, Julia and Dohrmann, Christian and Kortenkamp, Ulrich and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and Scherer, Petra and Selter, Christoph}}, booktitle = {{Mathematikfortbildungen professionalisieren: Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik}}, editor = {{Biehler, Rolf and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina and Scherer, Petra and Selter, Christoph}}, isbn = {{978-3-658-19028-6}}, pages = {{7–39}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Das Deutsche Zentrum für Lehrerbildung Mathematik – DZLM}}}, doi = {{10.1007/978-3-658-19028-6_2}}, year = {{2018}}, } @inbook{36478, author = {{Bruns, Julia and Eichen, Lars}}, booktitle = {{Mathematikfortbildungen professionalisieren. Konzepte, Beispiele und Erfahrungen des Deutschen Zentrums für Lehrerbildung Mathematik}}, editor = {{Biehler, Rolf and Lange, Thomas and Leuders, Timo and Rösken-Winter, Bettina}}, pages = {{417--434}}, publisher = {{Springer}}, title = {{{EmMa - Fortbildung für elementarpädagogische Fachpersonen zur frühen mathematischen Bildung}}}, doi = {{10.1007/978-3-658-19028-6_21}}, year = {{2018}}, } @book{36475, editor = {{Gasteiger, Hedwig and Bruns, Julia}}, title = {{{Methoden empirischer Bildungsforschung im Kontext Frühkindliche Bildung und Entwicklung}}}, year = {{2018}}, } @unpublished{19940, abstract = {{Two smooth map germs are right-equivalent if and only if they generate two Lagrangian submanifolds in a cotangent bundle which have the same contact with the zero-section. In this paper we provide a reverse direction to this classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a symplectic manifold have the same contact with a third Lagrangian submanifold if and only if the intersection problems correspond to stably right equivalent map germs. We, therefore, obtain a correspondence between local Lagrangian intersection problems and catastrophe theory while the classical version only captures tangential intersections. The correspondence is defined independently of any Lagrangian fibration of the ambient symplectic manifold, in contrast to other classical results. Moreover, we provide an extension of the correspondence to families of local Lagrangian intersection problems. This gives rise to a framework which allows a natural transportation of the notions of catastrophe theory such as stability, unfolding and (uni-)versality to the geometric setting such that we obtain a classification of families of local Lagrangian intersection problems. An application is the classification of Lagrangian boundary value problems for symplectic maps.}}, author = {{Offen, Christian}}, booktitle = {{arXiv:1811.10165}}, title = {{{Local intersections of Lagrangian manifolds correspond to catastrophe theory}}}, year = {{2018}}, } @article{19943, abstract = {{In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group action by conformal symplectic symmetries has the effect that the flow map cannot degenerate in a direction which is tangential to the action. This imposes restrictions on which singularities can occur in boundary value problems. Our results generalise classical results about conjugate loci on Riemannian manifolds to a large class of Hamiltonian boundary value problems with, for example, scaling symmetries. }}, author = {{McLachlan, Robert I and Offen, Christian}}, journal = {{New Zealand Journal of Mathematics}}, keywords = {{Hamiltonian boundary value problems, singularities, conformal symplectic geometry, catastrophe theory, conjugate loci}}, pages = {{83--99}}, title = {{{Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci}}}, doi = {{10.53733/34 }}, volume = {{48}}, year = {{2018}}, }