@article{34839, abstract = {{We describe the relations among the ℓ-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the other two conjectures for nilpotent groups.}}, author = {{Klüners, Jürgen and Wang, Jiuya}}, issn = {{0002-9939}}, journal = {{Proceedings of the American Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{7}}, pages = {{2793--2805}}, publisher = {{American Mathematical Society (AMS)}}, title = {{{ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group}}}, doi = {{10.1090/proc/15882}}, volume = {{150}}, year = {{2022}}, } @article{34835, abstract = {{We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. }}, author = {{Klüners, Jürgen}}, issn = {{0065-1036}}, journal = {{Acta Arithmetica}}, keywords = {{Algebra and Number Theory}}, number = {{2}}, pages = {{165--184}}, publisher = {{Institute of Mathematics, Polish Academy of Sciences}}, title = {{{The asymptotics of nilpotent Galois groups}}}, doi = {{10.4064/aa211207-16-5}}, volume = {{204}}, year = {{2022}}, } @article{44328, abstract = {{In this paper, we study equivalences between the categories of quasi–coherent sheaves on non–commutative noetherian schemes. In particular, we give a new proof of Căldăraru's conjecture about Morita equivalences of Azumaya algebras on noetherian schemes. Moreover, we derive necessary and sufficient condition for two reduced non–commutative curves to be Morita equivalent.}}, author = {{Burban, Igor and Drozd, Yu.}}, journal = {{Advances in Mathematics}}, title = {{{Morita theory for non-commutative noetherian schemes}}}, doi = {{10.1016/j.aim.2022.108273}}, volume = {{399}}, year = {{2022}}, } @article{44327, author = {{Burban, Igor and Peruzzi, A.}}, journal = {{Journal of Geometry and Physics}}, title = {{{On elliptic solutions of the associative Yang-Baxter equation}}}, volume = {{176}}, year = {{2022}}, } @article{44624, author = {{Faulwasser, Timm and Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Schaller, Manuel and Worthmann, Karl}}, journal = {{Mathematics of Control, Signals, and Systems}}, pages = {{759--788}}, publisher = {{Springer}}, title = {{{Manifold turnpikes, trims, and symmetries}}}, volume = {{34}}, year = {{2022}}, } @article{33741, abstract = {{There are many concepts of signed graph coloring which are defined by assigning colors to the vertices of the graphs. These concepts usually differ in the number of self-inverse colors used. We introduce a unifying concept for this kind of coloring by assigning elements from symmetric sets to the vertices of the signed graphs. In the first part of the paper, we study colorings with elements from symmetric sets where the number of self-inverse elements is fixed. We prove a Brooks’-type theorem and upper bounds for the corresponding chromatic numbers in terms of the chromatic number of the underlying graph. These results are used in the second part where we introduce the symset-chromatic number χsym(G,σ) of a signed graph (G,σ). We show that the symset-chromatic number gives the minimum partition of a signed graph into independent sets and non-bipartite antibalanced subgraphs. In particular, χsym(G,σ)≤χ(G). In the final section we show that these colorings can also be formalized as DP-colorings.}}, author = {{Cappello, Chiara and Steffen, Eckhard}}, issn = {{0218-0006}}, journal = {{Annals of Combinatorics}}, keywords = {{Discrete Mathematics and Combinatorics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Symmetric Set Coloring of Signed Graphs}}}, doi = {{10.1007/s00026-022-00593-4}}, year = {{2022}}, } @article{33950, author = {{Cappello, Chiara and Steffen, Eckhard}}, issn = {{0166-218X}}, journal = {{Discrete Applied Mathematics}}, keywords = {{Applied Mathematics, Discrete Mathematics and Combinatorics}}, pages = {{183--193}}, publisher = {{Elsevier BV}}, title = {{{Frustration-critical signed graphs}}}, doi = {{10.1016/j.dam.2022.08.010}}, volume = {{322}}, year = {{2022}}, } @inproceedings{45679, author = {{Bruns, Julia and Reuter, D.}}, booktitle = {{Beiträge zum Mathematikunterricht 2022}}, publisher = {{WTM-Verlag}}, title = {{{„Ich hab als Erstes die angeguckt“ – Muster- und Strukturerkennung mit Eye-Tracking besser verstehen?}}}, year = {{2022}}, } @inproceedings{45678, author = {{Bruns, Julia and Hagena, M. and Gasteiger, H.}}, booktitle = {{Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)}}, editor = {{Hodgen, J. and Geraniou, E. and Bolondi, G. and Ferretti, F.}}, location = {{Free University of Bozen-Bolzano and ERME}}, title = {{{Effects of Facilitator Professional Development on Teachers’ Learning – An Intervention Study in the Context of Early Mathematics Education}}}, year = {{2022}}, } @article{45677, author = {{Bruns, Julia and Langer, W. and Erhorn, J.}}, journal = {{German Journal of Exercise and Sport Research}}, number = {{3}}, pages = {{386–397}}, title = {{{Entwicklung und Validierung eines videobasierten Testinstruments zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse im inklusiven Sportunterricht}}}, doi = {{10.1007/s12662-022-00807-0}}, volume = {{52}}, year = {{2022}}, } @article{34820, abstract = {{The construct of noticing is considered to be of crucial importance for professional action of (prospective) physical education (PE) teachers in the context of (inclusive) PE. In order to implement the demands of inclusive PE teaching, noticingwith regard to processes of recognition proves to be particularly significant. Due to the relevance of physicality, the design of recognition relationships that encourage pupils' development results in specific requirements for the selective attention and the theory-based interpretation of processes of recognition and disregard in complex teaching situations. This facet of competence has hardly been studied so far, partly due to the lack of instruments for standardised assessment of this construct. In the context of this paper, the development and validation of a standardised, video vignette-based test instrument for the measurement of noticingwith regard to processes of recognition of prospective PE teachers is presented. The validation focuses on the content of the test and the internal structure of the instrument as well as on correlations with related constructs in terms of content. The results from three consecutive validation studies provide indications of the reliability and validity of the test score interpretation of the instrument ViProQiS_A. The findings so far indicate that the standardised measurement of noticingwith regard to processes of recognitionin inclusive PE could be realized on the basis of the test instrument developed here.}}, author = {{Langer, Wiebke and Bruns, Julia and Erhorn, Jan}}, issn = {{2509-3150}}, journal = {{German Journal of Exercise and Sport Research}}, keywords = {{Physical education teacher education, Competence modelling and, measurement, Inclusive physical education, Video-based items, Noticing}}, number = {{3}}, pages = {{386--397}}, publisher = {{Springer}}, title = {{{Development and validation of a video-based test instrument to measure noticing with regard to processes ofrecognition in inclusive physical education}}}, doi = {{10.1007/s12662-022-00807-0}}, volume = {{52}}, year = {{2022}}, } @article{34819, abstract = {{Teachers expect facilitators to have own teaching experience as a teacher in order to be able to carry out effective teacher professional development programs. As part of the project EmMa(M), it is investigated, to which extent the teaching experience of facilitators influences the development of early childhood teachers' (n = 83) mathematical pedagogical content knowledge (MPCK) and early childhood teachers' enjoyment of mathematics in the context of a teacher professional development program. It turns out that the teaching experience of the facilitators has no influence on the development of early childhood teachers' MPCK, but favors the development of early childhood teachers' enjoyment of mathematics. Controlling for this increased enjoyment an influence of teaching experience on the development of early childhood teachers' MPCK emerges, but in favor of the participating facilitators who have no teaching experience but have a university degree.}}, author = {{Hagena, Maike and Bruns, Julia and Gasteiger, Hedwig}}, issn = {{1862-5215}}, journal = {{Zeitschrift für Erziehungswissenschaft}}, keywords = {{Facilitator professional development, Early childhood teachers, Teaching, experience, Early mathematics education}}, number = {{6}}, pages = {{1455–1480}}, publisher = {{Springer Vieweg-springer Fachmedien Wiesbaden Gmbh}}, title = {{{Einfluss der Berufserfahrung von Multiplikatorinnen und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen zur frühen mathematischen Bildung. Zeitschrift Für Erziehungswissenschaft}}}, doi = {{10.1007/s11618-022-01122-y}}, volume = {{25}}, year = {{2022}}, } @inbook{36472, author = {{Reuter, Dinah and Bruns, Julia}}, booktitle = {{Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik}}, isbn = {{9783662632130}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{Muster- und Strukturerkennungsprozesse bei potenziell mathematisch begabten Grundschulkindern untersuchen – Das Potenzial von Eye-Tracking und retrospektivem Interview im Vergleich}}}, doi = {{10.1007/978-3-662-63214-7_3}}, year = {{2022}}, } @article{45854, abstract = {{In a previous paper the authors developed an algorithm to classify certain quaternary quadratic lattices over totally real fields. The present article applies this algorithm to the classification of binary Hermitian lattices over totally imaginary fields. We use it in particular to classify the 48-dimensional extremal even unimodular lattices over the integers that admit a semilarge automorphism.}}, author = {{Kirschmer, Markus and Nebe, Gabriele}}, issn = {{1058-6458}}, journal = {{Experimental Mathematics}}, keywords = {{General Mathematics}}, number = {{1}}, pages = {{280--301}}, publisher = {{Informa UK Limited}}, title = {{{Binary Hermitian Lattices over Number Fields}}}, doi = {{10.1080/10586458.2019.1618756}}, volume = {{31}}, year = {{2022}}, } @article{34677, author = {{Black, Tobias and Wu, Chunyan}}, issn = {{0944-2669}}, journal = {{Calculus of Variations and Partial Differential Equations}}, keywords = {{Applied Mathematics, Analysis}}, number = {{3}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation}}}, doi = {{10.1007/s00526-022-02201-y}}, volume = {{61}}, year = {{2022}}, } @article{19941, abstract = {{In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized partial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation.}}, author = {{McLachlan, Robert I and Offen, Christian}}, journal = {{Journal of Geometric Mechanics}}, number = {{3}}, pages = {{447 -- 471}}, publisher = {{AIMS}}, title = {{{Backward error analysis for variational discretisations of partial differential equations}}}, doi = {{10.3934/jgm.2022014}}, volume = {{14}}, year = {{2022}}, } @article{23382, abstract = {{Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes.}}, author = {{Offen, Christian and Ober-Blöbaum, Sina}}, journal = {{Chaos: An Interdisciplinary Journal of Nonlinear Science}}, publisher = {{AIP}}, title = {{{Symplectic integration of learned Hamiltonian systems}}}, doi = {{10.1063/5.0065913}}, volume = {{32(1)}}, year = {{2022}}, } @inproceedings{40613, author = {{Dröse, Jennifer}}, booktitle = {{Beiträge zum Mathematikunterricht}}, title = {{{Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen}}}, year = {{2022}}, } @inproceedings{47520, author = {{Graf, Lara Marie and Häsel-Weide, Uta and Nührenbörger, Marcus and Höveler, Karina}}, booktitle = {{Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, location = {{Frankfurt am Main}}, pages = {{773--776}}, title = {{{Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen}}}, year = {{2022}}, } @inproceedings{47519, author = {{Schwerin, Imke}}, booktitle = {{Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, location = {{Frankfurt am Main}}, pages = {{401--404}}, title = {{{Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis}}}, year = {{2022}}, }