TY - CHAP AU - Lankeit, Elisa AU - Biehler, Rolf ED - Hochmuth, Reinhard ED - Biehler, Rolf ED - Liebendörfer, Michael ED - Schaper, Niclas ID - 42652 SN - 2197-8751 T2 - Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse TI - Vorkurse und ihre Wirkungen im Übergang Schule – Hochschule ER - TY - BOOK ED - Hochmuth, Reinhard ED - Biehler, Rolf ED - Liebendörfer, Michael ED - Schaper, Niclas ID - 42650 SN - 2197-8751 TI - Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse ER - TY - JOUR AB - 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. AU - Burban, Igor AU - Drozd, Yu. ID - 44328 JF - Advances in Mathematics TI - Morita theory for non-commutative noetherian schemes VL - 399 ER - TY - GEN AU - Burban, Igor AU - Alfes-Neumann, C. AU - Raum, M. ID - 44537 TI - A classification of polyharmonic Maa forms via quiver representations ER - TY - JOUR AU - Burban, Igor AU - Peruzzi, A. ID - 44327 JF - Journal of Geometry and Physics TI - On elliptic solutions of the associative Yang-Baxter equation VL - 176 ER - TY - JOUR AU - Faulwasser, Timm AU - Flaßkamp, Kathrin AU - Ober-Blöbaum, Sina AU - Schaller, Manuel AU - Worthmann, Karl ID - 44624 JF - Mathematics of Control, Signals, and Systems TI - Manifold turnpikes, trims, and symmetries VL - 34 ER - TY - JOUR AB - 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. AU - Cappello, Chiara AU - Steffen, Eckhard ID - 33741 JF - Annals of Combinatorics KW - Discrete Mathematics and Combinatorics SN - 0218-0006 TI - Symmetric Set Coloring of Signed Graphs ER - TY - JOUR AU - Cappello, Chiara AU - Steffen, Eckhard ID - 33950 JF - Discrete Applied Mathematics KW - Applied Mathematics KW - Discrete Mathematics and Combinatorics SN - 0166-218X TI - Frustration-critical signed graphs VL - 322 ER - TY - CONF AU - Bruns, Julia AU - Reuter, D. ID - 45679 T2 - Beiträge zum Mathematikunterricht 2022 TI - „Ich hab als Erstes die angeguckt“ – Muster- und Strukturerkennung mit Eye-Tracking besser verstehen? ER - TY - CONF AU - Bruns, Julia AU - Hagena, M. AU - Gasteiger, H. ED - Hodgen, J. ED - Geraniou, E. ED - Bolondi, G. ED - Ferretti, F. ID - 45678 T2 - Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) TI - Effects of Facilitator Professional Development on Teachers’ Learning – An Intervention Study in the Context of Early Mathematics Education ER - TY - JOUR AU - Bruns, Julia AU - Langer, W. AU - Erhorn, J. ID - 45677 IS - 3 JF - German Journal of Exercise and Sport Research TI - Entwicklung und Validierung eines videobasierten Testinstruments zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse im inklusiven Sportunterricht VL - 52 ER - TY - JOUR AB - 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. AU - Langer, Wiebke AU - Bruns, Julia AU - Erhorn, Jan ID - 34820 IS - 3 JF - German Journal of Exercise and Sport Research KW - Physical education teacher education KW - Competence modelling and KW - measurement KW - Inclusive physical education KW - Video-based items KW - Noticing SN - 2509-3142 TI - Development and validation of a video-based test instrument to measure noticing with regard to processes ofrecognition in inclusive physical education VL - 52 ER - TY - JOUR AB - 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. AU - Hagena, Maike AU - Bruns, Julia AU - Gasteiger, Hedwig ID - 34819 IS - 6 JF - Zeitschrift für Erziehungswissenschaft KW - Facilitator professional development KW - Early childhood teachers KW - Teaching KW - experience KW - Early mathematics education SN - 1434-663X TI - Einfluss der Berufserfahrung von Multiplikatorinnen und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen zur frühen mathematischen Bildung. Zeitschrift Für Erziehungswissenschaft VL - 25 ER - TY - CHAP AU - Reuter, Dinah AU - Bruns, Julia ID - 36472 SN - 9783662632130 T2 - Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik TI - Muster- und Strukturerkennungsprozesse bei potenziell mathematisch begabten Grundschulkindern untersuchen – Das Potenzial von Eye-Tracking und retrospektivem Interview im Vergleich ER - TY - JOUR AU - Schönherr, Johanna AU - Schukajlow, S. AU - Blomberg, J. AU - Leopold, C. ID - 45334 IS - 2 JF - Applied Cognitive Psychology, ac3930 TI - Effects of drawing instructions and strategic knowledge on mathematical modeling performance: Mediated by the use of the drawing strategy VL - 36 ER - TY - CONF AU - Schönherr, Johanna AU - Schukajlow, S. AU - Leopold, C. ID - 45339 T2 - Proceedings of the 45th PME Conference TI - Drawing instructions, strategic knowledge, strategy-based motivation, and students' use of drawings VL - 3 ER - TY - JOUR AB - 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. AU - Kirschmer, Markus AU - Nebe, Gabriele ID - 45854 IS - 1 JF - Experimental Mathematics KW - General Mathematics SN - 1058-6458 TI - Binary Hermitian Lattices over Number Fields VL - 31 ER - TY - JOUR AU - Black, Tobias AU - Wu, Chunyan ID - 34677 IS - 3 JF - Calculus of Variations and Partial Differential Equations KW - Applied Mathematics KW - Analysis SN - 0944-2669 TI - Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation VL - 61 ER - TY - CONF AU - Kolbe, Tim AU - Wessel, Lena ID - 46163 T2 - Fourth conference of the International Network for Didactic Research in University Mathematics TI - Self-regulated learning in a mathematics course for engineers in the first semester: insights into students reported resource management and cognitive strategies ER - TY - JOUR AB - 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. AU - McLachlan, Robert I AU - Offen, Christian ID - 19941 IS - 3 JF - Journal of Geometric Mechanics TI - Backward error analysis for variational discretisations of partial differential equations VL - 14 ER -