TY - JOUR AB - An initial-boundary value problem for a coupled chemotaxis-Navier–Stokes model with porous medium type diffusion is considered. Previous related literature has provided profound knowledge in cases when the system is augmented with no-flux/no-flux/no-slip boundary conditions for the density of cells, the chemical concentration and the fluid velocity field, respectively; in particular, available qualitative results strongly indicate that only trivial solution behavior can be expected on large time scales. In line with refined modeling approaches to oxygen evolution near fluid-air interfaces, this study now focuses on situations involving a fixed chemoattractant concentration on the boundary. Despite an apparent loss of mathematically favorable energy structures thereby induced, by means of an alternative variational approach a basic theory of global existence is developed in a natural framework of weak solvability. Beyond this, some additional qualitative information on the large time behavior of these solutions is derived by identifying a certain global relaxation property. Specifically, a second result asserts, within a suitable topological setting, the existence of a bounded set which eventually absorbs each individual of the obtained trajectories, and the diameter of which is bounded only by the physically relevant quantities of total population size and prescribed boundary concentration of the chemical signal. AU - Black, Tobias AU - Winkler, Michael ID - 34676 IS - 01 JF - Mathematical Models and Methods in Applied Sciences KW - Applied Mathematics KW - Modeling and Simulation SN - 0218-2025 TI - Global weak solutions and absorbing sets in a chemotaxis-Navier–Stokes system with prescribed signal concentration on the boundary VL - 32 ER - TY - CONF AU - Liebendörfer, Michael AU - Profeta, Angelo AU - Krämer, Sandra AU - Schlüter, Sarah AU - Becher, Silvia AU - Biehler, Rolf AU - Mai, Tobias AU - Schmitz, Angela ID - 39062 TI - Enriching videos with interactive questions to enhance students’ cognitive activity: concept and implementation ER - TY - CONF AU - Griese, Birgit AU - Nieszporek, Ralf AU - Biehler, Rolf ID - 39058 TI - Facilitators’ views on content goals, learning obstacles, and teaching resources in reference to conditional probability ER - TY - CONF AU - Podworny, Susanne AU - Fleischer, Yannik AU - Stroop, Dietlinde AU - Biehler, Rolf ID - 39064 TI - An example of rich, real and multivariate survey data for use in school ER - TY - JOUR AU - Kang, Kyungkeun AU - Lee, Jihoon AU - Winkler, Michael ID - 35483 JF - Discrete and Continuous Dynamical Systems TI - Global weak solutions to a chemotaxis-Navier-Stokes system in $R^3$. VL - 42 ER - TY - JOUR AB - We consider the generators $L_k$ of Heckman-Opdam diffusion processes in the compact and non-compact case in $N$ dimensions for root systems of type $A$ and $B$, with a multiplicity function of the form $k=κk_0$ with some fixed value $k_0$ and a varying constant $κ\in\,[0,\infty[$. Using elementary symmetric functions, we present polynomials which are simultaneous eigenfunctions of the $L_k$ for all $κ\in\,]0,\infty[$. This leads to martingales associated with the Heckman-Opdam diffusions $ (X_{t,1},\ldots,X_{t,N})_{t\ge0}$. As our results extend to the freezing case $κ=\infty$ with a deterministic limit after some renormalization, we find formulas for the expectations $\mathbb E(\prod_{j=1}^N(y-X_{t,j})),$ $y\in\mathbb C$. AU - Rösler, Margit AU - Voit, Michael ID - 38039 IS - 780 JF - Contemporary Mathematics TI - Elementary symmetric polynomials and martingales for Heckman-Opdam processes ER - TY - CONF AU - Häsel-Weide, Uta AU - Nührenbörger, M. ED - Hodgen, J. ED - Geraniou, E. ED - Bolondi, G. ED - Ferretti, F. ID - 40312 T2 - Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) TI - Inclusive math practices in primary school. Twelfth Congress of the European Society for Research in Mathematics Education ER - TY - CONF AB - We report on our work with students in our data science courses, focusing on the analysis of students’ results. This study represents an in-depth analysis of students’ creation and documentation of machine learning models. The students were supported by educationally designed Jupyter Notebooks, which are used as worked examples. Using the worked example, students document their results in a so-called computational essay. We examine which aspects of creating computational essays are difficult for students to find out how worked examples should be designed to support students without being too prescriptive. We analyze the computational essays produced by students and draw consequences for redesigning our worked example. AU - Fleischer, Yannik AU - Hüsing, Sven AU - Biehler, Rolf AU - Podworny, Susanne AU - Schulte, Carsten ED - Peters, S. A. ED - Zapata-Cardona, L. ED - Bonafini, F. ED - Fan, A. ID - 35674 T2 - Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics TI - Jupyter Notebooks for Teaching, Learning, and Doing Data Science ER - TY - JOUR AB - This study examines modelling with machine learning. In the context of a yearlong data science course, the study explores how upper secondary students apply machine learning with Jupyter Notebooks and document the modelling process as a computational essay incorporating the different steps of the CRISP-DM cycle. The students’ work is based on a teaching module about decision trees in machine learning and a worked example of such a modelling process. The study outlines the students’ performance in carrying out the machine learning technically and reasoning about bias in the data, different data preparation steps, the application context, and the resulting decision model. Furthermore, the context of the study and the theoretical backgrounds are presented. AU - Fleischer, Yannik AU - Biehler, Rolf AU - Schulte, Carsten ID - 35672 IS - 2 JF - Statistics Education Research Journal KW - Education KW - Statistics and Probability SN - 1570-1824 TI - Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks VL - 21 ER - TY - JOUR AU - Bellomo, Nicolas AU - Outada, Nisrine AU - Soler, Juan AU - Tao, Youshan AU - Winkler, Michael ID - 35479 JF - Mathematical Models & Methods in Applied Sciences TI - Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision. VL - 32 ER - TY - JOUR AU - Lankeit, Johannes AU - Winkler, Michael ID - 35530 JF - Journal of Evolution Equations TI - Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptiva effects. VL - 22 ER - TY - JOUR AU - Fuhrmann, Jan AU - Lankeit, Johannes AU - Winkler, Michael ID - 35481 JF - Journal de Mathématiques Pures et Appliquées TI - A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system. VL - 162 ER - TY - JOUR AU - Wang, Yulan AU - Winkler, Michael AU - Xiang, Zhaoyin ID - 35565 JF - Acta Mathematica Sinica (English Series) TI - A smallness condition ensuring boundedness in a two-dimensional chemotaxis-Navier-Stokes system involving Dirichlet boundary conditions for the signal. VL - 38 ER - TY - JOUR AU - Wang, Yulan AU - Winkler, Michael AU - Xiang, Zhaoyin ID - 35560 JF - Analysis and Applications TI - Global mass-preserving solutions to a chemotaxis-fluid model involving Dirichlet boundary conditions for the signal. VL - 20 ER - TY - CHAP AU - Häsel-Weide, Uta AU - Wienhues, Inga AU - Kordes, L. ED - Bonow, J. ED - Dexel, T. ED - Rink, R. ED - Schreiber, Chr. ED - Walter, D. ID - 34413 T2 - Digitale Medien und Heterogenität – Chancen und Herausforderungen für die Mathematikdidaktik TI - Multiplikative Beziehungen erkennen und nutzen – Initiierung von Lernprozessen durch Entdeckervideos ER - TY - JOUR AU - Graczyk, P. AU - Luks, Tomasz AU - Sawyer, P. ID - 40053 IS - 4 JF - Canadian Journal of Mathematics SN - 0008-414X TI - Potential kernels for radial Dunkl Laplacians VL - 74 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35556 JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics TI - Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy. VL - 152 ER - TY - JOUR AU - Tao, Youshan AU - Winkler, Michael ID - 35548 JF - SIAM Journal on Mathematical Analysis TI - Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system VL - 54 ER - TY - JOUR AU - Li, Genglin AU - Winkler, Michael ID - 35532 JF - Communications on Pure and Applied Analysis TI - Nonnegative solutions to a doubly degenerate nutrient taxis system VL - 21 ER - TY - GEN AB - We discuss various connections between ideal classes, divisors, Picard and Chow groups of orders in number fields. As a result of these, we give a method to compute Chow groups of such orders and show that there are infinitely many number fields which contain orders with trivial Chow groups. AU - Kirschmer, Markus AU - Klüners, Jürgen ID - 42647 T2 - arXiv:2208.14688 TI - Chow groups of orders in number fields ER - TY - CHAP AU - Liebendörfer, Michael AU - Hochmuth, Reinhard AU - Biehler, Rolf AU - Schaper, Niclas AU - Büdenbender-Kuklinski, Christiane AU - Lankeit, Elisa AU - Ruge, Johanna AU - Schürmann, Mirko ED - Hochmuth, Reinhard ED - Biehler, Rolf ED - Liebendörfer, Michael ED - Schaper, Niclas ID - 42654 SN - 2197-8751 T2 - Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse TI - Ein Rahmenmodell für hochschuldidaktische Maßnahmen in der Mathematik ER - TY - JOUR AB - 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. AU - Klüners, Jürgen AU - Wang, Jiuya ID - 34839 IS - 7 JF - Proceedings of the American Mathematical Society KW - Applied Mathematics KW - General Mathematics SN - 0002-9939 TI - ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group VL - 150 ER - TY - JOUR AB - We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups. AU - Klüners, Jürgen ID - 34835 IS - 2 JF - Acta Arithmetica KW - Algebra and Number Theory SN - 0065-1036 TI - The asymptotics of nilpotent Galois groups VL - 204 ER - TY - CHAP AU - Hochmuth, Reinhard AU - Biehler, Rolf AU - Schaper, Niclas AU - Liebendörfer, Michael AU - Büdenbender-Kuklinski, Christiane AU - Lankeit, Elisa AU - Ruge, Johanna AU - Schürmann, Mirko ED - Reinhard, Hochmuth ED - Biehler, Rolf ED - Liebendörfer, Michael ED - Schaper, Niclas ID - 42651 SN - 2197-8751 T2 - Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse TI - Einführung in das WiGeMath-Projekt: Wirkung und Gelingensbedingungen von Unterstützungsmaßnahmen für mathematikbezogenes Lernen in der Studieneingangsphase ER - TY - CHAP AU - Schürmann, Mirko AU - Liebendörfer, Michael AU - Büdenbender-Kuklinski, Christiane AU - Lankeit, Elisa AU - Ruge, Johanna AU - Schaper, Niclas AU - Biehler, Rolf AU - Hochmuth, Reinhard ED - Hochmuth, Reinhard ED - Biehler, Rolf ED - Liebendörfer, Michael ED - Schaper, Niclas ID - 42655 SN - 2197-8751 T2 - Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse TI - Evaluation von Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen ER - TY - CHAP AU - Podworny, Susanne AU - Frischemeier, Daniel AU - Biehler, Rolf ID - 43231 SN - 9783031207471 T2 - Statistics for Empowerment and Social Engagement TI - Civic Statistics for Prospective Teachers: Developing Content and Pedagogical Content Knowledge Through Project Work ER - TY - CHAP AU - Frischemeier, Daniel AU - Podworny, Susanne AU - Biehler, Rolf ID - 43230 SN - 9783031207471 T2 - Statistics for Empowerment and Social Engagement TI - Data Visualization Packages for Non-inferential Civic Statistics in High School Classrooms ER - TY - CHAP AU - Ridgway, Jim AU - Campos, Pedro AU - Biehler, Rolf ID - 43232 SN - 9783031207471 T2 - Statistics for Empowerment and Social Engagement TI - Data Science, Statistics, and Civic Statistics: Education for a Fast Changing World ER - TY - GEN AU - Kirschmer, Markus AU - Klüners, Jürgen ID - 43392 TI - Chow groups of orders in number fields ER - TY - CHAP AU - Bauer, Thomas AU - Biehler, Rolf AU - Lankeit, Elisa ED - Hochmuth, Reinhard ED - Biehler, Rolf ED - Liebendörfer, Michael ED - Schaper, Niclas ID - 42649 SN - 2197-8751 T2 - Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse TI - Mini-Aufgaben in mathematischen Übungsgruppen zur Analysis: Charakteristika von Aufgaben und Abstimmungsverhalten von Studierenden ER - TY - CHAP AU - Lankeit, Elisa AU - Biehler, Rolf ED - Hochmuth, Reinhard ED - Biehler, Rolf ED - Liebendörfer, Michael ED - Schaper, Niclas ID - 42653 SN - 2197-8751 T2 - Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen - Konzepte, Praxisbeispiele und Untersuchungsergebnisse TI - Mathematik-Vorkurse zur Vorbereitung auf das Studium – Zielsetzungen und didaktische Konzepte ER - 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 -