Nonnegative solutions to a doubly degenerate nutrient taxis system - Li, Genglin; Winkler, Michael (Communications on Pure and Applied Analysis)

Chow groups of orders in number fields - Kirschmer, Markus; Klüners, Jürgen (arXiv:2208.14688)
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.

ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group - Klüners, Jürgen; Wang, Jiuya (Proceedings of the American Mathematical Society)
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.
Keywords: Applied Mathematics; General Mathematics

The asymptotics of nilpotent Galois groups - Klüners, Jürgen (Acta Arithmetica)
We prove an upper bound for the asymptotics of counting functions of number fields with nilpotent Galois groups.
Keywords: Algebra and Number Theory

Chow groups of orders in number fields - Kirschmer, Markus; Klüners, Jürgen

Morita theory for non-commutative noetherian schemes - Burban, Igor; Drozd, Yu. (Advances in Mathematics)
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.

A classification of polyharmonic Maa forms via quiver representations - Burban, Igor; Alfes-Neumann, C.; Raum, M.

On elliptic solutions of the associative Yang-Baxter equation - Burban, Igor; Peruzzi, A. (Journal of Geometry and Physics)

Manifold turnpikes, trims, and symmetries - Faulwasser, Timm; Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Schaller, Manuel; Worthmann, Karl (Mathematics of Control, Signals, and Systems)

Symmetric Set Coloring of Signed Graphs - Cappello, Chiara; Steffen, Eckhard (Annals of Combinatorics)
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.
Keywords: Discrete Mathematics and Combinatorics

Frustration-critical signed graphs - Cappello, Chiara; Steffen, Eckhard (Discrete Applied Mathematics)
Keywords: Applied Mathematics; Discrete Mathematics and Combinatorics

„Ich hab als Erstes die angeguckt“ – Muster- und Strukturerkennung mit Eye-Tracking besser verstehen? - Bruns, Julia; Reuter, D. (Beiträge zum Mathematikunterricht 2022)

Effects of Facilitator Professional Development on Teachers’ Learning – An Intervention Study in the Context of Early Mathematics Education - Bruns, Julia; Hagena, M.; Gasteiger, H. (Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12))

Entwicklung und Validierung eines videobasierten Testinstruments zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse im inklusiven Sportunterricht - Bruns, Julia; Langer, W.; Erhorn, J. (German Journal of Exercise and Sport Research)

Development and validation of a video-based test instrument to measure noticing with regard to processes ofrecognition in inclusive physical education - Langer, Wiebke; Bruns, Julia; Erhorn, Jan (German Journal of Exercise and Sport Research)
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.
Keywords: Physical education teacher education; Competence modelling and; measurement; Inclusive physical education; Video-based items; Noticing

Einfluss der Berufserfahrung von Multiplikatorinnen und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen zur frühen mathematischen Bildung. Zeitschrift Für Erziehungswissenschaft - Hagena, Maike; Bruns, Julia; Gasteiger, Hedwig (Zeitschrift für Erziehungswissenschaft)
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.
Keywords: Facilitator professional development; Early childhood teachers; Teaching; experience; Early mathematics education

Muster- und Strukturerkennungsprozesse bei potenziell mathematisch begabten Grundschulkindern untersuchen – Das Potenzial von Eye-Tracking und retrospektivem Interview im Vergleich - Reuter, Dinah; Bruns, Julia (Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik)

Binary Hermitian Lattices over Number Fields - Kirschmer, Markus; Nebe, Gabriele (Experimental Mathematics)
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.
Keywords: General Mathematics

Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation - Black, Tobias; Wu, Chunyan (Calculus of Variations and Partial Differential Equations)
Keywords: Applied Mathematics; Analysis

Backward error analysis for variational discretisations of partial differential equations - McLachlan, Robert I; Offen, Christian (Journal of Geometric Mechanics)
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.