@article{59258, author = {{Winkler, Michael}}, issn = {{0095-4616}}, journal = {{Applied Mathematics & Optimization}}, number = {{2}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}}}, doi = {{10.1007/s00245-025-10243-9}}, volume = {{91}}, year = {{2025}}, } @misc{64736, booktitle = {{J. Lie Theory}}, editor = {{Frahm, Jan and Glöckner, Helge and Hilgert, Joachim and Olafsson, Gestur}}, number = {{4}}, title = {{{Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday}}}, volume = {{35}}, year = {{2025}}, } @phdthesis{64770, author = {{Pinaud, Matthieu}}, title = {{{Manifold of mappings and regularity properties of half-Lie groups}}}, doi = {{10.17619/UNIPB/1-2211}}, year = {{2025}}, } @unpublished{59794, abstract = {{The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep networks are often unable to handle time-series data appearing at irregular intervals. These issues can be resolved by considering continuous-depth networks based on the neural ODE framework in combination with reversible integration methods that allow for variable time-steps. Reversibility of the method ensures that the memory requirement for training is independent of network depth, while variable time-steps are required for assimilating time-series data on irregular intervals. However, at present, there are no known higher-order reversible methods with this property. High-order methods are especially important when a high level of accuracy in learning is required or when small time-steps are necessary due to large errors in time integration of neural ODEs, for instance in context of complex dynamical systems such as Kepler systems and molecular dynamics. The requirement of small time-steps when using a low-order method can significantly increase the computational cost of training as well as inference. In this work, we present an approach for constructing high-order reversible methods that allow adaptive time-stepping. Our numerical tests show the advantages in computational speed when applied to the task of learning dynamical systems.}}, author = {{Maslovskaya, Sofya and Ober-Blöbaum, Sina and Offen, Christian and Singh, Pranav and Wembe Moafo, Boris Edgar}}, title = {{{Adaptive higher order reversible integrators for memory efficient deep learning}}}, year = {{2025}}, } @article{61518, abstract = {{Abstract Teacher professional development (TPD) is a crucial support mechanism for mathematics teachers. Strategies for implementing TPD include disseminating educative curriculum materials or conducting TPD courses. However, it remains unclear whether different implementations of the same TPD support mathematics teachers in distinct ways. This study investigated two implementations of the TPD EmMa-FS which focuses early mathematics education (EME) for German vocational school (VS) teachers who instruct prospective early childhood (EC) educators. One group of teachers received an in-person TPD course along with educative curriculum materials (n PM  = 26), whereas the other received only the educative curriculum materials (n M  = 15). The effects on VS teachers’ beliefs and knowledge concerning EME were examined using a t-test and repeated measures ANOVA. To assess how teachers in the different implementation groups made use of the TPD in their lesson planning, participants submitted hypothetical lesson sequences on early numeracy, which were analysed for instructional quality, covered content, and the visible implementation of the provided educative curriculum materials using qualitative content analysis. The results indicated that both TPD implementations positively affected VS teachers’ knowledge related to EME but not their beliefs. While the instructional quality of the lesson sequences varied across both groups, participants who received the TPD course appeared to use the educative curriculum materials more often and to cover more content.}}, author = {{Richter, Alix and Bruns, Julia and Gasteiger, Hedwig}}, issn = {{0173-5322}}, journal = {{Journal für Mathematik-Didaktik}}, number = {{1}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften}}}, doi = {{10.1007/s13138-025-00259-7}}, volume = {{46}}, year = {{2025}}, } @article{61519, abstract = {{ Zusammenfassung: Frühe mathematische Bildung, die ihren Ausgangspunkt in den (Spiel-)Situationen der Kindertagesstätte nimmt, kann breite mathematische Erfahrungen ermöglichen, wenn die (Spiel-)Situationen entsprechende Möglichkeiten bieten. Erste Studien weisen darauf hin, dass in diesen Situationen verschiedene mathematische Inhalte angesprochen werden können. Allerdings konzentrieren sich bisherige Studien auf ausgewählte Kontexte oder Inhaltsbereiche. Diese Studie zielt daher auf eine vertiefte Analyse der Gelegenheiten für mathematische Erfahrungen, die in verschiedenen (Spiel-)Situationen im Alltag der Kindertagesstätte entstehen können. Dazu wurde eine videobasierte Beobachtungsstudie mittels einer Action-Kamera in einer Kindertagesstätte durchgeführt. Die Ergebnisse zeigen, dass eine Vielfalt von mathematischen Inhalten in (Spiel-)Situationen in der Kindertagesstätte beobachtet werden kann, einzelne Inhalte jedoch nur in formellen Lernsituationen auftreten. }}, author = {{Bruns, Julia and Mette, Tessa}}, issn = {{2191-9186}}, journal = {{Frühe Bildung}}, number = {{4}}, pages = {{193--200}}, publisher = {{Hogrefe Publishing Group}}, title = {{{Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?}}}, doi = {{10.1026/2191-9186/a000730}}, volume = {{14}}, year = {{2025}}, } @article{57472, abstract = {{In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting.}}, author = {{Bot, Radu Ioan and Sonntag, Konstantin}}, journal = {{Journal of Mathematical Analysis and Applications}}, keywords = {{Pareto optimization, Lyapunov analysis, gradient-like dynamical systems, inertial dynamics, asymptotic vanishing damping, Tikhonov regularization, strong convergence}}, title = {{{Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}}}, year = {{2025}}, } @article{62283, author = {{Rezat, Sebastian and Doligkeit, Nadja}}, journal = {{mathematik lehren}}, number = {{252}}, pages = {{16–22}}, title = {{{Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken}}}, year = {{2025}}, } @inbook{62645, author = {{Häsel-Weide, Uta and Nührenbörger, Marcus}}, booktitle = {{Handbuch Lehrerinnen- und Lehrerbildung}}, editor = {{Cramer, C. and König, J. and Rothland, M.}}, pages = {{549--555}}, publisher = {{Klinkhardt}}, title = {{{ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule}}}, doi = {{10.35468/hblb2025-070}}, year = {{2025}}, } @phdthesis{62750, abstract = {{Diese Dissertation enthält Beiträge zum Bereich der Mehrzieloptimierung mit einem Fokus auf unbeschränkten Problemen, die auf einem allgemeinen Hilbertraum definiert sind. Für Mehrzieloptimierungsprobleme mit lokal Lipschitz-stetigen Zielfunktionen definieren wir ein multikriterielles Subdifferential, das wir erstmals im Kontext allgemeiner Hilberträume analysieren. Aufbauend auf diesen theoretischen Untersuchungen präsentieren wir ein Abstiegsverfahren, bei welchem in jeder Iteration eine Abstiegsrichtung mittels einer numerischen Approximation des multikriteriellen Subdifferentials bestimmt wird. Im Kontext konvexer, stetig differenzierbarer Zielfunktionen mit Lipschitz-stetigen Gradienten, führen wir eine Familie von dynamischen Gradientensystemen mit Trägheitsterm ein, die bekannte kontinuierliche Systeme aus der skalaren Optimierung verallgemeinern. Wir stellen drei neue Systeme vor: eines mit konstanter Dämpfung, eines mit asymptotisch abnehmender Dämpfung und eines, das zusätzlich eine zeitabhängige Tikhonov-Regularisierung beinhaltet. Aufbauend auf den Untersuchungen der neuen dynamischen Gradientensysteme, entwickeln wir ein beschleunigtes Gradientenverfahren zur Mehrzieloptimierung, das auf einer Diskretisierung des multikriteriellen Gradientensystems mit asymptotisch abnehmender Dämpfung beruht. Das hergeleitete Verfahren bewahrt die günstigen Konvergenzeigenschaften des kontinuierlichen Systems und erreicht eine schnellere Konvergenz als klassische Verfahren.}}, author = {{Sonntag, Konstantin}}, publisher = {{Paderborn University}}, title = {{{First-order methods and gradient dynamical systems for multiobjective optimization}}}, doi = {{10.17619/UNIPB/1-2457}}, year = {{2025}}, } @article{62980, abstract = {{We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.}}, author = {{Kopylov, Denis A. and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina R. and Sperling, Jan}}, issn = {{2643-1564}}, journal = {{Physical Review Research}}, number = {{3}}, publisher = {{American Physical Society (APS)}}, title = {{{Multiphoton, multimode state classification for nonlinear optical circuits}}}, doi = {{10.1103/sv6z-v1gk}}, volume = {{7}}, year = {{2025}}, } @inproceedings{63036, author = {{Rezat, Sebastian and Glasnović Gracin, Dubravka and Van Steenbrugge, Hendrik and Sievert, Henning}}, booktitle = {{Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development.}}, editor = {{Pepin, Birgit and Kohanová, Iveta and Langfeldt, Marit Buset}}, isbn = {{978-82-691902-2-9}}, location = {{Trondheim, Norway}}, pages = {{72–91}}, publisher = {{Norwegian University of Science and Technology.}}, title = {{{The quality of print and digital mathematics curriculum resources}}}, year = {{2025}}, } @inproceedings{63034, author = {{Stallmeister, Lea and Rezat, Sebastian}}, booktitle = {{Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development}}, editor = {{Pepin, Birgit and Kohanová, Iveta and Langfeldt, Marit Buset}}, isbn = {{978-82-691902-2-9}}, location = {{Trondheim, Norway}}, publisher = {{Norwegian University of Science and Technology}}, title = {{{Students’ use of different material resources for specific purposes in the process of learning mathematics}}}, year = {{2025}}, } @article{60196, abstract = {{This paper examines the governance and quality control of digital curriculum resources (DCR) for K-12 mathematics education in Germany. It focuses on approval processes and criteria set by the 16 federal states, arguing that these have the potential to influence the development of DCR. Using qualitative content analysis, the study explores three research questions: which DCR require official approval, the criteria applied for approval, and the extent to which these criteria are mathematics-specific. Findings indicate that 10 federal states maintain official approval systems, covering digital equivalents of printed textbooks and selected supplemental materials. However, most DCR fall outside these regulated processes, leaving their evaluation largely to individual schools and teachers. The study identifies 17 categories of quality criteria, but reveals a lack of detailed, mathematics-specific requirements. Instead, many criteria are broad references to didactical principles and educational goals, leaving the interpretation and application of these quality standards open-ended. Subject-specific criteria are included but remain limited in specificity. The study underscores the need for research-informed, mathematics-specific quality standards to guide DCR development and approval, emphasizing their importance amidst challenges like artificial intelligence. Policymakers are urged to adopt clearer criteria to ensure high-quality DCR to be used in schools.}}, author = {{Rezat, Sebastian}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, keywords = {{governance, digital curriculum resources, digital textbooks, digital curriculum materials, quality}}, pages = {{ 891–904}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The quality of digital curriculum resources for mathematics in German educational policy}}}, doi = {{10.1007/s11858-025-01708-w}}, volume = {{57}}, year = {{2025}}, } @unpublished{63150, author = {{Cummings, Charley and Gratz, Sira and Kirkman, Ellen and Letz, Janina Carmen and Rock, J. Daisie and Špenko, Špela}}, pages = {{1--9}}, title = {{{An equivalence linking CM-types $A_\infty$ and $D_\infty$}}}, year = {{2025}}, } @unpublished{63149, author = {{Kekkou, Antonia and Letz, Janina Carmen and Stephan, Marc}}, pages = {{1--37}}, title = {{{Regular sequences for triangulated categories}}}, year = {{2025}}, } @unpublished{63148, author = {{Letz, Janina Carmen}}, pages = {{1--7}}, title = {{{The Rouquier dimension of the category of perfect complexes over a regular ring}}}, year = {{2025}}, } @article{59507, abstract = {{Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they respect important physical laws of the dynamical system, such as unitarity and energy conservation in the context of quantum dynamical systems, for instance. In this article we develop a high-order commutator free Lie group integrator for non-autonomous differential equations evolving on quadratic Lie groups. Instead of matrix exponentials, which are expensive to evaluate and need to be approximated by appropriate rational functions in order to preserve the Lie group structure, the proposed method is obtained as a composition of Cayley transforms which naturally respect the structure of quadratic Lie groups while being computationally efficient to evaluate. Unlike Cayley-Magnus methods the method is also free from nested matrix commutators.}}, author = {{Wembe Moafo, Boris Edgar and Offen, Cristian and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Singh, Pranav}}, journal = {{J. Comput. Appl. Math}}, number = {{15}}, title = {{{Commutator-free Cayley methods}}}, doi = {{10.1016/j.cam.2025.117184}}, volume = {{477}}, year = {{2025}}, } @unpublished{63187, author = {{Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}}, booktitle = {{arXiv:2512.14285}}, title = {{{Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor}}}, year = {{2025}}, } @unpublished{63384, abstract = {{Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how small the matrices in such a linear representation can be. The minimal dimension of such a representation is the \emph{linear dimension of the group action} and this has applications in cryptography and cryptosystems. We develop the idea of linear dimension from an algebraic point of view by using the theory of permutation modules. We give structural results about representations of minimal dimension and investigate the implications of faithfulness, transitivity and primitivity on the linear dimension. Furthermore, we compute the linear dimension of several classes of finite primitive permutation groups. We also study wreath products, allowing us to determine the linear dimension of imprimitive group actions. Finally, we give the linear dimension of almost simple finite $2$-transitive groups, some of which may be used for further applications in cryptography. Our results also open up many new questions about linear representations of group actions.}}, author = {{Devillers, Alice and Giudici, Michael and Hawtin, Daniel R. and Klawuhn, Lukas-André Dominik and Morgan, Luke}}, title = {{{Linear dimension of group actions}}}, year = {{2025}}, }