@article{56131, abstract = {{This article provides a comprehensive mathematical-didactic analysis of how the highly relevant topic symmetry can be prepared for the university education of PSTs. Methodologically, the analysis is embedded in a design research cycle and serves as preparation for the actual design of learning activities. The procedure of "specifying and structuring" learning objects is used and adapted in such a way that, in addition to mathematical aspects, profession-oriented references to school mathematics are also considered. An essential result of the analysis is the formulation of so-called interface aspects to symmetry, which prove to be helpful in establishing such references. }}, author = {{Hoffmann, Max}}, journal = {{Recherches en Didactique des Mathématiques}}, number = {{2}}, pages = {{85--120}}, title = {{{Symmetry as a Topic for the University Education of Pre-Service Teachers}}}, doi = {{10.46298/rdm.14256}}, volume = {{45}}, year = {{2025}}, } @inproceedings{65246, author = {{Hoffmann, Max}}, booktitle = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}}, editor = {{Bosch, Marianna and Bolondi, Giorgio and Carreira, Susana and Gaidoschik, Michael and Spagnolo, Camilla}}, pages = {{2245--2252}}, publisher = {{Free University of Bozen-Bolzano and ERME}}, title = {{{Using scriptwriting as a response format for interface tasks: Exemplary analyses in the context of symmetry}}}, year = {{2025}}, } @article{53413, abstract = {{For negatively curved symmetric spaces it is known that the poles of the scattering matrices defined via the standard intertwining operators for the spherical principal representations of the isometry group are either given as poles of the intertwining operators or as quantum resonances, i.e. poles of the meromorphically continued resolvents of the Laplace-Beltrami operator. We extend this result to classical locally symmetric spaces of negative curvature with convex-cocompact fundamental group using results of Bunke and Olbrich. The method of proof forces us to exclude the spectral parameters corresponding to singular Poisson transforms.}}, author = {{Delarue, Benjamin and Hilgert, Joachim}}, issn = {{0949-5932}}, journal = {{Journal of Lie Theory}}, number = {{(4)}}, pages = {{787----804}}, title = {{{Quantum resonances and scattering poles of classical rank one locally symmetric spaces}}}, volume = {{35}}, year = {{2025}}, } @article{51208, abstract = {{AbstractApproximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.}}, author = {{Gebken, Bennet}}, issn = {{0926-6003}}, journal = {{Computational Optimization and Applications}}, keywords = {{Applied Mathematics, Computational Mathematics, Control and Optimization}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{A note on the convergence of deterministic gradient sampling in nonsmooth optimization}}}, doi = {{10.1007/s10589-024-00552-0}}, year = {{2024}}, } @article{46019, abstract = {{We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent.}}, author = {{Sonntag, Konstantin and Peitz, Sebastian}}, journal = {{Journal of Optimization Theory and Applications}}, publisher = {{Springer}}, title = {{{Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}}}, doi = {{10.1007/s10957-024-02389-3}}, year = {{2024}}, } @unpublished{51334, abstract = {{The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem.}}, author = {{Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Volkwein, Stefan}}, booktitle = {{arXiv:2402.06376}}, title = {{{A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces}}}, year = {{2024}}, } @unpublished{52691, abstract = {{We prove Feynman-Kac formulas for the semigroups generated by selfadjoint operators in a class containing Fr\"ohlich Hamiltonians known from solid state physics. The latter model multi-polarons, i.e., a fixed number of quantum mechanical electrons moving in a polarizable crystal and interacting with the quantized phonon field generated by the crystal's vibrational modes. Both the electrons and phonons can be confined to suitable open subsets of Euclidean space. We also include possibly very singular magnetic vector potentials and electrostatic potentials. Our Feynman-Kac formulas comprise Fock space operator-valued multiplicative functionals and can be applied to every vector in the underlying Hilbert space. In comparison to the renormalized Nelson model, for which analogous Feynman-Kac formulas are known, the analysis of the creation and annihilation terms in the multiplicative functionals requires novel ideas to overcome difficulties caused by the phonon dispersion relation being constant. Getting these terms under control and generalizing other construction steps so as to cover confined systems are the main achievements of this article.}}, author = {{Hinrichs, Benjamin and Matte, Oliver}}, booktitle = {{arXiv:2403.12147}}, title = {{{Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains}}}, year = {{2024}}, } @article{52726, abstract = {{Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.}}, author = {{Bick, Christian and von der Gracht, Sören}}, issn = {{2051-1329}}, journal = {{Journal of Complex Networks}}, keywords = {{Applied Mathematics, Computational Mathematics, Control and Optimization, Management Science and Operations Research, Computer Networks and Communications}}, number = {{2}}, publisher = {{Oxford University Press (OUP)}}, title = {{{Heteroclinic dynamics in network dynamical systems with higher-order interactions}}}, doi = {{10.1093/comnet/cnae009}}, volume = {{12}}, year = {{2024}}, } @article{49905, abstract = {{For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t  = 5, and m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l.}}, author = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0209-9683}}, journal = {{Combinatorica}}, keywords = {{Computational Mathematics, Discrete Mathematics and Combinatorics}}, pages = {{429--440}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}}}, doi = {{10.1007/s00493-023-00078-9}}, volume = {{44}}, year = {{2024}}, } @article{53101, abstract = {{In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way.}}, author = {{Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei, Flóra Orsolya}}, issn = {{2158-2491}}, journal = {{Journal of Computational Dynamics}}, keywords = {{Optimal control problem, Lagrangian system, Hamiltonian system, Variations, Pontryagin's maximum principle.}}, pages = {{0--0}}, publisher = {{American Institute of Mathematical Sciences (AIMS)}}, title = {{{A new Lagrangian approach to control affine systems with a quadratic Lagrange term}}}, doi = {{10.3934/jcd.2024017}}, year = {{2024}}, } @article{53542, abstract = {{AbstractThis work deals with the extension problem for the fractional Laplacian on Riemannian symmetric spaces G/K of noncompact type and of general rank, which gives rise to a family of convolution operators, including the Poisson operator. More precisely, motivated by Euclidean results for the Poisson semigroup, we study the long-time asymptotic behavior of solutions to the extension problem for $$L^1$$ L 1 initial data. In the case of the Laplace–Beltrami operator, we show that if the initial data are bi-K-invariant, then the solution to the extension problem behaves asymptotically as the mass times the fundamental solution, but this convergence may break down in the non-bi-K-invariant case. In the second part, we investigate the long-time asymptotic behavior of the extension problem associated with the so-called distinguished Laplacian on G/K. In this case, we observe phenomena which are similar to the Euclidean setting for the Poisson semigroup, such as $$L^1$$ L 1 asymptotic convergence without the assumption of bi-K-invariance.}}, author = {{Papageorgiou, Efthymia}}, issn = {{1424-3199}}, journal = {{Journal of Evolution Equations}}, keywords = {{Mathematics (miscellaneous)}}, number = {{2}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Asymptotic behavior of solutions to the extension problem for the fractional Laplacian on noncompact symmetric spaces}}}, doi = {{10.1007/s00028-024-00959-6}}, volume = {{24}}, year = {{2024}}, } @article{52584, author = {{Rezat, Sebastian}}, journal = {{ZDM – Mathematics Education}}, publisher = {{Springer}}, title = {{{Research on curriculum resources in mathematics education: a survey of the field}}}, doi = {{10.1007/s11858-024-01559-x}}, year = {{2024}}, } @article{51841, abstract = {{athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung. Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich. Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen? Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen, ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.}}, author = {{Barzel, Bärbel and Greefrath, Gilbert and Nagel, Mareike and Hoffmann, Max}}, journal = {{mathematik lehren}}, pages = {{42 -- 47}}, title = {{{Digitalisierung als Chance für alle Prinzipien guten Unterrichts}}}, volume = {{242}}, year = {{2024}}, } @inbook{50554, author = {{Prediger, Susanne and Wessel, Lena}}, booktitle = {{Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis}}, editor = {{Efing, Christian and Kalkavan-Aydin, Zeynep}}, isbn = {{978-3-11-074544-3}}, pages = {{363--372}}, publisher = {{DE GRUYTER}}, title = {{{31 Sprachbildung im berufsbezogenen Mathematikunterricht.}}}, volume = {{Band 3}}, year = {{2024}}, } @article{51207, abstract = {{Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the asymptotic growth of $\Gamma$ in the two direction defined by the two factors. We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of $\Gamma$.}}, author = {{Weich, Tobias and Wolf, Lasse Lennart}}, journal = {{Geom Dedicata}}, title = {{{Temperedness of locally symmetric spaces: The product case}}}, doi = {{https://doi.org/10.1007/s10711-024-00904-4}}, volume = {{218}}, year = {{2024}}, } @article{54078, author = {{Häsel-Weide, Uta and Graf, Lara Marie and Höveler, K. and Nührenbörger, M.}}, journal = {{HLZ – Herausforderung Lehrer*innenbildung}}, number = {{1}}, title = {{{Fachbezogene Professionalisierung von fachfremd Mathematik unterrichtenden Lehrkräften: Retrospektive Selbsteinschätzungen zur Expertise im Umgang mit Schwierigkeiten beim Mathematiklernen im Anfangsunterricht der Grundschule}}}, doi = {{10.11576/hlz-6727}}, volume = {{7}}, year = {{2024}}, } @article{54144, abstract = {{AbstractIn this paper, we propose a novel conceptual framework tailored for modeling the meaning of mathematical concepts in university-level mathematics, addressing their rigorous nature and their relationships with related concepts as well as interpretations in various contexts. Within this framework, we present a model of meaning for the concepts of total differentiability and total derivative that provides a variety of possible interpretations and aspects. We then use the proposed model of meaning as a tool for analyzing three different textbooks for mathematics majors on the topic of multidimensional differentiability. Our paper is an example of a subject matter analysis of a topic in university mathematics carried out in a structured way. The model of meaning for total differentiability presented in this paper could inspire course design and analysis including the design of assignments and assessments for students. Moreover, it could serve as a valuable research tool for further analyses. For example, it could be used as a framework for analyzing courses taught or as a basis for developing a test instrument to assess students’ understanding. With our textbook analysis, we begin to examine the landscape of textbooks regarding differentiability concepts in the multidimensional case, shedding light on the diversity of meaning facets that are covered in the textbooks. These results could be useful for guiding instructors and learners in selecting and using textbooks for teaching and learning based on their respective needs.}}, author = {{Lankeit, Elisa and Biehler, Rolf}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The meaning landscape of the concept of the total derivative in multivariable real analysis textbooks: an analysis based on a new model of meaning}}}, doi = {{10.1007/s11858-024-01584-w}}, year = {{2024}}, } @article{53534, abstract = {{It is known that the notion of a transitive subgroup of a permutation group $G$ extends naturally to subsets of $G$. We consider subsets of the general linear group $\operatorname{GL}(n,q)$ acting transitively on flag-like structures, which are common generalisations of $t$-dimensional subspaces of $\mathbb{F}_q^n$ and bases of $t$-dimensional subspaces of $\mathbb{F}_q^n$. We give structural characterisations of transitive subsets of $\operatorname{GL}(n,q)$ using the character theory of $\operatorname{GL}(n,q)$ and interpret such subsets as designs in the conjugacy class association scheme of $\operatorname{GL}(n,q)$. In particular we generalise a theorem of Perin on subgroups of $\operatorname{GL}(n,q)$ acting transitively on $t$-dimensional subspaces. We survey transitive subgroups of $\operatorname{GL}(n,q)$, showing that there is no subgroup of $\operatorname{GL}(n,q)$ with $1