@article{57580, abstract = {{We investigate dispersive and Strichartz estimates for the Schrödinger equation involving the fractional Laplacian in real hyperbolic spaces and their discrete analogues, homogeneous trees. Due to the Knapp phenomenon, the Strichartz estimates on Euclidean spaces for the fractional Laplacian exhibit loss of derivatives. A similar phenomenon appears on real hyperbolic spaces. However, such a loss disappears on homogeneous trees, due to the triviality of the estimates for small times.}}, author = {{Palmirotta, Guendalina and Sire, Yannick and Anker, Jean-Philippe}}, journal = {{Journal of Differential Equations}}, keywords = {{Schrödinger equation, Fractional Laplacian, Dispersive estimates, Strichartz estimates, Real hyperbolic spaces, Homogeneous trees}}, publisher = {{Elsevier}}, title = {{{The Schrödinger equation with fractional Laplacian on hyperbolic spaces and homogeneous trees}}}, doi = {{10.1016/j.jde.2025.114065}}, year = {{2026}}, } @unpublished{65232, abstract = {{On finite regular graphs, we construct Patterson-Sullivan distributions associated with eigenfunctions of the discrete Laplace operator via their boundary values on the phase space. These distributions are closely related to Wigner distributions defined via a pseudo-differential calculus on graphs, which appear naturally in the study of quantum chaos. Using a pairing formula, we prove that Patterson-Sullivan distributions are also related to invariant Ruelle distributions arising from the transfer operator of the geodesic flow on the shift space. Both relationships provide discrete analogues of results for compact hyperbolic surfaces obtained by Anantharaman-Zelditch and by Guillarmou-Hilgert-Weich.}}, author = {{Arends, Christian and Palmirotta, Guendalina}}, booktitle = {{arXiv:2603.09779}}, pages = {{38}}, title = {{{Patterson-Sullivan distributions of finite regular graphs}}}, year = {{2026}}, } @proceedings{64797, editor = {{Birk, Lisa and Loth, Gerrit and Jotzo, Luca and Binder, Karin and Frischemeier, Daniel}}, location = {{Münster}}, publisher = {{International Association for Statistics Education}}, title = {{{14th IASE Satellite Conference "Statistics and Data Science Education in STEAM"}}}, doi = {{10.52041/iase25.158}}, year = {{2026}}, } @article{63135, abstract = {{We propose a definition of Coxeter-Dynkin algebras of canonical type generalising the definition as a path algebra of a quiver. Moreover, we construct two tilting objects over the squid algebra - one via generalised APR-tilting and one via one-point-extensions and reflection functors - and identify their endomorphism algebras with the Coxeter-Dynkin algebra. This shows that our definition gives another representative in the derived equivalence class of the squid algebra, and hence of the corresponding canonical algebra. Finally, we have a closer look at the Grothendieck group and the Euler form which illustrates the connection to Saito's classification of marked extended affine root systems. On the other hand, this enables us to prove that in the domestic case Coxeter-Dynkin algebras are of finite representation type.}}, author = {{Perniok, Daniel}}, journal = {{Journal of Pure and Applied Algebra}}, number = {{5}}, title = {{{Coxeter-Dynkin algebras of canonical type}}}, doi = {{10.1016/j.jpaa.2026.108250}}, volume = {{230}}, year = {{2026}}, } @article{65512, abstract = {{Zusammenfassung Risikokompetenz beinhaltet auch die Fähigkeit, stochastische Informationen, wie beispielsweise Anteile und Wahrscheinlichkeiten, richtig zu versprachlichen. Aus der Forschung zu bedingten Wahrscheinlichkeiten und Bayesianischen Aufgaben ist bekannt, dass die Nutzung von Visualisierungen und sogenannten „natürlichen Häufigkeiten“ (z. B. „80 von 100 Personen“) statt Wahrscheinlichkeiten in Prozent Verwechslungen beim Bestimmen von Wahrscheinlichkeiten eindämmen kann. Über den umgekehrten Prozess – das Versprachlichen von in Visualisierungen dargestellten Informationen – ist bisher jedoch wenig bekannt, obwohl diese Versprachlichungen auch für den Aufbau konzeptuellen Wissen als essentiell angesehen werden. In der vorliegenden Studie wurde daher untersucht, wie gut Schüler:innen die Versprachlichung von in Visualisierungen dargestellten Anteilen und natürlichen Häufigkeiten gelingt. Dazu wurde mit 138 Realschüler:innen aus der 9. Jahrgangsstufe ein Papier-und-Bleistift-Test durchgeführt, bei dem den Teilnehmenden nacheinander je ein (vollständig ausgefülltes) Baumdiagramm und ein Netzdiagramm präsentiert wurde. Die Schüler:innen sollten die inhaltliche Bedeutung der in der Visualisierung dargestellten stochastischen Informationen möglichst genau versprachlichen. Fokus der Studie ist der Einfluss der Visualisierung (Baumdiagramm vs. Netzdiagramm) und des Informationsformats der Visualisierung (Anteile in Prozent vs. natürliche Häufigkeiten) auf die richtige Versprachlichung von verschiedenen Relationstypen (Schnittinformationen vs. bedingte Informationen). Die Ergebnisse zeigen unter anderem, dass Informationen in natürlichen Häufigkeiten deutlich besser versprachlicht werden als in Prozenten und dass Schnittinformationen in Prozent besser anhand von Netzdiagrammen als von Baumdiagrammen versprachlicht werden. Die gewonnenen Erkenntnisse geben überdies Einblicke in typische (fehlerhafte) Versprachlichungen von Schüler:innen und könnten als Basis für die Entwicklung eines sprachsensiblen Unterrichts zu Anteilen und Wahrscheinlichkeiten im schulischen Stochastikunterricht dienen.}}, author = {{Rößner, Michael and Binder, Karin and Albrecht, Julian}}, issn = {{0173-5322}}, journal = {{Journal für Mathematik-Didaktik}}, number = {{1}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Versprachlichung von Anteilen und natürlichen Häufigkeiten anhand von Baum- und Netzdiagrammen Verbalization of proportions and natural frequencies based on tree diagrams and net diagrams}}}, doi = {{10.1007/s13138-026-00267-1}}, volume = {{47}}, year = {{2026}}, } @article{32099, author = {{Weich, Tobias and Budde, Julia}}, journal = {{Journal of Functional Analysis}}, number = {{1}}, title = {{{Wave Front Sets of Nilpotent Lie Group Representations}}}, doi = {{ https://doi.org/10.1016/j.jfa.2024.110684}}, volume = {{288}}, year = {{2025}}, } @article{56960, author = {{Black, Tobias}}, issn = {{0893-9659}}, journal = {{Applied Mathematics Letters}}, publisher = {{Elsevier BV}}, title = {{{Absence of dead-core formations in chemotaxis systems with degenerate diffusion}}}, doi = {{10.1016/j.aml.2024.109361}}, volume = {{161}}, year = {{2025}}, } @inbook{57020, abstract = {{AbstractIn this symposium we investigate students’ agency of selecting and using (digital) resources for developing their own learning paths. For that, we first review the literature related to students’ selection and use of resources in mathematics education in different pedagogical settings (presentation 1). Second, we develop insights from the different studies that participate in this symposium (presentation 2–6), at school as well as at university level. Results show that attempts have been made to provide students opportunities to develop agency of their mathematics learning, in particular with the development and provision of numerous digital tools and learning resources at university level and related to innovative pedagogical approaches. At the same time, it is not obvious how these tools and resources help students to develop deeper conceptual understandings. Certainly, students often ‘demand’ more student-centered and autonomous education approaches (e.g., at university level), also in mathematics education. Further, it seems that authentic problem-based education approaches are more motivating for students. These ‘innovative’ approaches necessitate particular types of structure and support for students. Moreover, they require different ways of providing resources that students can and want to interact with, and that help students to navigate through the curriculum to develop their own learning paths. At the same time, teachers also need support on how to orchestrate student learning with the available resources in such environments, so to be able to attend to students’ individual needs. The symposium comprised altogether six presentations:Birgit Pepin & Sebastian Rezat: Students’ agency of selecting and using (digital) resources for developing their own learning paths: An overviewAnnalisa Cusi & Agnese I. Telloni: Learning through digital curriculum resource design: students’ reflections on their role as designersVilma Mesa, Lelia Burley-Sanford, Xinyi Hao, & Carlos Quiroz: Interactive features in university textbooks and their use by teachers and studentsSebastian Rezat: Fostering university students’ reading and understanding of mathematical text in a flipped classroom approach with a digital marking toolBirgit Pepin & Ulises Salinas: Challenge/problem-based mathematics learning at university level: The case of the modeling weekFarzad Radmehr: Problem-posing: An inclusive activity for improving teaching and learning of mathematics at university level}}, author = {{Pepin, Birgit and Rezat, Sebastian}}, booktitle = {{Recent Advances in Mathematics Textbook Research and Development}}, editor = {{Qi, Chunxia and Fan, Lianghuo and Liu, Jian and Liu, Qimeng and Dong, Lianchun}}, isbn = {{9789819784257}}, pages = {{123–126}}, publisher = {{Springer Nature}}, title = {{{Symposium—Towards innovative practices in mathematics education: Teachers’ and students’ choice and use of digital resources}}}, doi = {{10.1007/978-981-97-8426-4_17}}, year = {{2025}}, } @inbook{57022, abstract = {{AbstractEven in the digital age, learning mathematics at an academic level still requires much interaction with mathematical texts. Understanding and developing disciplinary literacy skills at all levels is an increasing matter of interest.}}, author = {{Rezat, Sebastian}}, booktitle = {{Recent Advances in Mathematics Textbook Research and Development}}, editor = {{Qi, Chunxia and Fan, Lianghuo and Liu, Jian and Liu, Qimeng and Dong, Lianchun}}, isbn = {{9789819784257}}, pages = {{133–136}}, publisher = {{Springer Nature}}, title = {{{Fostering university students’ reading and understanding of mathematical text in a flipped classroom approach with a digital marking tool}}}, doi = {{10.1007/978-981-97-8426-4_20}}, year = {{2025}}, } @article{58353, abstract = {{Abstract Statistics and machine learning are critical because they play an essential role in our everyday lives and the careers we may pursue in the future. It may be beneficial to introduce machine learning, such as decision trees (DTs), at an early stage of education. The data-based construction of DTs is an example of a machine learning process, which can be addressed in mathematics or statistics teaching because of relatively low prior knowledge requirements. This paper focuses on investigating how sixth-grade students create and evaluate data-based DTs. The basis is a teaching unit that aims to lay the foundation for machine learning and enhance students’ understanding of the process. We investigate students’ processes in detail while they build DTs with data cards about food items to predict whether a new item is recommendable. After the teaching unit, an interview study examines students’ strategies for creating decision trees. The findings contribute to understanding students’ learning processes and the challenges when working with decision trees.}}, author = {{Podworny, Susanne and Biehler, Rolf and Fleischer, Yannik}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Young students’ engagement with data to create decision trees}}}, doi = {{10.1007/s11858-024-01649-w}}, year = {{2025}}, } @article{59414, author = {{Häsel-Weide, Uta and Nührenbörger, M.}}, journal = {{Zeitschrift für Grundschulforschung}}, title = {{{Unterrichtsintegrierte Förderung von mathematischen Basiskompetenzen. Empirische Rekonstruktion interferierender Praktiken der Förderung im Mathematikunterricht der Grundschule}}}, doi = {{ https://doi.org/10.1007/s42278-025-00223-x }}, year = {{2025}}, } @article{59622, abstract = {{Abstract This study explores how high school students construct decision trees using data cards and the software CODAP (codap.concord.org) in interviews after attending a teaching unit. We conceptualized data-based decision tree construction using nine key aspects that we intended to teach, tested variations of two design elements in teaching, and analyzed the interviews qualitatively to compare student behavior to intended outcomes. We found high alignment to intentions but also deviations in data activities and informal or context-based rather than data-based reasoning. The design element of context-free (blinded) data seems to enhance data-based reasoning, while the design element of data card use showed diagnostic potential.}}, author = {{Fleischer, Yannik and Biehler, Rolf}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, number = {{1}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Exploring students’ constructions of data-based decision trees after an introductory teaching unit on machine learning}}}, doi = {{10.1007/s11858-025-01663-6}}, volume = {{57}}, year = {{2025}}, } @unpublished{59664, abstract = {{Given a sequence of polynomials $(P_n)_{n \in \mathbb{N}}$ with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting zero distribution of $P_n$ as $\mathrm{deg}\, P_n \to \infty$. The method is based on establishing an equivalence between the existence of a limiting empirical zero distribution $\mu$ and the existence of an exponential profile $g$ associated with the coefficients of the polynomials $(P_n)_{n \in \mathbb{N}}$. The exponential profile $g$, which can be roughly described by $[z^k]P_n(z) \approx \exp(n g(k/n))$, offers a direct route to computing the Cauchy transform $G$ of $\mu$: the functions $t \mapsto tG(t)$ and $\alpha \mapsto \exp(-g'(\alpha))$ are mutual inverses. This relationship, in various forms, has previously appeared in the literature, most notably in the paper [Van Assche, Fano and Ortolani, SIAM J. Math. Anal., 1987]. As a first contribution, we present a self-contained probabilistic proof of this equivalence by representing the polynomials as generating functions of sums of independent Bernoulli random variables. This probabilistic framework naturally lends itself to tools from large deviation theory, such as the exponential change of measure. The resulting theorems generalize and unify a range of previously known results, which were traditionally established through analytic or combinatorial methods. Secondly, using the profile-based approach, we investigate how the exponential profile and the limiting zero distribution behave under certain operations on polynomials, including finite free convolutions, Hadamard products, and repeated differentiation. In particular, our approach yields new proofs of the convergence results `$\boxplus_n \to \boxplus$' and `$\boxtimes_n \to \boxtimes$', extending them to cases where the distributions are not necessarily compactly supported.}}, author = {{Jalowy, Jonas and Kabluchko, Zakhar and Marynych, Alexander}}, booktitle = {{arXiv:2504.11593}}, title = {{{Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation}}}, year = {{2025}}, } @article{59665, author = {{Erbar, Matthias and Huesmann, Martin and Jalowy, Jonas and Müller, Bastian}}, issn = {{0022-1236}}, journal = {{Journal of Functional Analysis}}, number = {{4}}, publisher = {{Elsevier BV}}, title = {{{Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy}}}, doi = {{10.1016/j.jfa.2025.110974}}, volume = {{289}}, year = {{2025}}, } @article{59792, abstract = {{Abstract Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing certain symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788 2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized the classical concept of static turnpike to manifold turnpike we extend the exponential turnpike property to the exponential trim turnpike for control systems with symmetries induced by abelian or non-abelian groups. Our analysis is mainly based on the geometric reduction of control systems with symmetries. More concretely, we first reduce the control system on the quotient space and state the turnpike theorem for the reduced problem. Then we use the group properties to obtain the trim turnpike theorem for the full problem. Finally, we illustrate our results on the Kepler problem and the rigid body problem. }}, author = {{Flaßkamp, Kathrin and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}}, issn = {{0932-4194}}, journal = {{Mathematics of Control, Signals, and Systems}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Trim turnpikes for optimal control problems with symmetries}}}, doi = {{10.1007/s00498-025-00408-w}}, year = {{2025}}, } @article{59806, abstract = {{We introduce a model of information dissemination in signed networks. It is a discrete-time process in which uninformed actors incrementally receive information from their informed neighbors or from the outside. Our goal is to minimize the number of confused actors — that is, the number of actors who receive contradictory information. We prove upper bounds for the number of confused actors in signed networks and in equivalence classes of signed networks. In particular, we show that there are signed networks where, for any information placement strategy, almost 60% of the actors are confused. Furthermore, this is also the case when considering the minimum number of confused actors within an equivalence class of signed graphs.}}, author = {{Jin, Ligang and Steffen, Eckhard}}, issn = {{0166-218X}}, journal = {{Discrete Applied Mathematics}}, pages = {{99--106}}, publisher = {{Elsevier BV}}, title = {{{Information dissemination and confusion in signed networks}}}, doi = {{10.1016/j.dam.2025.04.049}}, volume = {{373}}, year = {{2025}}, } @inbook{60048, author = {{Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael}}, booktitle = {{Lecture Notes in Computer Science}}, isbn = {{9783031917356}}, issn = {{0302-9743}}, publisher = {{Springer Nature Switzerland}}, title = {{{On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies}}}, doi = {{10.1007/978-3-031-91736-3_19}}, year = {{2025}}, } @article{58516, abstract = {{Abstract Academic emotions play a crucial role in mathematics learning, significantly influencing motivation, academic achievement, and career aspirations in mathematics. With the notable increase in research on emotions in recent years, our review uses Pekrun’s control-value theory with two primary objectives: to systematically describe the characteristics of emotions in recent research through a systematic review, and to synthesize evidence on the relationships between specific emotions, control-value antecedents, and mathematics achievement via a meta-analysis. The systematic review of 112 studies revealed that more than 100 specific emotions have been addressed in recent research, which we analyzed based on key emotion characteristics: valence and activation, type of object, temporal stability, and social context. The findings from the systematic review provide an overview of mathematics-specific objects that emotions have referred to in the most recent research. The subsequent meta-analysis demonstrated that mathematics achievement (e.g., test scores and grades) was positively related to enjoyment, hope, and pride ( $$\overline{r}$$ r ¯  = .247, .224, and .344, respectively) but negatively related to anger, boredom, frustration, hopelessness, and shame ( $$\overline{r}$$ r ¯ = − .322, − .187, − .207, − .378, and − .291, respectively). Theoretical and practical implications of these results are discussed.}}, author = {{Schönherr, Johanna and Schukajlow, Stanislaw and Pekrun, Reinhard}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Emotions in mathematics learning: a systematic review and meta-analysis}}}, doi = {{10.1007/s11858-025-01651-w}}, year = {{2025}}, } @article{59703, author = {{Schönherr, Johanna and Mayer, Richard E.}}, issn = {{0361-476X}}, journal = {{Contemporary Educational Psychology}}, publisher = {{Elsevier BV}}, title = {{{Maximizing the benefits of student-generated drawing for real-world problem solving}}}, doi = {{10.1016/j.cedpsych.2025.102369}}, volume = {{81}}, year = {{2025}}, } @article{60102, abstract = {{ Zusammenfassung: Studien haben gezeigt, dass frühe numerische Kompetenzen einen Einfluss auf die spätere mathematische Entwicklung haben. Vor diesem Hintergrund ist es wichtig, die numerischen Kompetenzen bereits im Kindergartenalter zu erfassen, um Kinder, denen wichtige Kompetenzen für die mathematische Entwicklung fehlen, und für die das Risiko der Entwicklung von Rechenschwierigkeiten besteht, frühzeitig und praxistauglich zu identifizieren. In der Studie wird ein Screening zur Erfassung der numerischen Kompetenzen im Kindergartenalter präsentiert, bei dem ausgewählte Aufgaben in einem Gruppensetting durchgeführt werden können. An der Validierung nahmen Kinder im Alter von vier bis sechs Jahren aus der Schweiz ( n = 431) und aus Deutschland ( n = 325) teil. Die Ergebnisse zeigen, dass mit dem Screening in verschiedenen Gruppen (Schweiz, Deutschland) mit wenigen Ausnahmen dieselben Eigenschaften gemessen werden. Die prognostische Validität für den Zeitpunkt kurz vor Schuleintritt ist zufriedenstellend. Der Testwert auf Basis des Gruppensettings lässt sich valide interpretieren, da sich keine Unterschiede zwischen Kindern, die die Aufgaben einzeln gelöst haben und Kindern, die die Aufgaben in Gruppen bearbeitet haben, gezeigt haben. Zusammenfassend lässt sich sagen, dass das Screening durch die Kombination von Einzel- und Kleingruppentests die Erfassung numerischer Fähigkeiten im Kindergarten in kurzer Zeit zuverlässig und valide ermöglicht. }}, author = {{Gloor, Noemi and Kucian, Karin and Bruns, Julia and Gasteiger, Hedwig and Moser Opitz, Elisabeth}}, issn = {{2191-9186}}, journal = {{Frühe Bildung}}, publisher = {{Hogrefe Publishing Group}}, title = {{{Erfassung der numerischen Kompetenzen im Kindergartenalter}}}, doi = {{10.1026/2191-9186/a000699}}, year = {{2025}}, }