@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}}, } @article{63587, author = {{Suri, Ali}}, journal = {{Differential Geometry and its Applications}}, publisher = {{Elsevier}}, title = {{{Stochastic Euler-Poincaré reduction for central extension}}}, doi = {{https://doi.org/10.1016/j.difgeo.2025.102290}}, volume = {{101}}, year = {{2025}}, } @inproceedings{63589, author = {{Cruzeiro, Ana Bela and Suri, Ali}}, isbn = {{978-3-032-03920-0}}, publisher = {{Springer}}, title = {{{Stochastic Perturbation of Geodesics on the Manifold of Riemannian Metrics}}}, doi = {{https://doi.org/10.1007/978-3-032-03921-7_41}}, year = {{2025}}, } @unpublished{63602, abstract = {{We show that, on a smoothly paracompact convenient manifold $M$ modeled on a convenient space with the bornological approximation property, the dual map of a Poisson bracket factors as a smooth section of the vector bundle $L_{skew}^2(T^*M,\mathbb R)$.}}, author = {{Michor, P. W. and Rahangdale, Praful}}, title = {{{Poisson bivectors on infinite dimensional manifolds}}}, year = {{2025}}, } @inproceedings{63622, author = {{Garnelo Abellanas, Irene}}, booktitle = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}}, title = {{{Towards design principles for learning environments based on theorem provers}}}, year = {{2025}}, } @inproceedings{63629, author = {{Garnelo Abellanas, Irene}}, booktitle = {{Beiträge zum Mathematikunterricht 2025}}, title = {{{Ein Designprinzip für Lernumgebungen zu inter-aktiven Theorembeweisern}}}, year = {{2025}}, } @inproceedings{47534, abstract = {{In this proceeding we consider a translation invariant Nelson type model in two spatial dimensions modeling a scalar relativistic particle in interaction with a massive radiation field. As is well-known, the corresponding Hamiltonian can be defined with the help of an energy renormalization. First, we review a Feynman-Kac formula for the semigroup generated by this Hamiltonian proven by the authors in a recent preprint (where several matter particles and exterior potentials are treated as well). After that, we employ a few technical key relations and estimates obtained in our preprint to present an otherwise self-contained derivation of new Feynman-Kac formulas for the fiber Hamiltonians attached to fixed total momenta of the translation invariant system. We conclude by inferring an alternative derivation of the Feynman-Kac formula for the full translation invariant Hamiltonian.}}, author = {{Hinrichs, Benjamin and Matte, Oliver}}, booktitle = {{Proceedings of the 2023 RIMS Workshop 'Mathematical Aspects of Quantum Fields and Related Topics'}}, editor = {{Hiroshima, Fumio}}, number = {{3}}, title = {{{Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions}}}, volume = {{2310}}, year = {{2025}}, } @unpublished{63642, abstract = {{We prove absence of ground states in the infrared-divergent spin boson model at large coupling. Our key argument reduces the proof to verifying long range order in the dual one-dimensional continuum Ising model, i.e., to showing that the respective two point function is lower bounded by a strictly positive constant. We can then use known results from percolation theory to establish long range order at large coupling. Combined with the known existence of ground states at small coupling, our result proves that the spin boson model undergoes a phase transition with respect to the coupling strength. We also present an expansion for the vacuum overlap of the spin boson ground state in terms of the Ising $n$-point functions, which implies that the phase transition is unique, i.e., that there is a critical coupling constant below which a ground state exists and above which none can exist.}}, author = {{Betz, Volker and Hinrichs, Benjamin and Kraft, Mino Nicola and Polzer, Steffen}}, booktitle = {{arXiv:2501.19362}}, title = {{{On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model}}}, year = {{2025}}, } @unpublished{63644, abstract = {{We study the ultraviolet problem for models of a finite-dimensional quantum mechanical system linearly coupled to a bosonic quantum field, such as the (many-)spin boson model or its rotating-wave approximation. If the state change of the system upon emission or absorption of a boson is either given by a normal matrix or by a 2-nilpotent one, which is the case for the previously named examples, we prove an optimal renormalization result. We complement it, by proving the norm resolvent convergence of appropriately regularized models to the renormalized one. Our method consists of a dressing transformation argument in the normal case and an appropriate interior boundary condition for the 2-nilpotent case.}}, author = {{Hinrichs, Benjamin and Lampart, Jonas and Valentín Martín, Javier}}, booktitle = {{arXiv:2502.04876}}, title = {{{Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions}}}, year = {{2025}}, } @unpublished{63643, abstract = {{In this short communication we discuss the ultraviolet renormalization of the van Hove-Miyatake scalar field, generated by any distributional source. An abstract algebraic approach, based on the study of a special class of ground states of the van Hove-Miyatake dynamical map is compared with an Hamiltonian renormalization that makes use of a non-unitary dressing transformation. The two approaches are proved to yield equivalent results.}}, author = {{Falconi, Marco and Hinrichs, Benjamin}}, booktitle = {{arXiv:2505.19977}}, title = {{{Ultraviolet Renormalization of the van Hove-Miyatake Model: an Algebraic and Hamiltonian Approach}}}, year = {{2025}}, } @unpublished{63645, abstract = {{In this paper we construct the non-trivial, renormalized Hamiltonian for a class of spin-boson models with supercritical form factors, including the one describing the Weisskopf-Wigner spontaneous emission. The renormalization is performed through both a self-energy and mass renormalization, in the so-called Hamiltonian formalism of constructive quantum field theory, implemented by a non-unitary dressing transformation. This solves the problem of triviality for unitarily-renormalized supercritical spin-boson models.}}, author = {{Falconi, Marco and Hinrichs, Benjamin and Valentín Martín, Javier}}, booktitle = {{arXiv:2508.00805}}, title = {{{Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors}}}, year = {{2025}}, } @unpublished{63646, abstract = {{We study the behavior of a probability measure near the bottom of its support in terms of time averaged quotients of its Laplace transform. We discuss how our results are connected to both rank-one perturbation theory as well as renewal theory. We further apply our results in order to derive criteria for the existence and non-existence of ground states for a finite dimensional quantum system coupled to a bosonic field.}}, author = {{Hinrichs, Benjamin and Polzer, Steffen}}, booktitle = {{arXiv:2511.02867}}, title = {{{Wiener-Type Theorems for the Laplace Transform. With Applications to Ground State Problems}}}, year = {{2025}}, } @unpublished{63647, abstract = {{We study the convergence rate of translation-invariant discrete-time quantum dynamics on a one-dimensional lattice. We prove that the cumulative distributions function of the ballistically scaled position $\mathbb X(n)/{n}$ after $n$ steps converges at a rate of $n^{-1/3}$ in the Lévy metric as $n\to\infty$. In the special case of step-coin quantum walks with two-dimensional coin space, we recover the same convergence rate for the supremum distance and prove optimality.}}, author = {{Hinrichs, Benjamin and Mittenbühler, Pascal}}, booktitle = {{arXiv:2511.13409}}, title = {{{On the Optimal Rate of Convergence for Translation-Invariant 1D Quantum Walks}}}, year = {{2025}}, } @article{63649, author = {{Glöckner, Helge and Schmeding, Alexander and Suri, Ali}}, issn = {{2972-4589}}, journal = {{Geometric Mechanics}}, number = {{04}}, pages = {{383--437}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{Manifolds of continuous BV-functions and vector measure regularity of Banach–Lie groups}}}, doi = {{10.1142/s2972458925500029}}, volume = {{01}}, year = {{2025}}, } @inproceedings{63697, author = {{Stallmeister, Lea and Rezat, Sebastian}}, booktitle = {{Beiträge zum Mathematikunterricht 2025. 58. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Schick, Lisa and Platz, Melanie and Lambert, Anselm}}, location = {{Universität des Saarlandes, Saarbrücken}}, publisher = {{WTM-Verlag}}, title = {{{Die Bedeutung des Mathematikschulbuchs in Zeiten der Ressourcenvielfalt}}}, doi = {{10.17877/DE290R-26373}}, year = {{2025}}, }