@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}},
}
@inproceedings{62062,
author = {{Neufeld, Inga and Häsel-Weide, Uta}},
booktitle = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}},
editor = {{Bosch, M. and Bolondi, G. and Carreira, S. and Spagnolo, C. and Gaidoschik, M.}},
location = {{Bozen, Italy}},
title = {{{Learning support practices in the fostering of basic arithmetic skills}}},
year = {{2025}},
}
@inproceedings{62063,
author = {{Häsel-Weide, Uta and Nührenbörger, Marcus}},
booktitle = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}},
editor = {{Bosch, M. and Bolondi, G. and Carreira, S. and Spagnolo, C. and Gaidoschik, M.}},
location = {{Bozen, Italy}},
title = {{{Practices in math discourses in inclusive primary school}}},
year = {{2025}},
}
@inbook{63730,
author = {{Bruns, Julia and Gasteiger, Hedwig and Lastering, Bernd and Schopferer, Theresa and Zech, Detlev}},
booktitle = {{25 Jahre Berufskolleg - Wegspuren und Zukunftspfade}},
editor = {{Pudenz, Stephanie and Schoell, Oliver and Cleef, Maria}},
pages = {{175--188}},
publisher = {{wbv}},
title = {{{Frühe mathematische Bildung als Ausbildungsinhalt der Erzieherinnen- und Erzieher-Ausbildung stärken}}},
year = {{2025}},
}
@article{55459,
author = {{Bullerjahn, Nils and Kovács, Balázs}},
journal = {{IMA Journal of Numerical Analysis}},
title = {{{Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions}}},
doi = {{10.1093/imanum/draf009}},
year = {{2025}},
}
@article{53141,
author = {{Edelmann, Dominik and Kovács, Balázs and Lubich, Christian}},
journal = {{IMA Journal of Numerical Analysis}},
number = {{5}},
pages = {{2581----2627}},
title = {{{Numerical analysis of an evolving bulk--surface model of tumour growth}}},
doi = {{10.1093/imanum/drae077}},
volume = {{45}},
year = {{2025}},
}
@article{55781,
abstract = {{In this paper, we prove that spatially semi-discrete evolving finite element
method for parabolic equations on a given evolving hypersurface of arbitrary
dimensions preserves the maximal $L^p$-regularity at the discrete level. We
first establish the results on a stationary surface and then extend them, via a
perturbation argument, to the case where the underlying surface is evolving
under a prescribed velocity field. The proof combines techniques in evolving
finite element method, properties of Green's functions on (discretised) closed
surfaces, and local energy estimates for finite element methods}},
author = {{Bai, Genming and Kovács, Balázs and Li, Buyang}},
journal = {{IMA Journal of Numerical Analysis}},
title = {{{Maximal regularity of evolving FEMs for parabolic equations on an evolving surface}}},
doi = {{10.1093/imanum/draf082.}},
year = {{2025}},
}
@article{56717,
abstract = {{We establish a multiresolution analysis on the space $\text{Herm}(n)$ of
$n\times n$ complex Hermitian matrices which is adapted to invariance under
conjugation by the unitary group $U(n).$ The orbits under this action are
parametrized by the possible ordered spectra of Hermitian matrices, which
constitute a closed Weyl chamber of type $A_{n-1}$ in $\mathbb R^n.$ The space
$L^2(\text{Herm}(n))^{U(n)}$ of radial, i.e. $U(n)$-invariant $L^2$-functions
on $\text{Herm}(n)$ is naturally identified with a certain weighted $L^2$-space
on this chamber.
The scale spaces of our multiresolution analysis are obtained by usual dyadic
dilations as well as generalized translations of a scaling function, where the
generalized translation is a hypergroup translation which respects the radial
geometry. We provide a concise criterion to characterize orthonormal wavelet
bases and show that such bases always exist. They provide natural orthonormal
bases of the space $L^2(\text{Herm}(n))^{U(n)}.$
Furthermore, we show how to obtain radial scaling functions from classical
scaling functions on $\mathbb R^{n}$. Finally, generalizations related to the
Cartan decompositions for general compact Lie groups are indicated.}},
author = {{Langen, Lukas and Rösler, Margit}},
journal = {{Indagationes Mathematicae}},
number = {{6}},
pages = {{1671--1694}},
publisher = {{Elsevier}},
title = {{{Multiresolution analysis on spectra of hermitian matrices}}},
volume = {{36}},
year = {{2025}},
}
@article{64289,
abstract = {{Abstract
Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations
$$\overline{\rho }$$
ρ
¯
of the Lie group
$${{\,\textrm{Diff}\,}}_c(M)$$
Diff
c
(
M
)
of compactly supported diffeomorphisms of a smooth manifold M that satisfy a so-called generalized positive energy condition. In particular, this captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by
$$\overline{\rho }$$
ρ
¯
. We show that if M is connected and
$$\dim (M) > 1$$
dim
(
M
)
>
1
, then any such representation is necessarily trivial on the identity component
$${{\,\textrm{Diff}\,}}_c(M)_0$$
Diff
c
(
M
)
0
. As an intermediate step towards this result, we determine the continuous second Lie algebra cohomology
$$H^2_\textrm{ct}(\mathcal {X}_c(M), \mathbb {R})$$
H
ct
2
(
X
c
(
M
)
,
R
)
of the Lie algebra of compactly supported vector fields. This is subtly different from Gelfand–Fuks cohomology in view of the compact support condition.}},
author = {{Janssens, Bas and Niestijl, Milan}},
issn = {{0010-3616}},
journal = {{Communications in Mathematical Physics}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms}}},
doi = {{10.1007/s00220-024-05226-w}},
volume = {{406}},
year = {{2025}},
}
@article{50299,
abstract = {{A finite classical polar space of rank $n$ consists of the totally isotropic
subspaces of a finite vector space over $\mathbb{F}_q$ equipped with a
nondegenerate form such that $n$ is the maximal dimension of such a subspace. A
$t$-$(n,k,\lambda)$ design in a finite classical polar space of rank $n$ is a
collection $Y$ of totally isotropic $k$-spaces such that each totally isotropic
$t$-space is contained in exactly $\lambda$ members of $Y$. Nontrivial examples
are currently only known for $t\leq 2$. We show that $t$-$(n,k,\lambda)$
designs in polar spaces exist for all $t$ and $q$ provided that
$k>\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a
probabilistic method by Kuperberg, Lovett, and Peled, and it is thus
nonconstructive.}},
author = {{Weiß, Charlene}},
journal = {{Des. Codes Cryptogr.}},
pages = {{971 -- 981}},
title = {{{Nontrivial $t$-designs in polar spaces exist for all $t$}}},
doi = {{10.1007/s10623-024-01471-1}},
volume = {{93}},
year = {{2025}},
}
@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}},
}