@article{45971,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation.</jats:p>}},
  author       = {{Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints}}},
  doi          = {{10.1093/imanum/drad037}},
  year         = {{2023}},
}

@article{53140,
  abstract     = {{We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup stable spaces and symmetric pressure stabilized formulations. We extend the results from Burman and Fernández [\textit{SIAM J. Numer. Anal.}, 47 (2009), pp. 409-439] and provide a unified theoretical analysis of backward difference formulae (BDF methods) of order 1 to 6. The main novelty of our approach lies in the use of Dahlquist's G-stability concept together with multiplier techniques introduced by Nevannlina-Odeh and recently by Akrivis et al. [\textit{SIAM J. Numer. Anal.}, 59 (2021), pp. 2449-2472] to derive optimal stability and error estimates for both the velocity and the pressure. When combined with a method dependent Ritz projection for the initial data, unconditional stability can be shown while for arbitrary interpolation, pressure stability is subordinate to the fulfillment of a mild inverse CFL-type condition between space and time discretizations.}},
  author       = {{Contri, Alessandro and Kovács, Balázs and Massing, André}},
  journal      = {{arXiv}},
  title        = {{{Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem: velocity and pressure estimates}}},
  doi          = {{10.48550/ARXIV.2312.05511}},
  year         = {{2023}},
}

@article{53142,
  author       = {{Berger, Thomas and Lanza, Lukas}},
  journal      = {{IMA Journal of Mathematical Control and Information,}},
  number       = {{4}},
  pages        = {{691--713}},
  title        = {{{Funnel control of linear systems with arbitrary relative degree under output measurement losses}}},
  doi          = {{doi: 10.1093/imamci/dnad029}},
  volume       = {{40}},
  year         = {{2023}},
}

@article{53143,
  author       = {{Lee, J. G. and Berger, Thomas and Trenn, S. and Shim, H.}},
  journal      = {{Automatica}},
  pages        = {{Article 111204}},
  title        = {{{Edge-wise funnel output synchronization of heterogeneous agents with relative degree one}}},
  doi          = {{doi: 10.1016/j.automatica.2023.111204 (open access)}},
  volume       = {{156}},
  year         = {{2023}},
}

@book{51101,
  author       = {{Werth, Gerda}},
  isbn         = {{9783658424442}},
  issn         = {{2661-8591}},
  publisher    = {{Springer Fachmedien Wiesbaden}},
  title        = {{{Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings}}},
  doi          = {{10.1007/978-3-658-42445-9}},
  year         = {{2023}},
}

@article{51103,
  author       = {{Werth, Gerda}},
  journal      = {{mathematik lehren}},
  pages        = {{15--19}},
  publisher    = {{Friedrich}},
  title        = {{{Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe}}},
  volume       = {{241}},
  year         = {{2023}},
}

@unpublished{53404,
  abstract     = {{In this short note we observe, on locally symmetric spaces of higher rank, a
connection between the growth indicator function introduced by Quint and the
modified critical exponent of the Poincar\'e series equipped with the
polyhedral distance. As a consequence, we provide a different characterization
of the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms
of the growth indicator function. Moreover, we explore the relationship between
these three objects and the temperedness.}},
  author       = {{Wolf, Lasse L. and Zhang, Hong-Wei}},
  booktitle    = {{arXiv:2311.11770}},
  title        = {{{$L^2$-spectrum, growth indicator function and critical exponent on  locally symmetric spaces}}},
  year         = {{2023}},
}

@article{53410,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.</jats:p>}},
  author       = {{Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}},
  issn         = {{1424-0637}},
  journal      = {{Annales Henri Poincaré}},
  keywords     = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}},
  number       = {{2}},
  pages        = {{1607--1656}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}}},
  doi          = {{10.1007/s00023-023-01379-x}},
  volume       = {{25}},
  year         = {{2023}},
}

@unpublished{53411,
  abstract     = {{We compute a Riemann-Roch formula for the invariant Riemann-Roch number of a
quantizable Hamiltonian $S^1$-manifold $(M,\omega,\mathcal{J})$ in terms of the
geometry of its symplectic quotient, allowing $0$ to be a singular value of the
moment map $\mathcal{J}:M\to\mathbb{R}$. The formula involves a new explicit
local invariant of the singularities. Our approach relies on a complete
singular stationary phase expansion of the associated Witten integral.}},
  author       = {{Delarue, Benjamin and Ioos, Louis and Ramacher, Pablo}},
  booktitle    = {{arXiv:2302.09894}},
  title        = {{{A Riemann-Roch formula for singular reductions by circle actions}}},
  year         = {{2023}},
}

@article{53538,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane.</jats:p>}},
  author       = {{Polychrou, G. and Papageorgiou, Efthymia and Fotiadis, A. and Daskaloyannis, C.}},
  issn         = {{1139-1138}},
  journal      = {{Revista Matemática Complutense}},
  keywords     = {{General Mathematics}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation}}},
  doi          = {{10.1007/s13163-023-00476-z}},
  year         = {{2023}},
}

@inbook{53565,
  author       = {{Schwerin, Imke}},
  booktitle    = {{Mathematikdidaktik Grundschule}},
  location     = {{Bremen}},
  publisher    = {{University of Bamberg Press}},
  title        = {{{Verdoppeln und Halbieren im Zahlenraum bis 100 - Erkenntnisse einer Interviewstudie in Klasse 2}}},
  year         = {{2023}},
}

@inproceedings{53439,
  author       = {{Rezat, Sebastian and Malik, Sara Naseem and Leifeld, Markus}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik  vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main}},
  pages        = {{1125–1128}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Mathematik – Lesen – Lernen: Ein Vorlesungskonzept zur Förderung mathematischer Lesekompetenz}}},
  doi          = {{10.17877/DE290R-23392}},
  year         = {{2023}},
}

@inproceedings{53441,
  author       = {{Leifeld, Markus and Rezat, Sebastian}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik  vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main}},
  pages        = {{993–996}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Verstehen schriftlicher Rechenverfahren durch algorithmisches Denken am Beispiel der schriftlichen Subtraktion}}},
  doi          = {{10.17877/DE290R-23760}},
  year         = {{2023}},
}

@inproceedings{53475,
  author       = {{Malik, Sara Naseem and Rezat, Sebastian}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik  vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Herausforderungen anwendungsbezogener Aufgaben - eine curriculare Perspektive auf den Forschungsstand}}},
  doi          = {{10.17877/DE290R-23380}},
  year         = {{2023}},
}

@inbook{46987,
  author       = {{Pepin, Birgit and Kock, Zeger-jan and Rezat, Sebastian}},
  booktitle    = {{Handbook of Digital Resources in Mathematics Education}},
  editor       = {{Pepin, Birgit and Gueudet, Ghislaine and Choppin, Jeff}},
  isbn         = {{9783030950606}},
  issn         = {{2197-1951}},
  pages        = {{1–28}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Toward student agency in the selection and use of digital resources for learning and studying mathematics}}},
  doi          = {{10.1007/978-3-030-95060-6_26-1}},
  year         = {{2023}},
}

@inbook{48067,
  author       = {{Gueudet, Ghislaine and Pepin, Birgit and Rezat, Sebastian}},
  booktitle    = {{Handbook of Digital Resources in Mathematics Education}},
  editor       = {{Pepin, Birgit and Gueudet, Ghislaine and Choppin, Jeffrey}},
  isbn         = {{9783030950606}},
  issn         = {{2197-1951}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Meta-Resources: Supporting the design of mathematics teaching and learning}}},
  doi          = {{10.1007/978-3-030-95060-6_36-1}},
  year         = {{2023}},
}

@inbook{49684,
  author       = {{Rezat, Sebastian and Geiger, Vince}},
  booktitle    = {{Handbook of Digital Resources in Mathematics Education}},
  editor       = {{Pepin, Birgit and Gueudet, Ghislaine and Choppin, Jeffrey}},
  isbn         = {{9783030950606}},
  issn         = {{2197-1951}},
  publisher    = {{Springer International Publishing}},
  title        = {{{The role of digital technologies in transforming student learning landscapes}}},
  doi          = {{10.1007/978-3-030-95060-6_21-1}},
  year         = {{2023}},
}

@inbook{46956,
  author       = {{Hattermann, Mathias and Rezat, Sebastian and Sträßer, Rudolf}},
  booktitle    = {{Handbuch der Mathematikdidaktik}},
  isbn         = {{9783662666036}},
  pages        = {{201–242}},
  publisher    = {{Springer}},
  title        = {{{Geometrie: Leitidee Raum und Form}}},
  doi          = {{10.1007/978-3-662-66604-3_7}},
  year         = {{2023}},
}

@article{45786,
  abstract     = {{Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers.}},
  author       = {{Hoffmann, Max and Biehler, Rolf}},
  issn         = {{1863-9690}},
  journal      = {{ZDM – Mathematics Education}},
  keywords     = {{General Mathematics, Education}},
  publisher    = {{Springer}},
  title        = {{{Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course}}},
  doi          = {{10.1007/s11858-023-01505-3}},
  year         = {{2023}},
}

@inbook{48319,
  author       = {{Leiss, Dominik and Gerlach, Kerstin and Wessel, Lena and Schmidt-Thieme, Barbara}},
  booktitle    = {{Handbuch der Mathematikdidaktik}},
  isbn         = {{9783662666036}},
  pages        = {{561--595}},
  publisher    = {{Springer Berlin Heidelberg}},
  title        = {{{Sprache und Mathematiklernen}}},
  doi          = {{10.1007/978-3-662-66604-3_18}},
  year         = {{2023}},
}