@misc{31385,
  author       = {{Hoffmann, Max}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{295–297}},
  title        = {{{Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie}}},
  doi          = {{10.1007/s00591-021-00299-3}},
  volume       = {{68}},
  year         = {{2021}},
}

@inbook{31364,
  author       = {{Hoffmann, Max}},
  booktitle    = {{ Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert}},
  editor       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  isbn         = {{9783662628539}},
  issn         = {{2197-8751}},
  pages        = {{179–204}},
  publisher    = {{Springer Berlin Heidelberg}},
  title        = {{{Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn}}},
  doi          = {{10.1007/978-3-662-62854-6_9}},
  year         = {{2021}},
}

@article{31261,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>For a compact Riemannian locally symmetric space $\mathcal M$ of rank 1 and an associated vector bundle $\mathbf V_{\tau }$ over the unit cosphere bundle $S^{\ast }\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\mathbf V_{\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\ast }\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\sigma )$ on compatible associated vector bundles $\mathbf W_{\sigma }$ over $\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\tau$ and $\sigma$ defining the bundles $\mathbf V_{\tau }$ and $\mathbf W_{\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\mathbf W_{\sigma }$. Our methods of proof are based on representation theory and Lie theory.</jats:p>}},
  author       = {{Küster, Benjamin and Weich, Tobias}},
  issn         = {{1073-7928}},
  journal      = {{International Mathematics Research Notices}},
  keywords     = {{General Mathematics}},
  number       = {{11}},
  pages        = {{8225--8296}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}}},
  doi          = {{10.1093/imrn/rnz068}},
  volume       = {{2021}},
  year         = {{2021}},
}

@article{31576,
  author       = {{Häsel-Weide, Uta and Nührenbürger, Marcus}},
  journal      = {{Zeitschrift für Grundschulforschung (ZfG)}},
  number       = {{14}},
  pages        = {{49--65}},
  publisher    = {{Springer}},
  title        = {{{Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.}}},
  year         = {{2021}},
}

@article{31577,
  author       = {{Häsel-Weide, Uta and Schöttler, Christian}},
  issn         = {{ 2701-9012}},
  journal      = {{Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP)}},
  number       = {{2}},
  title        = {{{Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen}}},
  year         = {{2021}},
}

@article{32810,
  author       = {{Li, Jiaao and Ma, Yulai and Shi, Yongtang and Wang, Weifan and Wu, Yezhou}},
  issn         = {{0195-6698}},
  journal      = {{European Journal of Combinatorics}},
  keywords     = {{Discrete Mathematics and Combinatorics}},
  publisher    = {{Elsevier BV}},
  title        = {{{On 3-flow-critical graphs}}},
  doi          = {{10.1016/j.ejc.2021.103451}},
  volume       = {{100}},
  year         = {{2021}},
}

@article{33278,
  abstract     = {{The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold.}},
  author       = {{Kolb, Martin and Weich, Tobias and Wolf, Lasse}},
  journal      = {{Annales Henri Poincaré }},
  number       = {{4}},
  pages        = {{1283--1296}},
  publisher    = {{Springer Science + Business Media}},
  title        = {{{Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature}}},
  volume       = {{23}},
  year         = {{2021}},
}

@article{33481,
  abstract     = {{While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction.}},
  author       = {{Richthammer, Thomas and Fiedler, Michael}},
  journal      = {{Stochastic Processes and their Applications}},
  pages        = {{1--32}},
  publisher    = {{Elsevier}},
  title        = {{{A lower bound on the displacement of particles in 2D Gibbsian particle systems}}},
  doi          = {{https://doi.org/10.1016/j.spa.2020.10.003}},
  volume       = {{132}},
  year         = {{2021}},
}

@article{34818,
  author       = {{Hanusch, Maximilian}},
  issn         = {{0926-2245}},
  journal      = {{Differential Geometry and its Applications}},
  keywords     = {{Geometry and Topology, Analysis}},
  publisher    = {{Elsevier BV}},
  title        = {{{Symmetries of analytic curves}}},
  doi          = {{10.1016/j.difgeo.2020.101687}},
  volume       = {{74}},
  year         = {{2021}},
}

@inbook{35752,
  author       = {{Frischemeier, Daniel and Podworny, Susanne and Biehler, Rolf}},
  booktitle    = {{Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik}},
  editor       = {{Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}},
  isbn         = {{9783662628539}},
  issn         = {{2197-8751}},
  pages        = {{227--249}},
  publisher    = {{Springer Spektrum}},
  title        = {{{Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“}}},
  doi          = {{10.1007/978-3-662-62854-6_11}},
  year         = {{2021}},
}

@article{45381,
  author       = {{Dröse, Jennifer and Prediger, S. and Neugebauer, P. and Danhier, R. D. and Mertins, B.}},
  journal      = {{International Electronic Journal of Mathematics Education, 16(1), em0625}},
  title        = {{{Investigating students' processes of noticing and interpreting syntactic language features in word problem solving through eye-tracking}}},
  doi          = {{doi.org/10.29333/iejme/9674n }},
  year         = {{2021}},
}

@article{45380,
  author       = {{Dröse, Jennifer and Prediger, S.}},
  journal      = {{Studies in Educational Evaluation, 68 (100953)}},
  pages        = {{1--15}},
  title        = {{{Identifying obstacles is not enough for everybody – Differential efficacy of an intervention fostering fifth graders’ comprehension for word problems}}},
  doi          = {{doi.org/10.1016/j.stueduc.2020.100953}},
  year         = {{2021}},
}

@article{31578,
  author       = {{Häsel-Weide, Uta and Seitz, Simone and Wallner, Melina and Wilke, Yannik and Heckmann, Lara}},
  journal      = {{QfI - Qualifizierung für Inklusion. Online-Zeitschrift zur Forschung über Aus-, Fort- und Weiterbildung pädagogischer Fachkräfte}},
  number       = {{1}},
  title        = {{{Mit Aufgaben im inklusiven Mathematikunterricht professionell umgehen - Erkenntnisse einer Interviewstudie mit Lehrpersonen der Sekundarstufe}}},
  doi          = {{10.21248/qfi.57}},
  volume       = {{3}},
  year         = {{2021}},
}

@inproceedings{31583,
  author       = {{Hattermann, Mathias and Häsel-Weide, Uta and Wallner, Melina}},
  booktitle    = {{Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education }},
  editor       = {{Inprasitha, M. and Changsri, N. and Boonsena, N.}},
  pages        = {{9--15}},
  title        = {{{Conceptualiziation processes of 6th graders for rotational symmetry}}},
  volume       = {{3}},
  year         = {{2021}},
}

@inproceedings{22894,
  abstract     = {{The first order optimality conditions of optimal control problems (OCPs) can
be regarded as boundary value problems for Hamiltonian systems. Variational or
symplectic discretisation methods are classically known for their excellent
long term behaviour. As boundary value problems are posed on intervals of
fixed, moderate length, it is not immediately clear whether methods can profit
from structure preservation in this context. When parameters are present,
solutions can undergo bifurcations, for instance, two solutions can merge and
annihilate one another as parameters are varied. We will show that generic
bifurcations of an OCP are preserved under discretisation when the OCP is
either directly discretised to a discrete OCP (direct method) or translated
into a Hamiltonian boundary value problem using first order necessary
conditions of optimality which is then solved using a symplectic integrator
(indirect method). Moreover, certain bifurcations break when a non-symplectic
scheme is used. The general phenomenon is illustrated on the example of a cut
locus of an ellipsoid.}},
  author       = {{Offen, Christian and Ober-Blöbaum, Sina}},
  issn         = {{2405-8963}},
  keywords     = {{optimal control, catastrophe theory, bifurcations, variational methods, symplectic integrators}},
  location     = {{Berlin, Germany}},
  pages        = {{334--339}},
  title        = {{{Bifurcation preserving discretisations of optimal control problems}}},
  doi          = {{https://doi.org/10.1016/j.ifacol.2021.11.099}},
  volume       = {{54(19)}},
  year         = {{2021}},
}

@inproceedings{21572,
  author       = {{Ridderbusch, Steffen and Offen, Christian and Ober-Blöbaum, Sina and Goulart, Paul}},
  booktitle    = {{2021 60th IEEE Conference on Decision and Control (CDC)}},
  location     = {{Austin, TX, USA}},
  pages        = {{2896}},
  publisher    = {{IEEE}},
  title        = {{{Learning ODE Models with Qualitative Structure Using Gaussian Processes }}},
  doi          = {{10.1109/CDC45484.2021.9683426}},
  year         = {{2021}},
}

@inproceedings{21592,
  abstract     = {{We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design.}},
  author       = {{Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}},
  location     = {{Rotterdam, the Netherlands}},
  pages        = {{1975--1980}},
  title        = {{{Multi-objective minimum time optimal control for low-thrust trajectory design}}},
  year         = {{2021}},
}

@inproceedings{29868,
  author       = {{Jiménez, F. and Ober-Blöbaum, Sina}},
  booktitle    = {{Nichtlineare Sci 31}},
  title        = {{{Fractional Damping Through Restricted Calculus of Variations}}},
  volume       = {{46}},
  year         = {{2021}},
}

@article{34827,
  abstract     = {{<jats:title>Zusammenfassung</jats:title><jats:p>Zu den ersten geometrischen Begriffen, die Kinder bereits im Elementar- und Primarbereich lernen, zählen u. a. Viereck, Rechteck und Quadrat. Studien zeigen, dass Lernende bereits früh individuelle Vorstellungen, sog. <jats:italic>individuelle Begriffskonzepte,</jats:italic> zu diesen Begriffen aufbauen. Zwar wird die Entwicklung von Begriffsverständnis in verschiedenen mathematikdidaktischen Stufenmodellen dargestellt, diese sind jedoch generisch und beschreiben nicht explizit die Entwicklung der ersten <jats:italic>individuellen Begriffskonzepte </jats:italic>von Lernenden zu Viereck, Rechteck und Quadrat. Aus empirischer Sicht liegen verschiedene Studien vor, die einzelne Aspekte der individuellen Begriffskonzepte von Lernenden unterschiedlicher Altersgruppen zu diesen Begriffen ausleuchten. Um Begriffsbildungsprozesse aus empirischer Sicht detaillierter entlang der jeweils vorherrschenden individuellen Begriffskonzepte zu beschreiben, fehlen insbesondere Studien in der Grundschule, die alle vier Klassenstufen betrachten und dabei differenzierte Erkenntnisse zu verschiedenen theoretischen Indikatoren des Begriffsverständnisses liefern. Daher geht die vorliegende Studie der Frage nach, welches Verständnis der Begriffe Viereck, Rechteck und Quadrat Schülerinnen und Schüler der Jahrgangsstufen 1, 2, 3 und 4 zeigen. Dazu wurde eine Quasi-Längsschnittstudie mit <jats:italic>N</jats:italic> = 456 Grundschulkindern (ca. 100 pro Jahrgangsstufe) durchgeführt. Die Ergebnisse geben detaillierte Einblicke in die individuellen Begriffskonzepte der Lernenden und zeigen, dass Lernende zunehmend Eigenschaften der Figuren berücksichtigen, jedoch individuelle Begriffskonzepte über lange Zeit auch prototypisch geprägt sind. Implikationen dieser Ergebnisse für Forschung und Praxis werden diskutiert.</jats:p>}},
  author       = {{Bruns, Julia and Unterhauser, Elisabeth and Gasteiger, Hedwig}},
  issn         = {{0173-5322}},
  journal      = {{Journal für Mathematik-Didaktik}},
  keywords     = {{Education, General Mathematics}},
  number       = {{2}},
  pages        = {{581--623}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Geometrisches Begriffsverständnis in der Grundschule am Beispiel der Begriffe Viereck, Rechteck und Quadrat}}},
  doi          = {{10.1007/s13138-021-00185-4}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45382,
  author       = {{Prediger, Susanne and Dröse, Jennifer}},
  journal      = {{Lernen und Lernstörungen, 10(2)}},
  title        = {{{Fehlerbearbeitung bei mathematischen Textaufgaben – Sprachliche und strategische Fehlerursachen und ihre Bearbeitung}}},
  doi          = {{doi.org/10.1024/2235-0977/a000330}},
  year         = {{2021}},
}