@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}},
}

@article{31263,
  author       = {{Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}},
  issn         = {{2644-9463}},
  journal      = {{Annales Henri Lebesgue}},
  pages        = {{81--119}},
  publisher    = {{Cellule MathDoc/CEDRAM}},
  title        = {{{High frequency limits for invariant Ruelle densities}}},
  doi          = {{10.5802/ahl.67}},
  volume       = {{4}},
  year         = {{2021}},
}

@article{36271,
  author       = {{Brennecken, Dominik and Hilgert, Joachim and Ciardo, Lorenzo}},
  journal      = {{Journal of Lie Theory}},
  number       = {{2}},
  pages        = {{459----468}},
  publisher    = {{Heldermann Verlag}},
  title        = {{{Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)}}},
  doi          = {{10.48550/arXiv.2008.07479}},
  volume       = {{31}},
  year         = {{2021}},
}

@misc{51556,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{171–173}},
  title        = {{{Philip Ording: 99 Variations on a Proof. Princeton University Press 2019}}},
  doi          = {{10.1007/s00591-021-00295-7}},
  volume       = {{68}},
  year         = {{2021}},
}

@misc{51555,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{175–177}},
  title        = {{{Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020}}},
  doi          = {{10.1007/s00591-021-00296-6}},
  volume       = {{68}},
  year         = {{2021}},
}

@article{45967,
  author       = {{Binz, Tim and Kovács, Balázs}},
  journal      = {{arXiv}},
  title        = {{{A convergent finite element algorithm for mean curvature flow in higher codimension}}},
  year         = {{2021}},
}

@article{45962,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow and powers of mean and inverse mean curvature flow. Error estimates are proved for semidiscretizations and full discretizations for the generalized flow. The algorithm proposed and studied here combines evolving surface finite elements, whose nodes determine the discrete surface, and linearly implicit backward difference formulae for time integration. The numerical method is based on a system coupling the surface evolution to nonlinear second-order parabolic evolution equations for the normal velocity and normal vector. A convergence proof is presented in the case of finite elements of polynomial degree at least 2 and backward difference formulae of orders 2 to 5. The error analysis combines stability estimates and consistency estimates to yield optimal-order $H^1$-norm error bounds for the computed surface position, velocity, normal vector, normal velocity and therefore for the mean curvature. The stability analysis is performed in the matrix–vector formulation and is independent of geometric arguments, which only enter the consistency analysis. Numerical experiments are presented to illustrate the convergence results and also to report on monotone quantities, e.g. Hawking mass for inverse mean curvature flow, and complemented by experiments for nonconvex surfaces.</jats:p>}},
  author       = {{Binz, Tim and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{2545--2588}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{A convergent finite element algorithm for generalized mean curvature flows of closed surfaces}}},
  doi          = {{10.1093/imanum/drab043}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45957,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>A proof of convergence is given for a bulk–surface finite element semidiscretisation of the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semidiscretisation is studied in an abstract weak formulation as a second-order system. Optimal-order uniform-in-time error estimates are shown in the $L^2$- and $H^1$-norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system. Numerical experiments illustrate the theoretical results.</jats:p>}},
  author       = {{Harder, Paula and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{3}},
  pages        = {{2589--2620}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions}}},
  doi          = {{10.1093/imanum/drab045}},
  volume       = {{42}},
  year         = {{2021}},
}

@article{45961,
  author       = {{Nick, Jörg and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{4}},
  pages        = {{997--1000}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}}},
  doi          = {{10.1007/s00211-021-01196-6}},
  volume       = {{147}},
  year         = {{2021}},
}

@article{45959,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{3}},
  pages        = {{595--643}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A convergent evolving finite element algorithm for Willmore flow of closed surfaces}}},
  doi          = {{10.1007/s00211-021-01238-z}},
  volume       = {{149}},
  year         = {{2021}},
}

@article{34629,
  author       = {{Hesse, Kerstin and Sloan, Ian H. and Womersley, Robert S.}},
  issn         = {{0377-0427}},
  journal      = {{Journal of Computational and Applied Mathematics}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  publisher    = {{Elsevier BV}},
  title        = {{{Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data}}},
  doi          = {{10.1016/j.cam.2020.113061}},
  volume       = {{382}},
  year         = {{2021}},
}