@inproceedings{45384,
  author       = {{Dröse, Jennifer}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2020 }},
  editor       = {{Siller, H.-S. and Weigel, W. and Wöler, J. F.}},
  pages        = {{233--236}},
  publisher    = {{WTM}},
  title        = {{{Verstehensgrundlagen diagnostizieren - Welche Wissenselemente fokussieren Lehrkräfte?}}},
  year         = {{2020}},
}

@inbook{45386,
  author       = {{Dröse, Jennifer and Eisen, V. and Prediger, Susanne and Altieri, M. and Schellenbach, M. and Menning, R.}},
  booktitle    = {{Mathematik lehren 223}},
  pages        = {{38--40}},
  title        = {{{Textaufgaben lesen lernen – eine digital gestützte Einheit mit App }}},
  year         = {{2020}},
}

@inbook{17994,
  abstract     = {{In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.}},
  author       = {{Gerlach, Raphael and Ziessler, Adrian}},
  booktitle    = {{Advances in Dynamics, Optimization and Computation}},
  editor       = {{Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}},
  isbn         = {{9783030512637}},
  issn         = {{2198-4182}},
  pages        = {{66--85}},
  publisher    = {{Springer International Publishing}},
  title        = {{{The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}}},
  doi          = {{10.1007/978-3-030-51264-4_3}},
  volume       = {{304}},
  year         = {{2020}},
}

@article{16712,
  abstract     = {{We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi) where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions.}},
  author       = {{Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}},
  issn         = {{1468-9367}},
  journal      = {{Dynamical Systems}},
  number       = {{2}},
  pages        = {{197--215}},
  title        = {{{On the equivariance properties of self-adjoint matrices}}},
  doi          = {{10.1080/14689367.2019.1661355}},
  volume       = {{35}},
  year         = {{2020}},
}

@article{51386,
  author       = {{Hilgert, Joachim and Barnum, H.}},
  journal      = {{J. of Lie Theory}},
  pages        = {{315--344}},
  title        = {{{Spectral Properties of Convex Bodies}}},
  volume       = {{30}},
  year         = {{2020}},
}

@misc{51559,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{301–305}},
  title        = {{{Titu Andreescu und Vlad Crisan: Mathematical Induction – A powerful and elegant method of proof. XYZ Press 2017 und Florian André Dalwigk: Vollständige Induktion – Beispiele und Aufgaben bis zum Umfallen. Springer Spektrum 2019}}},
  doi          = {{10.1007/s00591-020-00282-4}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51557,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{307–309}},
  title        = {{{Fabio Toscano: The Secret Formula – How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation. Princeton University Press 2020}}},
  doi          = {{10.1007/s00591-020-00283-3}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51561,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{123–124}},
  title        = {{{Robert Bosch: OPT ART – From Mathematical Optimization to Visual Design. Princeton University Press 2019}}},
  doi          = {{10.1007/s00591-020-00272-6}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51560,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{297–299}},
  title        = {{{David M. Bressoud: Calculus Reordered -- A History of the Big Ideas. Princeton University Press 2019}}},
  doi          = {{10.1007/s00591-020-00280-6}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51564,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{97–98}},
  title        = {{{Daniel Grieser: Mathematisches Problemlösen und Beweisen – Eine Entdeckungsreise in die Mathematik. 2. Auflage (Springer 2017)}}},
  doi          = {{10.1007/s00591-019-00254-3}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{51563,
  author       = {{Hilgert, Joachim}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{109–111}},
  title        = {{{Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019)}}},
  doi          = {{10.1007/s00591-019-00254-3}},
  volume       = {{67}},
  year         = {{2020}},
}

@article{45954,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45953,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>}},
  author       = {{Hipp, David and Kovács, Balázs}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{1}},
  pages        = {{638--728}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}}},
  doi          = {{10.1093/imanum/drz073}},
  volume       = {{41}},
  year         = {{2020}},
}

@article{45955,
  author       = {{Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and Lubich, Christian}},
  issn         = {{0025-5718}},
  journal      = {{Mathematics of Computation}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Algebra and Number Theory}},
  number       = {{329}},
  pages        = {{995--1038}},
  publisher    = {{American Mathematical Society (AMS)}},
  title        = {{{Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}}},
  doi          = {{10.1090/mcom/3597}},
  volume       = {{90}},
  year         = {{2020}},
}

@article{45952,
  author       = {{Kovács, Balázs and Li, Buyang and Lubich, Christian}},
  issn         = {{1463-9963}},
  journal      = {{Interfaces and Free Boundaries}},
  keywords     = {{Applied Mathematics}},
  number       = {{4}},
  pages        = {{443--464}},
  publisher    = {{European Mathematical Society - EMS - Publishing House GmbH}},
  title        = {{{A convergent algorithm for forced mean curvature flow driven by diffusion on the surface}}},
  doi          = {{10.4171/ifb/446}},
  volume       = {{22}},
  year         = {{2020}},
}

@inbook{34632,
  author       = {{Hesse, Kerstin}},
  booktitle    = {{Multivariate Algorithms and Information-Based Complexity}},
  editor       = {{Hickernell, Fred J. and Kritzer, Peter}},
  isbn         = {{9783110633115}},
  pages        = {{33--42 }},
  publisher    = {{De Gruyter}},
  title        = {{{RBF-based penalized least-squares approximation of noisy scattered data on the sphere}}},
  year         = {{2020}},
}

@article{53415,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Given a closed orientable hyperbolic manifold of dimension <jats:inline-formula><jats:alternatives><jats:tex-math>$$\ne 3$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                  <mml:mrow>
                    <mml:mo>≠</mml:mo>
                    <mml:mn>3</mml:mn>
                  </mml:mrow>
                </mml:math></jats:alternatives></jats:inline-formula> we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.
</jats:p>}},
  author       = {{Küster, Benjamin and Weich, Tobias}},
  issn         = {{0010-3616}},
  journal      = {{Communications in Mathematical Physics}},
  keywords     = {{Mathematical Physics, Statistical and Nonlinear Physics}},
  number       = {{2}},
  pages        = {{917--941}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Pollicott-Ruelle Resonant States and Betti Numbers}}},
  doi          = {{10.1007/s00220-020-03793-2}},
  volume       = {{378}},
  year         = {{2020}},
}

@inbook{44685,
  author       = {{Schumacher, Jan and Rezat, Sebastian}},
  booktitle    = {{Zeichen und Sprache im Mathematikunterricht: Semiotik in Theorie und Praxis}},
  editor       = {{Kadunz, Gert}},
  isbn         = {{9783662611937}},
  pages        = {{85–112}},
  publisher    = {{Springer}},
  title        = {{{Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen}}},
  doi          = {{10.1007/978-3-662-61194-4_5}},
  year         = {{2020}},
}

@inbook{44688,
  author       = {{Rezat, Sebastian}},
  booktitle    = {{Mobile Medien im Schulkontext}},
  editor       = {{Meister, Dorothee and Ilka, Mindt}},
  isbn         = {{9783658290382}},
  issn         = {{2512-112X}},
  publisher    = {{Springer}},
  title        = {{{Mathematiklernen mit digitalen Schulbüchern im Spannungsfeld zwischen Individualisierung und Kooperation}}},
  doi          = {{10.1007/978-3-658-29039-9_10}},
  year         = {{2020}},
}

@article{46159,
  author       = {{Leuders, Timo and Wessel, Lena}},
  issn         = {{0933-422X}},
  journal      = {{Pädagogik 2/2020}},
  number       = {{2}},
  pages        = {{26--30}},
  publisher    = {{Beltz Verlagsgruppe}},
  title        = {{{Differenziertes Üben gestalten. Zwischen Umsetzung in der Praxis und Fundierung in der Forschung.}}},
  year         = {{2020}},
}