@inbook{13108,
  abstract     = {{Diagrammatisches Schlie{\ss}en wird im Zusammenhang mit dem Lernen von Mathmematik und ihrer Symbolsprache als wesentliche Theorie der Wissenskonstruktion diskutiert. Dabei wird h{\"{a}}ufig davon ausgegangen, dass die Wissenskonstruktion im Sinne diagrammatischen Schlie{\ss}ens erfolgt. Deskriptive Rekonstruktionen diagrammatischen Schlie{\ss}ens bei Lernenden stellen jedoch ein Desiderat der mathematikdidaktischen Forschung dar. Der vorliegende Beitrag befasst sich mit der Fragestellung, wie sich diagrammatisches Schlie{\ss}en bei Lernenden rekonstruieren l{\"{a}}sst. Als m{\"{o}}gliche Werkzeuge f{\"{u}}r eine solche Rekonstruktion werden Toulmins Argumentationsschema und Vergnauds Schema-Begriff exemplarisch angewandt, um das diagrammatische Schlie{\ss}en eines Sch{\"{u}}lerpaars beim Einstieg in die Subtraktion negativer Zahlen zu rekonstruieren. Abschlie{\ss}end wird die tats{\"{a}}chliche Eignung der beiden Ans{\"{a}}tze zur Rekonstruktion diagrammatischen Schlie{\ss}ens diskutiert.}},
  author       = {{Schumacher, Jan and Rezat, Sebastian}},
  booktitle    = {{Zeichen und Sprache im Mathematikunterricht}},
  editor       = {{Kadunz, Gert}},
  publisher    = {{Springer}},
  title        = {{{Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge}}},
  doi          = {{10.1007/978-3-662-61194-4_5}},
  year         = {{2020}},
}

@inproceedings{31873,
  author       = {{Schumacher, Jan}},
  publisher    = {{LibreCat University}},
  title        = {{{Deduktion und Abduktion beim diagrammatischen Schließen – das didaktische Potential der Peirceschen Semiotik}}},
  doi          = {{10.17877/DE290R-21555}},
  year         = {{2020}},
}

@article{34789,
  author       = {{Amiri, Habib and Glöckner, Helge and Schmeding, Alexander}},
  issn         = {{0044-8753}},
  journal      = {{Archivum Mathematicum}},
  keywords     = {{22A22, 22E65, 22E67, 46T10, 47H30, 58D15, 58H05}},
  number       = {{5}},
  pages        = {{307–356}},
  title        = {{{Lie groupoids of mappings taking values in a Lie groupoid}}},
  doi          = {{10.5817/AM2020-5-307}},
  volume       = {{56}},
  year         = {{2020}},
}

@article{34787,
  author       = {{Glöckner, Helge and Masbough, Niku}},
  issn         = {{0146-4124}},
  journal      = {{Topology Proceedings}},
  keywords     = {{54B10, 54D45, 54D50}},
  pages        = {{35–38}},
  title        = {{{Products of regular locally compact spaces are k_R-spaces}}},
  volume       = {{55}},
  year         = {{2020}},
}

@unpublished{34808,
  abstract     = {{For suitable finite-dimensional smooth manifolds M (possibly with various
kinds of boundary or corners), locally convex topological vector spaces F and
non-negative integers k, we construct continuous linear operators S_n from the
space of F-valued k times continuously differentiable functions on M to the
corresponding space of smooth functions such that S_n(f) converges to f in
C^k(M,F) as n tends to infinity, uniformly for f in compact subsets of
C^k(M,F). We also study the existence of continuous linear right inverses for
restriction maps from C^k(M,F) to C^k(L,F) if L is a closed subset of M,
endowed with a C^k-manifold structure turning the inclusion map from L to M
into a C^k-map. Moreover, we construct continuous linear right inverses for
restriction operators between spaces of sections in vector bundles in many
situations, and smooth local right inverses for restriction operators between
manifolds of mappings. We also obtain smoothing results for sections in fibre
bundles.}},
  author       = {{Glöckner, Helge}},
  booktitle    = {{arXiv:2006.00254}},
  title        = {{{Smoothing operators for vector-valued functions and extension operators}}},
  year         = {{2020}},
}

@article{29399,
  author       = {{Limebeer, D. J. N. and Ober-Blöbaum, Sina and Farshi, F. H.}},
  journal      = {{IEEE Transactions on Automatic Control}},
  pages        = {{1381--1396}},
  title        = {{{Variational integrators for dissipative systems}}},
  volume       = {{65(4)}},
  year         = {{2020}},
}

@article{16297,
  abstract     = {{In real-world problems, uncertainties (e.g., errors in the measurement,
precision errors) often lead to poor performance of numerical algorithms when
not explicitly taken into account. This is also the case for control problems,
where optimal solutions can degrade in quality or even become infeasible. Thus,
there is the need to design methods that can handle uncertainty. In this work,
we consider nonlinear multi-objective optimal control problems with uncertainty
on the initial conditions, and in particular their incorporation into a
feedback loop via model predictive control (MPC). In multi-objective optimal
control, an optimal compromise between multiple conflicting criteria has to be
found. For such problems, not much has been reported in terms of uncertainties.
To address this problem class, we design an offline/online framework to compute
an approximation of efficient control strategies. This approach is closely
related to explicit MPC for nonlinear systems, where the potentially expensive
optimization problem is solved in an offline phase in order to enable fast
solutions in the online phase. In order to reduce the numerical cost of the
offline phase, we exploit symmetries in the control problems. Furthermore, in
order to ensure optimality of the solutions, we include an additional online
optimization step, which is considerably cheaper than the original
multi-objective optimization problem. We test our framework on a car
maneuvering problem where safety and speed are the objectives. The
multi-objective framework allows for online adaptations of the desired
objective. Alternatively, an automatic scalarizing procedure yields very
efficient feedback controls. Our results show that the method is capable of
designing driving strategies that deal better with uncertainties in the initial
conditions, which translates into potentially safer and faster driving
strategies.}},
  author       = {{Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}},
  journal      = {{International Journal of Robust and Nonlinear Control}},
  pages        = {{7593--7618}},
  title        = {{{Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty}}},
  doi          = {{10.1002/rnc.5197}},
  volume       = {{30(17)}},
  year         = {{2020}},
}

@article{29398,
  author       = {{Hernández Castellanos, C. I. O. and Schütze, G. and Sun, J.-Q. and Ober-Blöbaum, Sina and Morales-Luna, G.}},
  journal      = {{Mathematics}},
  title        = {{{Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping}}},
  volume       = {{8(11):1959}},
  year         = {{2020}},
}

@inproceedings{29422,
  author       = {{Lishkova, Y. and Ober-Blöbaum, Sina and Cannon, M. and Leyendecker, S.}},
  booktitle    = {{Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe}},
  title        = {{{A multirate variational approach to simulation and optimal control for flexible spacecraft}}},
  year         = {{2020}},
}

@inproceedings{29423,
  author       = {{Faulwasser, T. and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, K. }},
  booktitle    = {{24th International Symposium on Mathematical Theory of Networks and Systems}},
  title        = {{{A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems}}},
  year         = {{2020}},
}

@inproceedings{29424,
  author       = {{Cresson, J.  and Jiménez, F. and Ober-Blöbaum, Sina}},
  booktitle    = {{24th International Symposium on Mathematical Theory of Networks and Systems}},
  title        = {{{Modelling of the convection-diffusion equation through fractional restricted calculus of variations}}},
  year         = {{2020}},
}

@article{29545,
  author       = {{Jean, Frédéric and Maslovskaya, Sofya and Zelenko, Igor}},
  issn         = {{0046-5755}},
  journal      = {{Geometriae Dedicata}},
  keywords     = {{Geometry and Topology}},
  number       = {{1}},
  pages        = {{295--314}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry}}},
  doi          = {{10.1007/s10711-020-00581-z}},
  volume       = {{213}},
  year         = {{2020}},
}

@inproceedings{29546,
  author       = {{Maslovskaya, Sofya and Caillau, Jean-Baptiste and Djema, Walid and Giraldi, Laetitia and Jean-Luc, Jean-Luc and Pomet, Jean-Baptiste}},
  title        = {{{The turnpike property in maximization of microbial metabolite production}}},
  year         = {{2020}},
}

@article{31264,
  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}},
}

@inproceedings{31372,
  author       = {{Hoffmann, Max}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2020}},
  editor       = {{Siller, Hans-Stefan and Weigel, Wolfgang and Wörler, Jan Franz}},
  pages        = {{1353--1356}},
  publisher    = {{WTM-Verlag}},
  title        = {{{Schnittstellenaktivitäten zum Kongruenzsatz WSW}}},
  doi          = {{10.17877/DE290R-21368}},
  year         = {{2020}},
}

@misc{31386,
  author       = {{Hoffmann, Max}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{119–121}},
  title        = {{{Rezension: Andrew Granville und Jenniver Granville: Prime Supects: The Anatomy of Integers and Permutations}}},
  doi          = {{10.1007/s00591-019-00269-w}},
  volume       = {{67}},
  year         = {{2020}},
}

@misc{31384,
  author       = {{Hoffmann, Max}},
  booktitle    = {{Mathematische Semesterberichte}},
  pages        = {{115–116}},
  title        = {{{Rezension: Ehrhard Behrends: Parkettierungen der Ebene – Von Escher über Möbius zu Penrose}}},
  doi          = {{10.1007/s00591-019-00264-1}},
  volume       = {{67}},
  year         = {{2020}},
}

@book{31381,
  editor       = {{Hoffmann, Max}},
  title        = {{{Der Mathematikunterricht 66 (6): Geometrie in Schule und Lehramtsausbildung – ein Nachwuchsheft}}},
  year         = {{2020}},
}

@inbook{31551,
  author       = {{Häsel-Weide, Uta and Nührenbörger, Marcus}},
  booktitle    = {{Kinder lernen Zukunft – Anforderungen und tragfähige Grundlagen}},
  editor       = {{Hecker, Ulrich and Lassek, Maresi and Ramseger, Jörg}},
  pages        = {{108--118}},
  publisher    = {{Grundschulverband}},
  title        = {{{Tragfähige Grundlagen}}},
  volume       = {{Band 150}},
  year         = {{2020}},
}

@inbook{31552,
  author       = {{Heckmann, Lara and Häsel-Weide, Uta}},
  booktitle    = {{Beiträge zum Mathematikunterricht 2020}},
  editor       = {{Siller, Hans-Stefan and Weigel, Wolfgang and Wörler, Jan Franz}},
  isbn         = {{978-3-95987-139-6}},
  pages        = {{393--396}},
  publisher    = {{WTM Verlag}},
  title        = {{{Aufgaben für den inklusiven Mathematikunterricht - aus der Sicht von Lehrkräften.}}},
  year         = {{2020}},
}