@inproceedings{29421,
author = {{Ober-Blöbaum, Sina and Vermeeren, M.}},
booktitle = {{7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}},
pages = {{327--333}},
title = {{{Superconvergence of galerkin variational integrators}}},
volume = {{54(19)}},
year = {{2021}},
}
@article{16294,
abstract = {{Model predictive control is a prominent approach to construct a feedback
control loop for dynamical systems. Due to real-time constraints, the major
challenge in MPC is to solve model-based optimal control problems in a very
short amount of time. For linear-quadratic problems, Bemporad et al. have
proposed an explicit formulation where the underlying optimization problems are
solved a priori in an offline phase. In this article, we present an extension
of this concept in two significant ways. We consider nonlinear problems and -
more importantly - problems with multiple conflicting objective functions. In
the offline phase, we build a library of Pareto optimal solutions from which we
then obtain a valid compromise solution in the online phase according to a
decision maker's preference. Since the standard multi-parametric programming
approach is no longer valid in this situation, we instead use interpolation
between different entries of the library. To reduce the number of problems that
have to be solved in the offline phase, we exploit symmetries in the dynamical
system and the corresponding multiobjective optimal control problem. The
results are verified using two different examples from autonomous driving.}},
author = {{Ober-Blöbaum, Sina and Peitz, Sebastian}},
journal = {{International Journal of Robust and Nonlinear Control}},
pages = {{380--403}},
title = {{{Explicit multiobjective model predictive control for nonlinear systems with symmetries}}},
doi = {{10.1002/rnc.5281}},
volume = {{31(2)}},
year = {{2021}},
}
@article{29543,
author = {{Djema, Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}},
issn = {{0005-1098}},
journal = {{Automatica}},
keywords = {{Electrical and Electronic Engineering, Control and Systems Engineering}},
publisher = {{Elsevier BV}},
title = {{{Turnpike features in optimal selection of species represented by quota models}}},
doi = {{10.1016/j.automatica.2021.109804}},
volume = {{132}},
year = {{2021}},
}
@unpublished{31059,
abstract = {{In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.}},
author = {{Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}},
title = {{{Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}}},
year = {{2021}},
}
@unpublished{31058,
abstract = {{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 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.}},
author = {{Schütte, Philipp and Weich, Tobias and Delarue, Benjamin}},
title = {{{Resonances and weighted zeta functions for obstacle scattering via smooth models}}},
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}},
}
@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}},
}
@unpublished{31190,
abstract = {{For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of
arbitrary rank we determine the location of certain Ruelle-Taylor resonances
for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate
counting function for the Ruelle-Taylor resonances and establish a spectral gap
which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is
achieved by proving a quantum-classical correspondence, i.e. a
1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant
states and joint eigenfunctions of the algebra of invariant differential
operators on $G/K$.}},
author = {{Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}},
booktitle = {{arXiv:2103.05667}},
title = {{{Higher rank quantum-classical correspondence}}},
year = {{2021}},
}
@article{31193,
abstract = {{AbstractThe kinetic Brownian motion on the sphere bundle of a Riemannian manifold $$\mathbb {M}$$
M
is a stochastic process that models a random perturbation of the geodesic flow. If $$\mathbb {M}$$
M
is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the $$L^2$$
L
2
-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 Lennart}},
issn = {{1424-0637}},
journal = {{Annales Henri Poincaré}},
keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}},
number = {{4}},
pages = {{1283--1296}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature}}},
doi = {{10.1007/s00023-021-01121-5}},
volume = {{23}},
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}},
}
@unpublished{31210,
abstract = {{In this paper we complete the program of relating the Laplace spectrum for
rank one compact locally symmetric spaces with the first band Ruelle-Pollicott
resonances of the geodesic flow on its sphere bundle. This program was started
by Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and
Guillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for
general rank one spaces. Except for the case of hyperbolic surfaces a countable
set of exceptional spectral parameters always left untreated since the
corresponding Poisson transforms are neither injective nor surjective. We use
vector valued Poisson transforms to treat also the exceptional spectral
parameters. For surfaces the exceptional spectral parameters lead to discrete
series representations of $\mathrm{SL}(2,\mathbb R)$. In higher dimensions the
situation is more complicated, but can be described completely.}},
author = {{Arends, Christian and Hilgert, Joachim}},
booktitle = {{arXiv:2112.11073}},
pages = {{60}},
title = {{{Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters}}},
year = {{2021}},
}
@article{31261,
abstract = {{Abstract
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.}},
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{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}}},
volume = {{3}},
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}},
}
@inbook{31585,
author = {{Rezat, Sebastian}},
booktitle = {{Mathematics Education in the Digital Age. Learning, Practice and Theory}},
editor = {{Clark-Wilson, A.}},
pages = {{168--184}},
publisher = {{Routledge}},
title = {{{Challenges of making sense of tasks and automated feedback in digital mathematics textbooks}}},
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}},
}
@unpublished{32099,
author = {{Weich, Tobias and Budde, Julia}},
booktitle = {{arXiv:2103.02968v1}},
title = {{{Wave Front Sets of Nilpotent Lie Group Representations}}},
year = {{2021}},
}
@unpublished{32097,
author = {{Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin}},
booktitle = {{arXiv:2103.12127}},
title = {{{SRB Measures of Anosov Actions}}},
year = {{2021}},
}