@inproceedings{29427,
  author       = {{Jiménez, F. and Ober-Blöbaum, Sina}},
  booktitle    = {{6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018}},
  pages        = {{50--55}},
  title        = {{{A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings}}},
  volume       = {{51(3)}},
  year         = {{2018}},
}

@misc{45974,
  author       = {{Kovács, Balázs}},
  title        = {{{Numerical analysis of partial differential equations on and of evolving surfaces}}},
  year         = {{2018}},
}

@article{45950,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>}},
  author       = {{Karátson, János and Kovács, Balázs and Korotov, Sergey}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{2}},
  pages        = {{1241--1265}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}}},
  doi          = {{10.1093/imanum/dry086}},
  volume       = {{40}},
  year         = {{2018}},
}

@article{45949,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>}},
  author       = {{Karátson, János and Kovács, Balázs and Korotov, Sergey}},
  issn         = {{0272-4979}},
  journal      = {{IMA Journal of Numerical Analysis}},
  keywords     = {{Applied Mathematics, Computational Mathematics, General Mathematics}},
  number       = {{2}},
  pages        = {{1241--1265}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary}}},
  doi          = {{10.1093/imanum/dry086}},
  volume       = {{40}},
  year         = {{2018}},
}

@article{45947,
  author       = {{Kovács, Balázs and Lubich, Christian}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  keywords     = {{Applied Mathematics, Computational Mathematics}},
  number       = {{1}},
  pages        = {{121--152}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Linearly implicit full discretization of surface evolution}}},
  doi          = {{10.1007/s00211-018-0962-6}},
  volume       = {{140}},
  year         = {{2018}},
}

@article{45951,
  author       = {{Kovács, Balázs}},
  issn         = {{0749-159X}},
  journal      = {{Numerical Methods for Partial Differential Equations}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Numerical Analysis, Analysis}},
  number       = {{3}},
  pages        = {{1093--1112}},
  publisher    = {{Wiley}},
  title        = {{{Computing arbitrary Lagrangian Eulerian maps for evolving surfaces}}},
  doi          = {{10.1002/num.22340}},
  volume       = {{35}},
  year         = {{2018}},
}

@phdthesis{55291,
  author       = {{Technau, Marc}},
  publisher    = {{University of Würzburg}},
  title        = {{{On Beatty sets and some generalisations thereof}}},
  doi          = {{10.25972/WUP-978-3-95826-089-4}},
  year         = {{2018}},
}

@article{34843,
  abstract     = {{A polynomial time algorithm to find generators of the lattice of all subfields of a given number field was given in van Hoeij et al. (2013).

This article reports on a massive speedup of this algorithm. This is primary achieved by our new concept of Galois-generating subfields. In general this is a very small set of subfields that determine all other subfields in a group-theoretic way. We compute them by targeted calls to the method from van Hoeij et al. (2013). For an early termination of these calls, we give a list of criteria that imply that further calls will not result in additional subfields.

Finally, we explain how we use subfields to get a good starting group for the computation of Galois groups.}},
  author       = {{Elsenhans, Andreas-Stephan and Klüners, Jürgen}},
  issn         = {{0747-7171}},
  journal      = {{Journal of Symbolic Computation}},
  keywords     = {{Computational Mathematics, Algebra and Number Theory}},
  pages        = {{1--20}},
  publisher    = {{Elsevier BV}},
  title        = {{{Computing subfields of number fields and applications to Galois group computations}}},
  doi          = {{10.1016/j.jsc.2018.04.013}},
  volume       = {{93}},
  year         = {{2018}},
}

@inbook{42788,
  abstract     = {{We classify all one-class genera of admissible lattice chains of length at least 2 in hermitian spaces over number fields. If L is a lattice in the chain and p the prime ideal dividing the index of the lattices in the chain, then the {p}-arithmetic group Aut(L{p}) acts chamber transitively on the corresponding Bruhat-Tits building. So our classification provides a step forward to a complete classification of these chamber transitive groups which has been announced 1987 (without a detailed proof) by Kantor, Liebler and Tits. In fact we find all their groups over number fields and one additional building with a discrete chamber transitive group.}},
  author       = {{Kirschmer, Markus and Nebe, Gabriele}},
  booktitle    = {{Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory}},
  isbn         = {{9783319705651}},
  publisher    = {{Springer International Publishing}},
  title        = {{{One Class Genera of Lattice Chains Over Number Fields}}},
  doi          = {{10.1007/978-3-319-70566-8_22}},
  year         = {{2018}},
}

@article{42790,
  abstract     = {{We show that exceptional algebraic groups over number fields do not admit one-class genera of parahoric groups, except in the case G₂ . For the group G₂, we enumerate all such one-class genera for the usual seven-dimensional representation.}},
  author       = {{Kirschmer, Markus}},
  issn         = {{1246-7405}},
  journal      = {{Journal de Théorie des Nombres de Bordeaux}},
  keywords     = {{Algebra and Number Theory}},
  number       = {{3}},
  pages        = {{847--857}},
  publisher    = {{Cellule MathDoc/CEDRAM}},
  title        = {{{One-class genera of exceptional groups over number fields}}},
  doi          = {{10.5802/jtnb.1052}},
  volume       = {{30}},
  year         = {{2018}},
}

@article{6571,
  author       = {{Jurgelucks, Benjamin and Claes, Leander and Walther, Andrea and Henning, Bernd}},
  issn         = {{1055-6788}},
  journal      = {{Optimization Methods and Software}},
  number       = {{4-6}},
  pages        = {{868----888}},
  publisher    = {{Taylor and Francis Ltd.}},
  title        = {{{Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation}}},
  doi          = {{10.1080/10556788.2018.1435652}},
  volume       = {{33}},
  year         = {{2018}},
}

@unpublished{19940,
  abstract     = {{Two smooth map germs are right-equivalent if and only if they generate two
Lagrangian submanifolds in a cotangent bundle which have the same contact with
the zero-section. In this paper we provide a reverse direction to this
classical result of Golubitsky and Guillemin. Two Lagrangian submanifolds of a
symplectic manifold have the same contact with a third Lagrangian submanifold
if and only if the intersection problems correspond to stably right equivalent
map germs. We, therefore, obtain a correspondence between local Lagrangian
intersection problems and catastrophe theory while the classical version only
captures tangential intersections. The correspondence is defined independently
of any Lagrangian fibration of the ambient symplectic manifold, in contrast to
other classical results. Moreover, we provide an extension of the
correspondence to families of local Lagrangian intersection problems. This
gives rise to a framework which allows a natural transportation of the notions
of catastrophe theory such as stability, unfolding and (uni-)versality to the
geometric setting such that we obtain a classification of families of local
Lagrangian intersection problems. An application is the classification of
Lagrangian boundary value problems for symplectic maps.}},
  author       = {{Offen, Christian}},
  booktitle    = {{arXiv:1811.10165}},
  title        = {{{Local intersections of Lagrangian manifolds correspond to catastrophe  theory}}},
  year         = {{2018}},
}

@article{19943,
  abstract     = {{In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group action by conformal symplectic symmetries has the effect that the flow map cannot degenerate in a direction which is tangential to the action. This imposes restrictions on which singularities can occur in boundary value problems. Our results generalise classical results about conjugate loci on Riemannian manifolds to a large class of Hamiltonian boundary value problems with, for example, scaling symmetries. }},
  author       = {{McLachlan, Robert I and Offen, Christian}},
  journal      = {{New Zealand Journal of Mathematics}},
  keywords     = {{Hamiltonian boundary value problems, singularities, conformal symplectic geometry, catastrophe theory, conjugate loci}},
  pages        = {{83--99}},
  title        = {{{Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci}}},
  doi          = {{10.53733/34 }},
  volume       = {{48}},
  year         = {{2018}},
}

@article{21938,
  author       = {{Nüske, Feliks and Wu, Hao and Prinz, Jan-Hendrik and Wehmeyer, Christoph and Clementi, Cecilia and Noé, Frank}},
  issn         = {{0021-9606}},
  journal      = {{The Journal of Chemical Physics}},
  title        = {{{Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias}}},
  doi          = {{10.1063/1.4976518}},
  year         = {{2017}},
}

@article{21939,
  author       = {{Wu, Hao and Nüske, Feliks and Paul, Fabian and Klus, Stefan and Koltai, Péter and Noé, Frank}},
  issn         = {{0021-9606}},
  journal      = {{The Journal of Chemical Physics}},
  title        = {{{Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations}}},
  doi          = {{10.1063/1.4979344}},
  year         = {{2017}},
}

@inproceedings{8752,
  abstract     = {{In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated into a subdivision algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.}},
  author       = {{Peitz, Sebastian and Dellnitz, Michael}},
  booktitle    = {{NEO 2016}},
  isbn         = {{9783319640624}},
  issn         = {{1860-949X}},
  pages        = {{159--182}},
  title        = {{{Gradient-Based Multiobjective Optimization with Uncertainties}}},
  doi          = {{10.1007/978-3-319-64063-1_7}},
  year         = {{2017}},
}

@inproceedings{6572,
  author       = {{Jurgelucks, Benjamin and Feldmann, Nadine and Claes, Leander and Henning, Bernd and Walther, Andrea}},
  booktitle    = {{Proceedings of Meetings on Acoustics}},
  pages        = {{030010}},
  title        = {{{Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity}}},
  doi          = {{10.1121/2.0000707}},
  year         = {{2017}},
}

@article{16540,
  author       = {{Dellnitz, Michael and Klus, Stefan}},
  issn         = {{1468-9367}},
  journal      = {{Dynamical Systems}},
  pages        = {{61--79}},
  title        = {{{Sensing and control in symmetric networks}}},
  doi          = {{10.1080/14689367.2016.1215410}},
  year         = {{2017}},
}

@article{16581,
  author       = {{Dellnitz, Michael and Klus, Stefan and Ziessler, Adrian}},
  issn         = {{1536-0040}},
  journal      = {{SIAM Journal on Applied Dynamical Systems}},
  pages        = {{120--138}},
  title        = {{{A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty}}},
  doi          = {{10.1137/16m1072735}},
  year         = {{2017}},
}

@article{16657,
  author       = {{Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}},
  issn         = {{2405-8963}},
  journal      = {{IFAC-PapersOnLine}},
  pages        = {{8674--8679}},
  title        = {{{A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).}}},
  doi          = {{10.1016/j.ifacol.2017.08.1526}},
  year         = {{2017}},
}