@article{21944, author = {{Nüske, Feliks and Boninsegna, Lorenzo and Clementi, Cecilia}}, issn = {{0021-9606}}, journal = {{The Journal of Chemical Physics}}, title = {{{Coarse-graining molecular systems by spectral matching}}}, doi = {{10.1063/1.5100131}}, year = {{2019}}, } @inbook{8577, author = {{Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard}}, booktitle = {{Beiträge zum Mathematikunterricht 2019}}, title = {{{Erklärung von Mathematikleistung im Ingenieursstudium}}}, year = {{2019}}, } @article{16709, author = {{Sahai, Tuhin and Ziessler, Adrian and Klus, Stefan and Dellnitz, Michael}}, issn = {{0924-090X}}, journal = {{Nonlinear Dynamics}}, title = {{{Continuous relaxations for the traveling salesman problem}}}, doi = {{10.1007/s11071-019-05092-5}}, year = {{2019}}, } @article{10593, abstract = {{We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables. A numerical approximation of the Koopman operator therefore yields a linear system for the observation of an autonomous dynamical system. In our approach, by introducing a finite number of constant controls, the dynamic control system is transformed into a set of autonomous systems and the corresponding optimal control problem into a switching time optimization problem. This allows us to replace each of these systems by a K-ROM which can be solved orders of magnitude faster. By this approach, a nonlinear infinite-dimensional control problem is transformed into a low-dimensional linear problem. Using a recent convergence result for the numerical approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the value of the K-ROM based objective function converges in measure to the value of the full objective function. To illustrate the results, we consider the 1D Burgers equation and the 2D Navier–Stokes equations. The numerical experiments show remarkable performance concerning both solution times and accuracy.}}, author = {{Peitz, Sebastian and Klus, Stefan}}, issn = {{0005-1098}}, journal = {{Automatica}}, pages = {{184--191}}, title = {{{Koopman operator-based model reduction for switched-system control of PDEs}}}, doi = {{10.1016/j.automatica.2019.05.016}}, volume = {{106}}, year = {{2019}}, } @article{10595, abstract = {{In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set.}}, author = {{Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}}, issn = {{0925-5001}}, journal = {{Journal of Global Optimization}}, number = {{4}}, pages = {{891--913}}, title = {{{On the hierarchical structure of Pareto critical sets}}}, doi = {{10.1007/s10898-019-00737-6}}, volume = {{73}}, year = {{2019}}, } @inproceedings{10597, abstract = {{In comparison to classical control approaches in the field of electrical drives like the field-oriented control (FOC), model predictive control (MPC) approaches are able to provide a higher control performance. This refers to shorter settling times, lower overshoots, and a better decoupling of control variables in case of multi-variable controls. However, this can only be achieved if the used prediction model covers the actual behavior of the plant sufficiently well. In case of model deviations, the performance utilizing MPC remains below its potential. This results in effects like increased current ripple or steady state setpoint deviations. In order to achieve a high control performance, it is therefore necessary to adapt the model to the real plant behavior. When using an online system identification, a less accurate model is sufficient for commissioning of the drive system. In this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system identification is proposed. The method does not require high-frequency signal injection, but uses the measured values already required for the FCS-MPC. An evaluation of the least squares-based identification on a laboratory test bench showed that the model accuracy and thus the control performance could be improved by an online update of the prediction models.}}, author = {{Hanke, Soren and Peitz, Sebastian and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}}, booktitle = {{2019 IEEE International Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE)}}, isbn = {{9781538694145}}, title = {{{Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous Motor Application with Online Least Squares System Identification}}}, doi = {{10.1109/precede.2019.8753313}}, year = {{2019}}, } @inproceedings{13106, author = {{Schumacher, Jan}}, booktitle = {{Beiträge zum Mathematikunterricht 2019}}, location = {{Regensburg}}, title = {{{Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen}}}, year = {{2019}}, } @inproceedings{13107, abstract = {{In this paper, we first outline a Hypothetical Learning Trajectory (HLT), which aims at a formal understanding of the rules for manipulating integers. The HLT is based on task formats, which promote algebraic thinking in terms of generalizing rules from the analysis of patterns and should be familiar to students from their mathematics education experiences in elementary school. Second, we analyze two students' actual learning process based on Peircean semiotics. The analysis shows that the actual learning process diverges from the hypothesized learning process in that the students do not relate the different levels of the diagrams in a way that allows them to extrapolate the rule for the subtraction of negative numbers. Based on this finding, we point out consequences for the design of the tasks.}}, author = {{Schumacher, Jan and Rezat, Sebastian}}, booktitle = {{Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)}}, editor = {{Jankvist, Uffe Thomas and Van den Heuvel-Panhuizen, Marja and Veldhuis, Michiel}}, keywords = {{diagrammatic reasoning, hypothetical learning trajectory, induction extrapolatory method, integers, negative numbers, permanence principle, semiotics}}, location = {{Utrecht}}, publisher = {{Freudenthal Group & Freudenthal Institute, Utrecht University and ERME}}, title = {{{A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers}}}, year = {{2019}}, } @book{13139, editor = {{Rezat, Sebastian and Fan, Lianghuo and Hattermann, Mathias and Schumacher, Jan and Wuschke, Holger}}, location = {{Paderborn}}, pages = {{392}}, publisher = {{Universitätsbibliothek Paderborn}}, title = {{{Proceedings of the Third International Conference on Mathematics Textbook Research and Development: 16-19 September 2019 Paderborn, Germany}}}, doi = {{10.17619/UNIPB/1-768}}, year = {{2019}}, } @inproceedings{32089, author = {{Häsel-Weide, Uta and Nührenbörger, M.}}, booktitle = {{Proceedings of the Third International Conference on Mathematics Textbook Research an Development}}, editor = {{Rezat, Sebastian and Fan, L. and Hattermann, M. and Schumacher, J. and Wuschke, H.}}, pages = {{185--190}}, title = {{{Materials für inclusive mathematics education - Design principles an practices.}}}, year = {{2019}}, } @article{32090, author = {{Breucker, T. and Freesemann, O. and Häsel-Weide, Uta and Opitz, E. M. and Nührenbörger, M. and Wittich, C.}}, journal = {{Zeitschrift für Heilpädagogik}}, number = {{70}}, pages = {{316--326}}, title = {{{Fördern im inklusiven Mathematikunterricht im Spannungsfeld zwischen gemeinsamen Lernsituationen und gezielter Förderung.}}}, year = {{2019}}, } @misc{32091, author = {{Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}}, isbn = {{978-3122009946}}, pages = {{80}}, publisher = {{Klett}}, title = {{{Das Zahlenbuch 4. Förderheft}}}, year = {{2019}}, } @misc{31954, author = {{Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}}, isbn = {{ 978-3-12-200998-4}}, pages = {{144}}, publisher = {{Klett}}, title = {{{Das Zahlenbuch. Förderkommentar Lernen zum 4. Schuljahr}}}, year = {{2019}}, } @inbook{32092, author = {{Häsel-Weide, Uta}}, booktitle = {{Zwischen Persönlichkeitsbildung und Leistungsentwicklung. Fachspezifische Zugänge zu inklusivem Unterricht}}, editor = {{Baumert, B. and Willen, M.}}, isbn = {{ 978-3781523234}}, pages = {{175--181}}, publisher = {{Klinkhardt}}, title = {{{Lernumgebungen für den inklusiven Mathematikunterricht zwischen reichhaltiger Offenheit und fokussierter Förderung}}}, year = {{2019}}, } @article{34672, author = {{Black, Tobias}}, issn = {{1937-1179}}, journal = {{Discrete & Continuous Dynamical Systems - S}}, keywords = {{Applied Mathematics, Discrete Mathematics and Combinatorics, Analysis}}, number = {{2}}, pages = {{119--137}}, publisher = {{American Institute of Mathematical Sciences (AIMS)}}, title = {{{Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity}}}, doi = {{10.3934/dcdss.2020007}}, volume = {{13}}, year = {{2019}}, } @article{34669, author = {{Black, Tobias}}, issn = {{1422-6928}}, journal = {{Journal of Mathematical Fluid Mechanics}}, keywords = {{Applied Mathematics, Computational Mathematics, Condensed Matter Physics, Mathematical Physics}}, number = {{1}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The Stokes Limit in a Three-Dimensional Chemotaxis-Navier–Stokes System}}}, doi = {{10.1007/s00021-019-0464-z}}, volume = {{22}}, year = {{2019}}, } @article{34668, author = {{Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}}, issn = {{0170-4214}}, journal = {{Mathematical Methods in the Applied Sciences}}, keywords = {{General Engineering, General Mathematics}}, number = {{9}}, pages = {{3002--3020}}, publisher = {{Wiley}}, title = {{{A Keller‐Segel‐fluid system with singular sensitivity: Generalized solutions}}}, doi = {{10.1002/mma.5561}}, volume = {{42}}, year = {{2019}}, } @article{34671, author = {{Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}}, issn = {{0003-6811}}, journal = {{Applicable Analysis}}, keywords = {{Applied Mathematics, Analysis}}, number = {{16}}, pages = {{2877--2891}}, publisher = {{Informa UK Limited}}, title = {{{Stabilization in the Keller–Segel system with signal-dependent sensitivity}}}, doi = {{10.1080/00036811.2019.1585534}}, volume = {{99}}, year = {{2019}}, } @article{31265, author = {{Dyatlov, Semyon and Borthwick, David and Weich, Tobias}}, issn = {{1435-9855}}, journal = {{Journal of the European Mathematical Society}}, keywords = {{Applied Mathematics, General Mathematics}}, number = {{6}}, pages = {{1595--1639}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich}}}, doi = {{10.4171/jems/867}}, volume = {{21}}, year = {{2019}}, } @misc{31383, author = {{Hoffmann, Max}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{117–118}}, title = {{{Rezension: Klaus Volkert: In höheren Räumen – Der Weg der Geometrie in die vierte Dimension}}}, doi = {{10.1007/s00591-018-00244-x}}, volume = {{66}}, year = {{2019}}, }