@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{7767, author = {{Schumacher, Jan}}, booktitle = {{Beiträge zum Mathematikunterricht 2017}}, editor = {{Kortenkamp, Ulrich and Kuzle, Ana}}, publisher = {{WTM-Verlag}}, title = {{{Sinnkonstruktion beim Erkunden von Mustern und Strukturen}}}, year = {{2017}}, } @inproceedings{8559, author = {{Liebendörfer, Michael and Hochmuth, Reinhard}}, booktitle = {{Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings}}, editor = {{Göller, Robin and Biehler, Rolf and Hochmuth, Reinhard and Rück, Hans-Georg}}, pages = {{286--293}}, publisher = {{Universität Kassel}}, title = {{{Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations}}}, year = {{2017}}, } @article{8564, author = {{Liebendörfer, Michael and Schukajlow, Stanislaw}}, issn = {{1863-9690, 1863-9704}}, journal = {{ZDM}}, number = {{3}}, pages = {{355--366}}, title = {{{Interest development during the first year at university: do mathematical beliefs predict interest in mathematics?}}}, doi = {{10.1007/s11858-016-0827-3}}, volume = {{49}}, 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}}, } @phdthesis{10594, abstract = {{Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. Since – in contrast to the solution of a single objective optimization problem – the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging. This is even more the case when many problems have to be solved, when the number of objectives is high, or when the objectives are costly to evaluate. Consequently, this thesis is devoted to the identification and exploitation of structure both in the Pareto set and the dynamics of the underlying model as well as to the development of efficient algorithms for solving problems with additional parameters, with a high number of objectives or with PDE-constraints. These three challenges are addressed in three respective parts. In the first part, predictor-corrector methods are extended to entire Pareto sets. When certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent space can be approximated numerically which yields a direction for the predictor step. In the corrector step, the predicted set converges to the Pareto set at a new parameter value. The resulting algorithm is applied to an example from autonomous driving. In the second part, the hierarchical structure of Pareto sets is investigated. When considering a subset of the objectives, the resulting solution is a subset of the Pareto set of the original problem. Under additional smoothness assumptions, the respective subsets are located on the boundary of the Pareto set of the full problem. This way, the “skeleton” of a Pareto set can be computed and due to the exponential increase in computing time with the number of objectives, the computations of these subsets are significantly faster which is demonstrated using an example from industrial laundries. In the third part, PDE-constrained multiobjective optimal control problems are addressed by reduced order modeling methods. Reduced order models exploit the structure in the system dynamics, for example by describing the dynamics of only the most energetic modes. The model reduction introduces an error in both the function values and their gradients, which has to be taken into account in the development of algorithms. Both scalarization and set-oriented approaches are coupled with reduced order modeling. Convergence results are presented and the numerical benefit is investigated. The algorithms are applied to semi-linear heat flow problems as well as to the Navier-Stokes equations. }}, author = {{Peitz, Sebastian}}, title = {{{ Exploiting structure in multiobjective optimization and optimal control}}}, doi = {{10.17619/UNIPB/1-176}}, year = {{2017}}, } @inbook{31814, author = {{Häsel-Weide, Uta}}, booktitle = {{Mit Heterogenität im Mathematikunterricht umgehen lernen – Konzepte und Perspektiven für eine zentrale Anforderung an die Lehrerbildung}}, editor = {{Leuders, J. and Leuders, T. and Ruwisch, S. and Prediger, S.}}, isbn = {{978-3658169022}}, pages = {{17--28}}, publisher = {{Springer Spektrum}}, title = {{{Inklusiven Mathematikunterricht gestalten. Anforderungen an die Lehrerausbildung.}}}, year = {{2017}}, } @inproceedings{31816, author = {{Häsel-Weide, Uta}}, booktitle = {{Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education}}, editor = {{Dooley, T. and Gueudet, G.}}, pages = {{1292--1299}}, publisher = {{DCU Institude of Education and ERME}}, title = {{{Occasions for productive interactions in inclusives mathematics classrooms that arise following mistakes. }}}, year = {{2017}}, } @book{31856, editor = {{Häsel-Weide, Uta and Nührenbörger, M.}}, isbn = {{978-3-941649-22-4}}, pages = {{297}}, publisher = {{Grundschulverband e. V.}}, title = {{{Gemeinsam Mathematik lernen. Mit allen Kindern rechnen.}}}, year = {{2017}}, } @misc{31852, author = {{Häsel-Weide, Uta and Breucker, T. and Nührenbörger, Marcus}}, publisher = {{Klett}}, title = {{{Förderheft zum Zahlenbuch 1}}}, year = {{2017}}, } @misc{31853, author = {{Häsel-Weide, Uta and Nührenbörger, M.}}, publisher = {{Klett}}, title = {{{Förderkommentar Lernen zum Zahlenbuch 1}}}, year = {{2017}}, } @misc{31854, author = {{Häsel-Weide, Uta}}, publisher = {{Klett}}, title = {{{Das Zahlenbuch. Förderkommentar Lernen zum 2. Schuljahr}}}, year = {{2017}}, } @misc{31855, author = {{Häsel-Weide, Uta and Nührenbörger, M.}}, publisher = {{Klett}}, title = {{{Das Zahlenbuch 2. Förderheft.}}}, year = {{2017}}, } @inbook{31861, author = {{Häsel-Weide, Uta and Nührenbörger, M.}}, booktitle = {{Inklusiver Unterricht in der Grundschule}}, editor = {{Helmich, F. and Blumberg, E.}}, pages = {{213--228}}, publisher = {{Kohlhammer}}, title = {{{Produktives Fördern im inklusiven Mathematikunterricht - Möglichkeiten einer mathematisch ausgerichteten Diagnose und individuellen Förderung.}}}, year = {{2017}}, } @inbook{31862, author = {{Häsel-Weide, Uta and Prediger, S.}}, booktitle = {{Basiswissen Lehrerbildung: Mathematik unterrichten}}, editor = {{Abshagen, M. and Barzel, B. and Kramer, J. and Riecke-Baulecke, T. and Rösken-Winter, B. and Selter, C.}}, pages = {{167--181}}, publisher = {{Klett Kallmeyer}}, title = {{{Förderung und Diagnose im Mathematikunterricht - Begriffe, Planungsfragen und Ansätze.}}}, year = {{2017}}, }