@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{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},
keyword = {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},
}
@article{10596,
author = {Schütze, Oliver and Cuate, Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael},
issn = {0305-215X},
journal = {Engineering Optimization},
pages = {1--24},
title = {{Pareto Explorer: a global/local exploration tool for many-objective optimization problems}},
doi = {10.1080/0305215x.2019.1617286},
year = {2019},
}
@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 = {Semiotische Perspektiven auf das Lernen von Mathematik II},
editor = {Kadunz, Gert},
publisher = {Springer},
title = {{Rekonstruktion diagrammatischen Schließens beim Erlernen der Subtraktion negativer Zahlen. Vergleich zweier methodischer Zugänge}},
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{10597,
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},
}
@article{8753,
author = {Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael},
issn = {0167-8019},
journal = {Acta Applicandae Mathematicae},
number = {1},
pages = {171–199},
title = {{Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}},
doi = {10.1007/s10440-018-0209-7},
volume = {161},
year = {2019},
}
@misc{8482,
author = {Jurgelucks, Benjamin and Schulze, Veronika and Feldmann, Nadine and Claes, Leander},
title = {{Arbitrary sensitivity for inverse problems in piezoelectricity}},
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{21,
abstract = {We address the general mathematical problem of computing the inverse p-th
root of a given matrix in an efficient way. A new method to construct iteration
functions that allow calculating arbitrary p-th roots and their inverses of
symmetric positive definite matrices is presented. We show that the order of
convergence is at least quadratic and that adaptively adjusting a parameter q
always leads to an even faster convergence. In this way, a better performance
than with previously known iteration schemes is achieved. The efficiency of the
iterative functions is demonstrated for various matrices with different
densities, condition numbers and spectral radii.},
author = {Richters, Dorothee and Lass, Michael and Walther, Andrea and Plessl, Christian and Kühne, Thomas},
journal = {Communications in Computational Physics},
number = {2},
pages = {564--585},
publisher = {Global Science Press},
title = {{A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices}},
doi = {10.4208/cicp.OA-2018-0053},
volume = {25},
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},
}
@inproceedings{13106,
author = {Schumacher, Jan},
booktitle = {Beiträge zum Mathematikunterricht 2019},
location = {Regensburg},
title = {{Rekonstruktion diagrammatischen Schließens am Beispiel der Subtraktion negativer Zahlen}},
year = {2019},
}
@inbook{8573,
author = {Liebendörfer, Michael},
booktitle = {Beiträge zum Mathematikunterricht 2018},
editor = {Didaktik der Mathematik der Universität Paderborn, Fachgruppe},
pages = {1171--1174},
publisher = {WTM-Verlag},
title = {{Psychologische Grundbedürfnisse im frühen Mathematikstudium}},
year = {2018},
}
@article{8751,
author = {Peitz, Sebastian and Dellnitz, Michael},
issn = {2297-8747},
journal = {Mathematical and Computational Applications},
number = {2},
title = {{A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction}},
doi = {10.3390/mca23020030},
volume = {23},
year = {2018},
}
@inbook{8574,
author = {Liebendörfer, Michael and Kuklinski, Christiane and Hochmuth, Reinhard},
booktitle = {Beiträge zum Mathematikunterricht 2018},
editor = {Didaktik der Mathematik der Universität Paderborn, Fachgruppe},
pages = {1175--1178},
publisher = {WTM-Verlag},
title = {{Auswirkungen von innovativen Vorlesungen für Lehramtsstudierende in der Studieneingangsphase}},
year = {2018},
}
@inproceedings{7766,
author = {Schumacher, Jan},
booktitle = {Beiträge zum Mathematikunterricht 2018},
publisher = {WTM-Verlag},
title = {{Semiotische Analyse von Sinnkonstruktionsprozessen bei einem innermathematischen Zugang zum Erlernen negativer Zahlen}},
year = {2018},
}
@article{10142,
author = {Steffen, Eckhard},
journal = {Australasian Journal of Combinatorics},
number = {1},
pages = {153--160},
title = {{Approximating Vizing’s independence number conjecture}},
volume = {71},
year = {2018},
}
@article{8757,
author = {Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan},
issn = {1617-7061},
journal = {PAMM},
pages = {51--54},
title = {{POD-based multiobjective optimal control of PDEs with non-smooth objectives}},
doi = {10.1002/pamm.201710015},
year = {2018},
}
@inproceedings{8575,
abstract = {The transition from high school to university mathematics has proven to be difficult for many students but especially for pre-service secondary teachers. To support these students at mastering this transition, various universities have introduced support measures of various kinds. The WiGeMath project developed a taxonomy that makes it possible to describe and compare these measures concerning their goals as well as their frame characteristics. We will exemplify the use of the taxonomy in the description of one specific innovative measure that was part of the WiGeMath evaluations. Moreover, we will present first results concerning the goal-fulfilment of this measure concerning affective characteristics of the student cohort and their predominant beliefs.},
author = {Kuklinski, Christiane and Leis, Elena and Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Lankeit, Elisa and Neuhaus, Silke and Schaper, Niclas and Schürmann, Mirko},
booktitle = {Proceedings of the Second Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018, 5-7 April 2018)},
editor = {Durand-Guerrier, V. and Hochmuth, R. and Goodchild, S. and Hogstad, N.M.},
keyword = {Beliefs., Motivational developments, Novel approaches to teaching, Teacher education, Transition to and across university mathematics},
pages = {527--536},
publisher = {INDRUM Network, University of Agder},
title = {{Evaluating Innovative Measures in University Mathematics – The Case of Affective Outcomes in a Lecture focused on Problem-Solving}},
year = {2018},
}
@article{10129,
abstract = {There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measuring how far apart a non 3-edge-colorable graph is from being 3-edge-colorable. We study their interrelation and prove some new results. Besides getting new insight into the structure of snarks, we show that such measures give partial results with respect to these important conjectures. The paper closes with a list of open problems and conjectures.},
author = {Fiol, M. A. and Mazzuoccolo, Guiseppe and Steffen, Eckhard},
journal = {The Electronic Journal of Combinatorics},
keyword = {Cubic graph, Tait coloring, Snark, Boole coloring, Berge's conjecture, Tutte's 5-flow conjecture},
number = {4},
title = {{Measures of Edge-Uncolorability of Cubic Graphs}},
volume = {25},
year = {2018},
}