@article{37351, author = {{Tao, Youshan and Winkler, Michael}}, journal = {{Nonlinear Analysis}}, title = {{{A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy.}}}, volume = {{198}}, year = {{2020}}, } @article{37349, author = {{Stinner, Christian and Winkler, Michael}}, journal = {{Discrete and Continuous Dynamical Systems --A}}, pages = {{4039--4058}}, title = {{{Refined regularity and stabilization properties in a degenerate haptotaxis system}}}, volume = {{40}}, year = {{2020}}, } @inbook{35820, author = {{Biehler, Rolf and Liebendörfer, Michael and Schmitz, Angela and Fleischmann, Yael and Krämer, Sandra and Ostsieker, Laura and Schlüter, Sarah}}, booktitle = {{Beiträge zum Mathematikunterricht 2020}}, editor = {{Siller, H.-S. and Weigel, W. and Wörler, J. F.}}, publisher = {{WTM}}, title = {{{studiVEMINTvideos – Mathematische Lernvideos zur Studienvorbereitung und Unterstützung im ersten Studienjahr}}}, doi = {{10.17877/DE290R-21234}}, year = {{2020}}, } @article{37660, author = {{Rösler, Margit}}, issn = {{0022-1236}}, journal = {{Journal of Functional Analysis}}, keywords = {{Analysis}}, number = {{12}}, publisher = {{Elsevier BV}}, title = {{{Riesz distributions and Laplace transform in the Dunkl setting of type A}}}, doi = {{10.1016/j.jfa.2020.108506}}, volume = {{278}}, year = {{2020}}, } @article{40051, author = {{Luks, Tomasz and Xiao, Yimin}}, issn = {{0894-9840}}, journal = {{Journal of Theoretical Probability}}, number = {{1}}, pages = {{153--179}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Multiple Points of Operator Semistable Lévy Processes}}}, doi = {{10.1007/s10959-018-0859-4}}, volume = {{33}}, year = {{2020}}, } @article{37339, author = {{Steiner, Evi and Winkler, Michael}}, journal = {{Journal of Nonlinear Science}}, pages = {{1809--1847}}, title = {{{Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow}}}, volume = {{30}}, year = {{2020}}, } @article{34842, abstract = {{Let D<0 be a fundamental discriminant and denote by E(D) the exponent of the ideal class group Cl(D) of K=ℚ(√D). Under the assumption that no Siegel zeros exist we compute all such D with E(D) dividing 8. We compute all D with |D| ≤ 3.1⋅10²⁰ such that E(D) ≤ 8.}}, author = {{Elsenhans, Andreas-Stephan and Klüners, Jürgen and Nicolae, Florin}}, issn = {{0065-1036}}, journal = {{Acta Arithmetica}}, keywords = {{Algebra and Number Theory}}, number = {{3}}, pages = {{217--233}}, publisher = {{Institute of Mathematics, Polish Academy of Sciences}}, title = {{{Imaginary quadratic number fields with class groups of small exponent}}}, doi = {{10.4064/aa180220-20-3}}, volume = {{193}}, year = {{2020}}, } @article{34841, abstract = {{We give an exact formula for the number of G-extensions of local function fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application we give a lower bound for the corresponding counting problem by discriminant. }}, author = {{Klüners, Jürgen and Müller, Raphael}}, issn = {{0022-314X}}, journal = {{Journal of Number Theory}}, keywords = {{Algebra and Number Theory}}, pages = {{311--322}}, publisher = {{Elsevier BV}}, title = {{{The conductor density of local function fields with abelian Galois group}}}, doi = {{10.1016/j.jnt.2019.11.007}}, volume = {{212}}, year = {{2020}}, } @article{44331, abstract = {{In this paper, we study properties of the algebras of planar quasi-invariants. These algebras are Cohen–Macaulay and Gorenstein in codimension one. Using the technique of matrix problems, we classify all Cohen–Macaulay modules of rank one over them and determine their Picard groups. In terms of this classification, we describe the spectral modules of the planar rational Calogero–Moser systems. Finally, we elaborate the theory of the algebraic inverse scattering method, providing explicit computations of some ‘isospectral deformations’ of the planar rational Calogero–Moser system in the case of the split rational potential.}}, author = {{Burban, Igor and Zheglov, A.}}, journal = {{Proceedings of the London Mathematical Society}}, number = {{4}}, pages = {{1033–1082}}, title = {{{Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems}}}, doi = {{10.1112/plms.12341}}, volume = {{121}}, year = {{2020}}, } @inbook{45385, author = {{Dröse, Jennifer and Prediger, Susanne}}, booktitle = {{Sprachbildender Mathematikunterricht in der Sekundarstufe - ein forschungsbasiertes Praxisbuch }}, editor = {{Prediger, Susanne}}, pages = {{86--94}}, publisher = {{Cornelsen}}, title = {{{Lesen lernen von Aufgabentexten}}}, year = {{2020}}, } @inbook{45688, author = {{Bruns, Julia and Vogtländer, A.}}, booktitle = {{Frühe alltagsintegrierte mathematische Bildung. Handreichung für Lehrende}}, editor = {{Born-Rauchecker, E. and Vogtländer, A. and Weber, K.}}, pages = {{37--46}}, publisher = {{Kallmeyer}}, title = {{{Frühe alltagsintegrierte mathematische Bildung. Eine Einleitung}}}, year = {{2020}}, } @article{34816, abstract = {{ZusammenfassungFrühe mathematische Bildung findet in der Kindertagesstätte insbesondere in spontanen Alltagssituationen statt. Damit diese Alltagssituationen zu natürlichen Lernsituationen für die Kinder werden, müssen (angehende) frühpädagogische Fachkräfte zunächst das mathematische Potenzial in diesen Situationen erkennen. Diese Fähigkeit zur situativen Beobachtung und Wahrnehmung ist bisher unzureichend erforscht, was unter anderem auf begrenzte Methoden zur standardisierten Erfassung dieses Konstrukts zurückzuführen ist. Um diesem Bedarf zu begegnen, wurde das videobasierte Testinstrument Vimas_num zur Erfassung der Fähigkeit zur situativen Beobachtung und Wahrnehmung angehender frühpädagogischer Fachpersonen im Bereich Mengen und Zahlen entwickelt. Auf der Grundlage von drei aufeinander aufbauenden Studien wird die Validität verschiedener Aspekte der Testwertinterpretation untersucht. Die Ergebnisse geben Hinweise auf die Validität der Testwertinterpretation in Bezug auf den Testinhalt, die interne Struktur des Tests und die Zusammenhänge mit theoretisch verbundenen Konstrukten.}}, author = {{Bruns, Julia and Strahl, Carolin and Gasteiger, Hedwig}}, issn = {{0340-4099}}, journal = {{Unterrichtswissenschaft}}, keywords = {{Education}}, number = {{3}}, pages = {{345--371}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Situative Beobachtung und Wahrnehmung angehender frühpädagogischer Fachpersonen im Bereich Mathematik – Entwicklung und Validierung eines Testinstruments}}}, doi = {{10.1007/s42010-020-00091-7}}, volume = {{49}}, year = {{2020}}, } @inproceedings{36546, author = {{Meyer, Lena and Tabeling, Laura and Gasteiger, Hedwig and Bruns, Julia}}, booktitle = {{Beiträge zum Mathematikunterricht 2020}}, editor = {{Siller, Hans-Stefan and Weigel, Wolfgang and Wörler, Jan}}, location = {{Würzburg}}, pages = {{1253--1256}}, publisher = {{WTM-Verlag}}, title = {{{Interaktionen in mathematischen Spielsituationen in Kindertagesstätte und Familie}}}, year = {{2020}}, } @article{21529, abstract = {{ZusammenfassungDie Implementation früher mathematischer Bildung in Kindertagesstätten kann durch fachdidaktische Fortbildungen für frühpädagogische Fachkräfte unterstützt werden. Um Fachkräfte in der Breite zu erreichen, erscheint ein scaling up Ansatz geeignet, bei dem aufbauend auf das Fortbildungskonzept EmMa – Erzieherinnen und Erzieher machen Mathematik Multiplikatorinnen und Multiplikatoren qualifiziert werden. Dabei ergibt sich die Herausforderung, dass Fortbildende im Elementarbereich kaum mathematisches und mathematikdidaktisches Wissen mitbringen. Der Kontext dieser Studie ist der scaling up Prozess der Fortbildung EmMa unter diesen Umständen. Das Erkenntnisinteresse liegt in der Beschreibung und Bewertung der Adaptionshandlungen der Multiplikatorinnen und Multiplikatoren. Für die Bewertung der Adaptionen werden zwei Kriterien herangezogen: (1) das Kriterium der Präzision, das die Vollständigkeit und Klarheit der Inhalte umfasst und (2) das Kriterium der fachlichen Korrektheit, das durch das Ausbleiben fachbezogener Fehler beschrieben wird. Analysiert werden dabei die theoretischen, fachbezogenen Phasen der von Multiplikatorinnen und Multiplikatoren durchgeführten Fortbildung zur frühen mathematischen Bildung, da davon ausgegangen wird, dass insbesondere diese theoretischen Inhalte für diese Gruppe von Multiplikatorinnen und Multiplikatoren eine Herausforderung darstellen. Zur Untersuchung wurde eine videogestützte, qualitative Feldstudie mit N = 8 Fällen durchgeführt. Mit Hilfe der qualitativen Inhaltsanalyse wurden die Adaptionshandlungen der Multiplikatorinnen und Multiplikatoren charakterisiert und hinsichtlich ihrer Präzision und der fachlichen Fehler in diesen Adaptionen analysiert. Dabei zeigte sich, dass der eigenständige Umgang mit den mathematischen und mathematikdidaktischen Inhalten des Fortbildungskonzepts EmMa trotz intensiver Unterstützung anspruchsvoll und bei vielen Multiplikatorinnen und Multiplikatoren mit fachbezogenen Fehlern verbunden ist. Implikationen dieser Ergebnisse für die weitere Forschung werden diskutiert.}}, author = {{Bruns, Julia and Schopferer, Theresa and Gasteiger, Hedwig}}, issn = {{0173-5322}}, journal = {{Journal für Mathematik-Didaktik}}, number = {{1}}, pages = {{243--271}}, title = {{{Adaptionshandlungen von Multiplikatorinnen und Multiplikatoren zur frühen mathematischen Bildung – Beschreibung und Bewertung aus fachbezogener Perspektive}}}, doi = {{10.1007/s13138-020-00175-y}}, volume = {{42}}, year = {{2020}}, } @inbook{21530, author = {{Bruns, Julia and Carlsen, Martin and Eichen, Lars and Erfjord, Ingvald and Hundeland, Per Sigurd}}, booktitle = {{Mathematics Education in the Early Years}}, isbn = {{9783030347758}}, pages = {{317–332}}, publisher = {{Springer}}, title = {{{Situational Perception in Mathematics (SPiM)—Results of a Cross-Country Study in Austria and Norway}}}, doi = {{10.1007/978-3-030-34776-5_19}}, year = {{2020}}, } @inproceedings{36539, author = {{Bruns, Julia}}, booktitle = {{Beiträge zum Mathematikunterricht 2020}}, editor = {{Siller, Hans-Stefan and Weigel, Wolfgang and Wörler, Jan}}, location = {{Würzburg}}, pages = {{1245--1248}}, publisher = {{WTM-Verlag}}, title = {{{Mathematisches Fachwissen von frühpädagogischen Fachpersonen im Spannungsfeld zwischen Disziplin- und Praxis}}}, doi = {{10.37626/GA9783959871402.0}}, year = {{2020}}, } @inproceedings{45330, author = {{Schönherr, Johanna and Blomberg, J. and Schukajlow, S. and Rellensmann, J.}}, booktitle = {{Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education: PME}}, editor = {{Inprasitha, M. and Changsri, N. and Boonsena, N.}}, pages = {{46–54}}, title = {{{“Why don’t you make a drawing?" Motivation and strategy use in mathematical modelling}}}, year = {{2020}}, } @article{45338, author = {{Schönherr, Johanna and Schukajlow, S. and Leopold, C.}}, journal = {{ZDM – Mathematics Education}}, number = {{1}}, pages = {{97–110}}, title = {{{Measuring and investigating strategic knowledge about drawing to solve geometry modelling problems}}}, doi = {{10.1007/s11858-019-01085-1}}, volume = {{52}}, year = {{2020}}, } @article{34670, author = {{Black, Tobias}}, issn = {{0218-2025}}, journal = {{Mathematical Models and Methods in Applied Sciences}}, keywords = {{Applied Mathematics, Modeling and Simulation}}, number = {{06}}, pages = {{1075--1117}}, publisher = {{World Scientific Pub Co Pte Lt}}, title = {{{Global generalized solutions to a forager–exploiter model with superlinear degradation and their eventual regularity properties}}}, doi = {{10.1142/s0218202520400072}}, volume = {{30}}, year = {{2020}}, } @article{31376, author = {{Hoffmann, Max}}, journal = {{Der Mathematikunterricht}}, pages = {{36–47}}, title = {{{Zirkel und Lineal ohne Parallelenaxiom: Ein konstruktiver Zugang zur hyperbolischen Geometrie.}}}, volume = {{66 (6)}}, year = {{2020}}, } @article{46159, author = {{Leuders, Timo and Wessel, Lena}}, issn = {{0933-422X}}, journal = {{Pädagogik 2/2020}}, number = {{2}}, pages = {{26--30}}, publisher = {{Beltz Verlagsgruppe}}, title = {{{Differenziertes Üben gestalten. Zwischen Umsetzung in der Praxis und Fundierung in der Forschung.}}}, year = {{2020}}, } @article{46158, author = {{Wessel, Lena and Kuzu, T. and Prediger, Susanne}}, journal = {{Sprachbildender Mathematikunterricht in der Sekundarstufe - ein forschungsbasiertes Praxisbuch}}, pages = {{148–151}}, title = {{{Sprachbildender Vorstellungsaufbau für verschiedene mathematische Konzepte: Brüche in Klasse 6}}}, year = {{2020}}, } @book{48406, author = {{Wessel, Lena and Prediger, S. and Stein, A. and Wijers, M. and Jonker, V.}}, publisher = {{DZLM}}, title = {{{Language for Mathematics in Vocational Contexts. Handbook for teachers and facilitators}}}, year = {{2020}}, } @inbook{48405, author = {{Sprütten, F. and Wessel, Lena and Zentgraf, K. and Prediger, S.}}, booktitle = {{Sprachbildender Mathematikunterricht in der Sekundarstufe. Ein forschungsbasiertes Praxisbuch}}, editor = {{Prediger, S.}}, pages = {{115--130}}, publisher = {{Cornelsen Skriptor}}, title = {{{Fach- und sprachintegrierte Ansätze für Neuzugewanderte}}}, year = {{2020}}, } @article{45383, author = {{Dröse, Jennifer and Prediger, Susanne}}, journal = {{Journal für Mathematik-Didaktik, 41(2)}}, pages = {{399--422}}, title = {{{Enhancing Fifth Graders’ Awareness of Syntactic Features in Mathematical Word Problems: A Design Research Study on the Variation Principle}}}, doi = {{doi.org/10.1007/s13138-019-00153-z}}, year = {{2020}}, } @inbook{29413, author = {{Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. }}, booktitle = {{Advances in Dynamics, Optimization and Computation}}, editor = {{Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}}, pages = {{209--237}}, publisher = {{Springer International Publishing}}, title = {{{Symmetry in optimal control: A multiobjective model predictive control approach}}}, year = {{2020}}, } @article{31553, author = {{Seitz, Susanne and Häsel-Weide, Uta and Wilke, Yannik and Wallner, Melina}}, journal = {{K:ON Kölner Online-Journal für Lehrer*innenbildung}}, number = {{2}}, title = {{{Expertise von Lehrpersonen für inklusiven Mathematikunterricht der Sekundarstufe - Ausgangspunkte zur Professionalisierungsforschung.}}}, doi = {{10.18716/ojs/kON/2020.2.03}}, year = {{2020}}, } @inproceedings{45384, author = {{Dröse, Jennifer}}, booktitle = {{Beiträge zum Mathematikunterricht 2020 }}, editor = {{Siller, H.-S. and Weigel, W. and Wöler, J. F.}}, pages = {{233--236}}, publisher = {{WTM}}, title = {{{Verstehensgrundlagen diagnostizieren - Welche Wissenselemente fokussieren Lehrkräfte?}}}, year = {{2020}}, } @inbook{45386, author = {{Dröse, Jennifer and Eisen, V. and Prediger, Susanne and Altieri, M. and Schellenbach, M. and Menning, R.}}, booktitle = {{Mathematik lehren 223}}, pages = {{38--40}}, title = {{{Textaufgaben lesen lernen – eine digital gestützte Einheit mit App }}}, year = {{2020}}, } @inbook{17994, abstract = {{In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.}}, author = {{Gerlach, Raphael and Ziessler, Adrian}}, booktitle = {{Advances in Dynamics, Optimization and Computation}}, editor = {{Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}}, isbn = {{9783030512637}}, issn = {{2198-4182}}, pages = {{66--85}}, publisher = {{Springer International Publishing}}, title = {{{The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}}}, doi = {{10.1007/978-3-030-51264-4_3}}, volume = {{304}}, year = {{2020}}, } @article{16712, abstract = {{We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi) where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions.}}, author = {{Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}}, issn = {{1468-9367}}, journal = {{Dynamical Systems}}, number = {{2}}, pages = {{197--215}}, title = {{{On the equivariance properties of self-adjoint matrices}}}, doi = {{10.1080/14689367.2019.1661355}}, volume = {{35}}, year = {{2020}}, } @article{51386, author = {{Hilgert, Joachim and Barnum, H.}}, journal = {{J. of Lie Theory}}, pages = {{315--344}}, title = {{{Spectral Properties of Convex Bodies}}}, volume = {{30}}, year = {{2020}}, } @book{51488, editor = {{Hilgert, Joachim}}, publisher = {{Springer Spektrum}}, title = {{{Mathematik studieren -- Ein Ratgeber für Erstsemester und solche, die es vielleicht werden wollen}}}, year = {{2020}}, } @unpublished{51520, author = {{Hilgert, Joachim and Brennecken, D. and Ciardo, L.}}, title = {{{Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(ℝ)/SOn(ℝ)}}}, year = {{2020}}, } @misc{51559, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{301–305}}, title = {{{Titu Andreescu und Vlad Crisan: Mathematical Induction – A powerful and elegant method of proof. XYZ Press 2017 und Florian André Dalwigk: Vollständige Induktion – Beispiele und Aufgaben bis zum Umfallen. Springer Spektrum 2019}}}, doi = {{10.1007/s00591-020-00282-4}}, volume = {{67}}, year = {{2020}}, } @misc{51557, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{307–309}}, title = {{{Fabio Toscano: The Secret Formula – How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation. Princeton University Press 2020}}}, doi = {{10.1007/s00591-020-00283-3}}, volume = {{67}}, year = {{2020}}, } @misc{51561, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{123–124}}, title = {{{Robert Bosch: OPT ART – From Mathematical Optimization to Visual Design. Princeton University Press 2019}}}, doi = {{10.1007/s00591-020-00272-6}}, volume = {{67}}, year = {{2020}}, } @misc{51560, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{297–299}}, title = {{{David M. Bressoud: Calculus Reordered -- A History of the Big Ideas. Princeton University Press 2019}}}, doi = {{10.1007/s00591-020-00280-6}}, volume = {{67}}, year = {{2020}}, } @misc{51564, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{97–98}}, title = {{{Daniel Grieser: Mathematisches Problemlösen und Beweisen – Eine Entdeckungsreise in die Mathematik. 2. Auflage (Springer 2017)}}}, doi = {{10.1007/s00591-019-00254-3}}, volume = {{67}}, year = {{2020}}, } @misc{51563, author = {{Hilgert, Joachim}}, booktitle = {{Mathematische Semesterberichte}}, pages = {{109–111}}, title = {{{Claas Lattmann: Mathematische Modellierung bai Platon zwischen Thales und Euklid (De Gruyter 2019)}}}, doi = {{10.1007/s00591-019-00254-3}}, volume = {{67}}, year = {{2020}}, } @article{19945, abstract = {{Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations, …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is connected to conservation properties and other geometric features of solutions to the PDE and, therefore, of great interest for numerical integration. For the example of Burgers' equations and related PDEs we use Clebsch variables to lift the original system to a collective Hamiltonian system on a symplectic manifold whose structure is related to the original Lie-Poisson structure. On the collective Hamiltonian system a symplectic integrator can be applied. Our numerical examples show excellent conservation properties and indicate that the disadvantage of an increased phase-space dimension can be outweighed by the advantage of symplectic integration.}}, author = {{McLachlan, Robert I and Offen, Christian and Tapley, Benjamin K}}, issn = {{2158-2505}}, journal = {{Journal of Computational Dynamics}}, number = {{1}}, pages = {{111--130}}, publisher = {{American Institute of Mathematical Sciences (AIMS)}}, title = {{{Symplectic integration of PDEs using Clebsch variables}}}, doi = {{10.3934/jcd.2019005}}, volume = {{6}}, year = {{2019}}, } @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}}, }