@unpublished{46578, abstract = {{Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal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. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".}}, author = {{Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}}, booktitle = {{arXiv:2308.01113}}, title = {{{Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}}}, year = {{2023}}, } @article{34793, author = {{Glöckner, Helge and Hilgert, Joachim}}, issn = {{0022-0396}}, journal = {{Journal of Differential Equations}}, keywords = {{22E65, 28B05, 34A12, 34H05, 46E30, 46E40}}, pages = {{186–232}}, title = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}}, doi = {{10.1016/j.jde.2022.10.001}}, volume = {{343}}, year = {{2023}}, } @book{45191, editor = {{Gräßler, Iris and Maier, Günter W. and Steffen, Eckhard and Roesmann, Daniel}}, isbn = {{9783031261039}}, publisher = {{Springer International Publishing}}, title = {{{The Digital Twin of Humans}}}, doi = {{10.1007/978-3-031-26104-6}}, year = {{2023}}, } @article{52806, author = {{Gilbert, H. and Schürmann, M. and Liebendörfer, M. and Lawson, D. and Hodds, M.}}, issn = {{0020-739X}}, journal = {{International Journal of Mathematical Education in Science and Technology}}, keywords = {{Applied Mathematics, Education, Mathematics (miscellaneous)}}, pages = {{1--26}}, publisher = {{Informa UK Limited}}, title = {{{Post-pandemic online mathematics and statistics support: Practitioners’ opinions in Germany and Great Britain & Ireland}}}, doi = {{10.1080/0020739x.2023.2184282}}, year = {{2023}}, } @inbook{52811, author = {{Biehler, Rolf and Guntermann, Dominik and Liebendörfer, Michael and Krämer, Sandra and Schlüter, Sarah}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{407–410}}, publisher = {{WTM}}, title = {{{Fachdidaktisches Design von Begründungsvideos im Projekt studiVEMINTvideos}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{1}}, year = {{2023}}, } @inbook{52810, author = {{Göller, Robin and Gildehaus, Lara and Liebendörfer, Michael and Besser, Michael}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2021. Beiträge zum gleichnamigen Online-Symposium am 12 November 2021 aus Bochum}}, editor = {{Härterich, Jörg and Kallweit, Michael and Rolka, Katrin and Skill, Thomas}}, isbn = {{978-3-95987-264-5}}, pages = {{66–80}}, publisher = {{WTM}}, title = {{{Erfassung und Vergleich (mathematischer) Eingangsvoraussetzungen angehender Studierender verschiedener mathematikhaltiger Studiengänge}}}, year = {{2023}}, } @inbook{52809, author = {{Kempen, Leander and Liebendörfer, Michael}}, booktitle = {{Hanse-Kolloquium zur Hochschuldidaktik der Mathematik 2021. Beiträge zum gleichnamigen Online-Symposium am 12 November 2021 aus Bochum}}, editor = {{Härterich, Jörg and Kallweit, Michael and Rolka, Katrin and Skill, Thomas}}, isbn = {{978-3-95987-264-5}}, pages = {{91–106}}, publisher = {{WTM}}, title = {{{Zu digital - zu viel - zu schwer? Qualitative Einsichten in das Erleben und Handeln von Erstsemester-Studierenden der Mathematik während der Corona-Pandemie}}}, year = {{2023}}, } @inbook{52813, author = {{Schlüter, Sarah and Liebendörfer, Michael}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{1177–1180}}, publisher = {{WTM}}, title = {{{Bearbeitungsmuster von Studierenden im Umgang mit formalen Definitionen im Kontext konstanter Folgen}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{2}}, year = {{2023}}, } @inbook{52812, author = {{Krämer, Sandra and Liebendörfer, Michael}}, booktitle = {{Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}}, editor = {{Goethe-Universität Frankfur, IDMI-Primar}}, isbn = {{978-3-95987-208-9}}, pages = {{949–952}}, publisher = {{WTM}}, title = {{{Förderung prozeduraler Flexibilität durch Lernvideos mit interaktiven Aufgaben}}}, doi = {{10.37626/GA9783959872089.0}}, volume = {{2}}, year = {{2023}}, } @article{52807, abstract = {{Many preservice mathematics teachers lose their motivation during their first year at university. This phenomenon has been repeatedly described in recent years but is not yet fully under­stood. Since motivation may relate to different objects such as mathematics or teaching, we aim to qualitatively reconstruct different facets of the central motivational constructs of Situated-Expectancy-Value theory (intrinsic value, attainment value, utility value, cost, and expectancy of success) for preservice mathematics teachers. The analysis of longitudinal group interviews of 14 pre­service higher-secondary mathematic teachers from a German university revealed different objects of motivation (e.g., teaching mathematics, scientific mathematics, procedural mathematics, or proof-based mathematics) in preservice teachers' values and expectancy of success. Furthermore, relations between those values and expectancy of success were identified that played a significant role in preservice teachers’ motivational development over their first semester (e.g., relations of attain­ment value for scientific mathematics and psychological cost). Theoretical and practical implications towards a teaching-specific conceptualization of expectancy of success and values and value interventions are being discussed.}}, title = {{{Preservice teachers’ mathematics-related values and expectancy in the transition from school to university}}}, doi = {{10.48489/QUADRANTE.31191}}, year = {{2023}}, } @article{45971, abstract = {{Abstract An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation.}}, author = {{Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}}, issn = {{0272-4979}}, journal = {{IMA Journal of Numerical Analysis}}, keywords = {{Applied Mathematics, Computational Mathematics, General Mathematics}}, publisher = {{Oxford University Press (OUP)}}, title = {{{Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints}}}, doi = {{10.1093/imanum/drad037}}, year = {{2023}}, } @article{53140, abstract = {{We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup stable spaces and symmetric pressure stabilized formulations. We extend the results from Burman and Fernández [\textit{SIAM J. Numer. Anal.}, 47 (2009), pp. 409-439] and provide a unified theoretical analysis of backward difference formulae (BDF methods) of order 1 to 6. The main novelty of our approach lies in the use of Dahlquist's G-stability concept together with multiplier techniques introduced by Nevannlina-Odeh and recently by Akrivis et al. [\textit{SIAM J. Numer. Anal.}, 59 (2021), pp. 2449-2472] to derive optimal stability and error estimates for both the velocity and the pressure. When combined with a method dependent Ritz projection for the initial data, unconditional stability can be shown while for arbitrary interpolation, pressure stability is subordinate to the fulfillment of a mild inverse CFL-type condition between space and time discretizations.}}, author = {{Contri, Alessandro and Kovács, Balázs and Massing, André}}, journal = {{arXiv}}, title = {{{Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem: velocity and pressure estimates}}}, doi = {{10.48550/ARXIV.2312.05511}}, year = {{2023}}, } @article{53142, author = {{Berger, Thomas and Lanza, Lukas}}, journal = {{IMA Journal of Mathematical Control and Information,}}, number = {{4}}, pages = {{691--713}}, title = {{{Funnel control of linear systems with arbitrary relative degree under output measurement losses}}}, doi = {{doi: 10.1093/imamci/dnad029}}, volume = {{40}}, year = {{2023}}, } @article{53143, author = {{Lee, J. G. and Berger, Thomas and Trenn, S. and Shim, H.}}, journal = {{Automatica}}, pages = {{Article 111204}}, title = {{{Edge-wise funnel output synchronization of heterogeneous agents with relative degree one}}}, doi = {{doi: 10.1016/j.automatica.2023.111204 (open access)}}, volume = {{156}}, year = {{2023}}, } @book{51101, author = {{Werth, Gerda}}, isbn = {{9783658424442}}, issn = {{2661-8591}}, publisher = {{Springer Fachmedien Wiesbaden}}, title = {{{Neue Wege im mathematischen Unterricht: Auf den Spuren Mathilde Vaertings}}}, doi = {{10.1007/978-3-658-42445-9}}, year = {{2023}}, } @article{51103, author = {{Werth, Gerda}}, journal = {{mathematik lehren}}, pages = {{15--19}}, publisher = {{Friedrich}}, title = {{{Standardkonstruktionen eigenständig entdecken. Mathilde Vaertings Idee der Selbstständigkeitsprobe}}}, volume = {{241}}, year = {{2023}}, } @unpublished{53404, abstract = {{In this short note we observe, on locally symmetric spaces of higher rank, a connection between the growth indicator function introduced by Quint and the modified critical exponent of the Poincar\'e series equipped with the polyhedral distance. As a consequence, we provide a different characterization of the bottom of the $L^2$-spectrum of the Laplace-Beltrami operator in terms of the growth indicator function. Moreover, we explore the relationship between these three objects and the temperedness.}}, author = {{Wolf, Lasse L. and Zhang, Hong-Wei}}, booktitle = {{arXiv:2311.11770}}, title = {{{$L^2$-spectrum, growth indicator function and critical exponent on locally symmetric spaces}}}, year = {{2023}}, } @article{53410, abstract = {{AbstractWe consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.}}, author = {{Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}}, number = {{2}}, pages = {{1607--1656}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}}}, doi = {{10.1007/s00023-023-01379-x}}, volume = {{25}}, year = {{2023}}, } @unpublished{53411, abstract = {{We compute a Riemann-Roch formula for the invariant Riemann-Roch number of a quantizable Hamiltonian $S^1$-manifold $(M,\omega,\mathcal{J})$ in terms of the geometry of its symplectic quotient, allowing $0$ to be a singular value of the moment map $\mathcal{J}:M\to\mathbb{R}$. The formula involves a new explicit local invariant of the singularities. Our approach relies on a complete singular stationary phase expansion of the associated Witten integral.}}, author = {{Delarue, Benjamin and Ioos, Louis and Ramacher, Pablo}}, booktitle = {{arXiv:2302.09894}}, title = {{{A Riemann-Roch formula for singular reductions by circle actions}}}, year = {{2023}}, } @article{53538, abstract = {{AbstractWe study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane.}}, author = {{Polychrou, G. and Papageorgiou, Efthymia and Fotiadis, A. and Daskaloyannis, C.}}, issn = {{1139-1138}}, journal = {{Revista Matemática Complutense}}, keywords = {{General Mathematics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation}}}, doi = {{10.1007/s13163-023-00476-z}}, year = {{2023}}, }