@article{31189, abstract = {{Given a geometrically finite hyperbolic surface of infinite volume it is a classical result of Patterson that the positive Laplace-Beltrami operator has no $L^2$-eigenvalues $\geq 1/4$. In this article we prove a generalization of this result for the joint $L^2$-eigenvalues of the algebra of commuting differential operators on Riemannian locally symmetric spaces $\Gamma\backslash G/K$ of higher rank. We derive dynamical assumptions on the $\Gamma$-action on the geodesic and the Satake compactifications which imply the absence of the corresponding principal eigenvalues. A large class of examples fulfilling these assumptions are the non-compact quotients by Anosov subgroups.}}, author = {{Weich, Tobias and Wolf, Lasse Lennart}}, journal = {{Communications in Mathematical Physics}}, title = {{{Absence of principal eigenvalues for higher rank locally symmetric spaces}}}, doi = {{https://doi.org/10.1007/s00220-023-04819-1}}, volume = {{403}}, year = {{2023}}, } @unpublished{51206, abstract = {{We present a numerical algorithm for the computation of invariant Ruelle distributions on convex co-compact hyperbolic surfaces. This is achieved by exploiting the connection between invariant Ruelle distributions and residues of meromorphically continued weighted zeta functions established by the authors together with Barkhofen (2021). To make this applicable for numerics we express the weighted zeta as the logarithmic derivative of a suitable parameter dependent Fredholm determinant similar to Borthwick (2014). As an additional difficulty our transfer operator has to include a contracting direction which we account for with techniques developed by Rugh (1992). We achieve a further improvement in convergence speed for our algorithm in the case of surfaces with additional symmetries by proving and applying a symmetry reduction of weighted zeta functions.}}, author = {{Schütte, Philipp and Weich, Tobias}}, booktitle = {{arXiv:2308.13463}}, title = {{{Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces -- A Numerical Algorithm via Weighted Zeta Functions}}}, year = {{2023}}, } @article{51351, author = {{Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0166-218X}}, journal = {{Discrete Applied Mathematics}}, keywords = {{Applied Mathematics, Discrete Mathematics and Combinatorics}}, pages = {{185--189}}, publisher = {{Elsevier BV}}, title = {{{Bounds for the chromatic index of signed multigraphs}}}, doi = {{10.1016/j.dam.2023.05.008}}, volume = {{337}}, year = {{2023}}, } @inbook{45190, author = {{Cappello, Chiara and Steffen, Eckhard}}, booktitle = {{The Digital Twin of Humans}}, isbn = {{9783031261039}}, pages = {{93----110}}, publisher = {{Springer International Publishing}}, title = {{{Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks}}}, doi = {{10.1007/978-3-031-26104-6_5}}, year = {{2023}}, } @article{51357, author = {{Steffen, Eckhard and Wolf, Isaak Hieronymus}}, issn = {{0012-365X}}, journal = {{Discrete Mathematics}}, keywords = {{Discrete Mathematics and Combinatorics, Theoretical Computer Science}}, publisher = {{Elsevier BV}}, title = {{{Rotation r-graphs}}}, doi = {{10.1016/j.disc.2023.113457}}, year = {{2023}}, } @article{31210, abstract = {{In this paper we complete the program of relating the Laplace spectrum for rank one compact locally symmetric spaces with the first band Ruelle-Pollicott resonances of the geodesic flow on its sphere bundle. This program was started by Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and Guillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for general rank one spaces. Except for the case of hyperbolic surfaces a countable set of exceptional spectral parameters always left untreated since the corresponding Poisson transforms are neither injective nor surjective. We use vector valued Poisson transforms to treat also the exceptional spectral parameters. For surfaces the exceptional spectral parameters lead to discrete series representations of $\mathrm{SL}(2,\mathbb R)$. In higher dimensions the situation is more complicated, but can be described completely.}}, author = {{Arends, Christian and Hilgert, Joachim}}, issn = {{2270-518X}}, journal = {{Journal de l’École polytechnique — Mathématiques}}, keywords = {{Ruelle resonances, Poisson transforms, locally symmetric spaces, principal series representations}}, pages = {{335--403}}, title = {{{Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters}}}, doi = {{10.5802/jep.220}}, volume = {{10}}, year = {{2023}}, } @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}}, }