@article{49326, abstract = {{Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, issn = {{0036-1399}}, journal = {{SIAM Journal on Applied Mathematics}}, keywords = {{Applied Mathematics}}, number = {{6}}, pages = {{2329--2353}}, publisher = {{Society for Industrial & Applied Mathematics (SIAM)}}, title = {{{Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}}}, doi = {{10.1137/23m1561075}}, volume = {{83}}, year = {{2023}}, } @unpublished{49371, abstract = {{To model dynamical systems on networks with higher order (non-pairwise) interactions, we recently introduced a new class of ODEs on hypernetworks. Here we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady state branch "reluctant" if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady state branch.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, booktitle = {{arXiv:2311.17186}}, title = {{{Higher order interactions lead to "reluctant" synchrony breaking}}}, year = {{2023}}, } @article{49372, author = {{Klüners, Jürgen and Wang, Jiuya}}, issn = {{2730-9657}}, journal = {{La Matematica}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Idélic Approach in Enumerating Heisenberg Extensions}}}, doi = {{10.1007/s44007-023-00067-w}}, year = {{2023}}, } @article{49425, author = {{Seitz, Simone and Häsel-Weide, Uta and Wilke, Yannik and Wallner, Melina}}, journal = {{Teachers and Teaching}}, pages = {{1--16}}, title = {{{Expertise and professionalism for inclusive (mathematics) teaching and learning: reflections on findings from interdisciplinary professionalisation research}}}, doi = {{https://doi.org/10.1080/13540602.2023.2284876 }}, year = {{2023}}, } @inproceedings{34135, abstract = {{By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.}}, author = {{Lishkova, Yana and Scherer, Paul and Ridderbusch, Steffen and Jamnik, Mateja and Liò, Pietro and Ober-Blöbaum, Sina and Offen, Christian}}, booktitle = {{IFAC-PapersOnLine}}, location = {{ Yokohama, Japan}}, number = {{2}}, pages = {{3203--3210}}, publisher = {{Elsevier}}, title = {{{Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery}}}, doi = {{10.1016/j.ifacol.2023.10.1457}}, volume = {{56}}, year = {{2023}}, } @unpublished{44840, abstract = {{In this article we investigate the convergence behavior of gathering protocols with fixed circulant topologies using tools form dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we model a gathering protocol as a system of ordinary differential equations whose equilibria are exactly all possible gathering points. Then, we find necessary and sufficient conditions for the structure of the underlying interaction graph such that the protocol is stable and converging, i.e., gathering, in the distributive computing sense by using tools from dynamical systems. Moreover, these tools allow for a more fine grained analysis in terms of speed of convergence in the dynamical systems sense. In fact, we derive a decomposition of the state space into stable invariant subspaces with different convergence rates. In particular, this decomposition is identical for every (linear) circulant gathering protocol, whereas only the convergence rates depend on the weights in interaction graph itself.}}, author = {{Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael}}, booktitle = {{arXiv:2305.06632}}, keywords = {{Dynamical Systems, Coupled Systems, Distributed Computing, Robot Swarms, Autonomous Mobile Robots, Gathering}}, pages = {{38}}, title = {{{On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies}}}, year = {{2023}}, } @article{50298, abstract = {{A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces such that each totally isotropic $t$-space is contained in exactly one member of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost complete classification of such $t$-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces.}}, author = {{Schmidt, Kai-Uwe and Weiß, Charlene}}, journal = {{Combinatorial Theory}}, number = {{1}}, title = {{{Packings and Steiner systems in polar spaces}}}, doi = {{10.5070/c63160424}}, volume = {{3}}, year = {{2023}}, } @article{50297, abstract = {{We show that there exist ordered orthogonal arrays, whose sizes deviate from the Rao bound by a factor that is polynomial in the parameters of the ordered orthogonal array. The proof is nonconstructive and based on a probabilistic method due to Kuperberg, Lovett and Peled.}}, author = {{Schmidt, Kai‐Uwe and Weiß, Charlene}}, journal = {{Journal of Combinatorial Designs}}, number = {{9}}, pages = {{422--431}}, publisher = {{Wiley}}, title = {{{Existence of small ordered orthogonal arrays}}}, doi = {{10.1002/jcd.21903}}, volume = {{31}}, year = {{2023}}, } @phdthesis{50300, abstract = {{Digital communications relies heavily on the usage of different types of codes. Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs of binary codes and binary codes with constant weight. All these codes can be viewed as subsets of classical association schemes. A central coding-theoretic problem is to derive upper bounds for the size of codes. This thesis investigates Delsartes powerful linear program whose optimum is precisely such a bound for codes in association schemes. The linear programs for binary codes and binary constant-weight codes have been extensively studied since the 1970s, but their optimum is still unknown. We determine in a unified way the optimum of the linear program in several ordinary q-analogs as well as in their affine counterparts. In particular, bounds and constructions for codes in polar spaces are established, where the bounds are sharp up to a constant factor in many cases. Moreover, based on these results, an almost complete classification of Steiner systems in polar spaces is provided by showing that they could only exist in some corner cases.}}, author = {{Weiß, Charlene}}, title = {{{Linear programming bounds in classical association schemes}}}, doi = {{10.17619/UNIPB/1-1672}}, year = {{2023}}, } @unpublished{50299, abstract = {{A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space over $\mathbb{F}_p$ equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-$(n,k,\lambda)$ design in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $k$-spaces such that each totally isotropic $t$-space is contained in exactly $\lambda$ members of $Y$. Nontrivial examples are currently only known for $t\leq 2$. We show that $t$-$(n,k,\lambda)$ designs in polar spaces exist for all $t$ and $p$ provided that $k>\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a probabilistic method by Kuperberg, Lovett, and Peled, and it is thus nonconstructive.}}, author = {{Weiß, Charlene}}, booktitle = {{arXiv:2311.08288}}, title = {{{Nontrivial $t$-designs in polar spaces exist for all $t$}}}, year = {{2023}}, } @article{48596, author = {{Häsel-Weide, Uta and Schmidt, R. and Büker, Petra}}, journal = {{Zeitschrift für Schul- Und Professionsentwicklung. (PFLB)}}, number = {{1}}, pages = {{215--229}}, title = {{{„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung}}}, volume = {{5}}, year = {{2023}}, } @inproceedings{51131, author = {{Graf, Lara Marie and Häsel-Weide, Uta and Höveler, K. and Nührenbörger, M.}}, booktitle = {{Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13)}}, editor = {{Drijvers, P. and Csapodi, C. and Palmér, H. and Gosztonyi, K. and Kónya, E.}}, pages = {{3203--3210}}, title = {{{Insights into out-of-field teachers’ self-reports: Fostering the understanding of addition and subtraction as a basis for children to overcome difficulties in mathematics}}}, year = {{2023}}, } @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}}, } @article{31059, abstract = {{In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.}}, author = {{Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}}, journal = {{Communications in Mathematical Physics}}, pages = {{655--678}}, title = {{{Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}}}, doi = {{ttps://doi.org/10.1007/s00220-022-04538-z}}, volume = {{398}}, 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}}, } @unpublished{51207, abstract = {{Let $X=X_1\times X_2$ be a product of two rank one symmetric spaces of non-compact type and $\Gamma$ a torsion-free discrete subgroup in $G_1\times G_2$. We show that the spectrum of $\Gamma \backslash X$ is related to the asymptotic growth of $\Gamma$ in the two direction defined by the two factors. We obtain that $L^2(\Gamma \backslash G)$ is tempered for large class of $\Gamma$.}}, author = {{Weich, Tobias and Wolf, Lasse Lennart}}, booktitle = {{arXiv:2304.09573}}, title = {{{Temperedness of locally symmetric spaces: The product case}}}, 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}}, } @unpublished{51375, abstract = {{We consider the quantum dynamics of a many-fermion system in $\mathbb R^d$ with an ultraviolet regularized pair interaction as previously studied in [M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincar\'e 21.11 (2020)]. We provide a Lieb-Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb-Robinson bound on $L^2$-overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground states in the presence of a spectral gap. We also develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones, which opens the door to other applications of the Lieb-Robinson bounds.}}, author = {{Hinrichs, Benjamin and Lemm, Marius and Siebert, Oliver}}, booktitle = {{arXiv:2310.17736}}, title = {{{On Lieb-Robinson bounds for a class of continuum fermions}}}, year = {{2023}}, } @unpublished{51376, abstract = {{In the Bogoliubov-Fr\"ohlich model, we prove that an impurity immersed in a Bose-Einstein condensate forms a stable quasi-particle when the total momentum is less than its mass times the speed of sound. The system thus exhibits superfluid behavior, as this quasi-particle does not experience friction. We do not assume any infrared or ultraviolet regularization of the model, which contains massless excitations and point-like interactions.}}, author = {{Hinrichs, Benjamin and Lampart, Jonas}}, booktitle = {{arXiv:2311.05361}}, title = {{{A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate}}}, year = {{2023}}, } @article{31190, abstract = {{For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate counting function for the Ruelle-Taylor resonances and establish a spectral gap which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is achieved by proving a quantum-classical correspondence, i.e. a 1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant states and joint eigenfunctions of the algebra of invariant differential operators on $G/K$.}}, author = {{Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}}, journal = {{Analysis & PDE}}, number = {{10}}, pages = {{2241–2265}}, publisher = {{MSP}}, title = {{{Higher rank quantum-classical correspondence}}}, volume = {{16}}, year = {{2023}}, } @unpublished{51205, abstract = {{We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on vector spaces associated with the set of non backtracking paths in the graphs. The second kind of operators are averaging operators acting on vector spaces associated with the space of vertices of the graph. The choice of vector spaces reflects regularity properties. Our main results are correspondences between classical and quantum spectral objects as well as some automatic regularity properties for eigenfunctions of transfer operators.}}, author = {{Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}}, booktitle = {{arXiv:2307.10876}}, title = {{{Spectral correspondences for finite graphs without dead ends}}}, 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}}, } @article{51383, author = {{Hilgert, Joachim and Arends, C.}}, journal = {{J. de l'École polytechnique — Mathématiques}}, pages = {{335--403}}, title = {{{Spectral correspondences for rank one locally symmetric spaces - The case of exceptional parameters}}}, volume = {{10}}, year = {{2023}}, } @article{51384, author = {{Hilgert, Joachim and Glöckner, H.}}, journal = {{J. Diff. Equations}}, pages = {{186--232}}, title = {{{Aspects of control theory on infinite-dimensional Lie groups and G-manifolds}}}, volume = {{343}}, year = {{2023}}, } @unpublished{51499, author = {{Hilgert, Joachim and Arends, C. and Frahm, J.}}, title = {{{A pairing formula for resonant states on finite regular graphs}}}, year = {{2023}}, } @unpublished{51500, author = {{Hilgert, Joachim and Arends, C. and Frahm, J.}}, title = {{{Edge Laplacians and vector valued Poisson transforms for graphs}}}, year = {{2023}}, } @unpublished{51502, author = {{Hilgert, Joachim and Baier, T. and Kaya, O. and Mourao, J. and Nunes, J.}}, title = {{{Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem}}}, year = {{2023}}, } @unpublished{51521, author = {{Hilgert, Joachim and Guedes Bonthonneau, Y. and Guillarmou, C. and Weich, Tobias}}, title = {{{Ruelle-Taylor resonances of Anosov actions}}}, year = {{2023}}, } @unpublished{32447, abstract = {{We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas laid out in [H. Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order O(t−2) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.}}, author = {{Sonntag, Konstantin and Peitz, Sebastian}}, booktitle = {{arXiv:2307.00975}}, title = {{{Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping}}}, 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{34803, author = {{Celledoni, Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}}, journal = {{BIT Numerical Mathematics}}, publisher = {{Springer}}, title = {{{Deep neural networks on diffeomorphism groups for optimal shape reparametrization}}}, doi = {{10.1007/s10543-023-00989-05}}, volume = {{63}}, 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}}, } @article{34805, abstract = {{Let $E$ be a finite-dimensional real vector space and $M\subseteq E$ be a convex polytope with non-empty interior. We turn the group of all $C^\infty$-diffeomorphisms of $M$ into a regular Lie group.}}, author = {{Glöckner, Helge}}, journal = {{Journal of Convex Analysis}}, number = {{1}}, pages = {{343--358}}, publisher = {{Heldermann}}, title = {{{Diffeomorphism groups of convex polytopes}}}, volume = {{30}}, year = {{2023}}, } @article{34801, author = {{Glöckner, Helge and Tárrega, Luis}}, journal = {{Journal of Lie Theory}}, number = {{1}}, pages = {{271--296}}, publisher = {{Heldermann}}, title = {{{Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups }}}, volume = {{33}}, 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}}, } @inbook{16296, abstract = {{Multiobjective optimization plays an increasingly important role in modern applications, where several objectives 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 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 as is the case for models governed by partial differential equations (PDEs). To decrease the numerical effort to an affordable amount, surrogate models can be used to replace the expensive PDE evaluations. Existing multiobjective optimization methods using model reduction are limited either to low parameter dimensions or to few (ideally two) objectives. In this article, we present a combination of the reduced basis model reduction method with a continuation approach using inexact gradients. The resulting approach can handle an arbitrary number of objectives while yielding a significant reduction in computing time.}}, author = {{Banholzer, Stefan and Gebken, Bennet and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}}, booktitle = {{Non-Smooth and Complementarity-Based Distributed Parameter Systems}}, editor = {{Michael, Hintermüller and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich}}, isbn = {{978-3-030-79392-0}}, pages = {{43--76}}, publisher = {{Springer}}, title = {{{ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}}}, doi = {{10.1007/978-3-030-79393-7_3}}, year = {{2022}}, } @inbook{30294, abstract = {{With the ever increasing capabilities of sensors and controllers, autonomous driving is quickly becoming a reality. This disruptive change in the automotive industry poses major challenges for manufacturers as well as suppliers as entirely new design and testing strategies have to be developed to remain competitive. Most importantly, the complexity of autonomously driving vehicles in a complex, uncertain, and safety-critical environment requires new testing procedures to cover the almost infinite range of potential scenarios.}}, author = {{Peitz, Sebastian and Dellnitz, Michael and Bannenberg, Sebastian}}, booktitle = {{German Success Stories in Industrial Mathematics}}, editor = {{Bock, H. G. and Küfer, K.-H. and Maas, P. and Milde, A. and Schulz, V.}}, isbn = {{9783030814540}}, issn = {{1612-3956}}, publisher = {{Springer International Publishing}}, title = {{{Efficient Virtual Design and Testing of Autonomous Vehicles}}}, doi = {{10.1007/978-3-030-81455-7_23}}, volume = {{35}}, year = {{2022}}, } @article{30490, author = {{Cresson, Jacky and Jiménez, Fernando and Ober-Blöbaum, Sina}}, journal = {{AIMS}}, pages = {{57--89}}, title = {{{Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations}}}, volume = {{14(1)}}, year = {{2022}}, } @article{30861, abstract = {{AbstractWe consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the turnpike property. This property is further used in order to design simple and realistic suboptimal control strategies.}}, author = {{Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}}, issn = {{0022-3239}}, journal = {{Journal of Optimization Theory and Applications}}, keywords = {{Applied Mathematics, Management Science and Operations Research, Control and Optimization}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Turnpike Property in Optimal Microbial Metabolite Production}}}, doi = {{10.1007/s10957-022-02023-0}}, year = {{2022}}, } @article{31982, abstract = {{AbstractWe show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold $$\Sigma $$ Σ with Betti number $$b_1$$ b 1 , the order of vanishing of the Ruelle zeta function at zero equals $$4-b_1$$ 4 - b 1 , while in the hyperbolic case it is equal to $$4-2b_1$$ 4 - 2 b 1 . This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle $$S\Sigma $$ S Σ with harmonic 1-forms on $$\Sigma $$ Σ .}}, author = {{Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}}, issn = {{0020-9910}}, journal = {{Inventiones mathematicae}}, keywords = {{General Mathematics}}, number = {{1}}, pages = {{303--394}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}}}, doi = {{10.1007/s00222-022-01108-x}}, volume = {{229}}, year = {{2022}}, } @inbook{32233, author = {{Häsel-Weide, Uta and Wallner, Melina and Hattermann, M.}}, booktitle = {{Anfangsunterricht für alle Kinder - Willkommen in der Schule!}}, editor = {{Gutzmann, M. and Carle, U.}}, pages = {{200--215}}, title = {{{Symmetrieverständnis von Anfang an}}}, year = {{2022}}, }