@article{55277, author = {{Klahn, B. and Technau, Marc}}, journal = {{Int. J. Number Theory}}, number = {{10}}, pages = {{2443–2450}}, title = {{{Galois groups of (ⁿ₀)+(ⁿ₁)X+…+(ⁿ₆)X⁶}}}, doi = {{10.1142/S1793042123501208}}, volume = {{19}}, year = {{2023}}, } @article{55279, author = {{Minelli, P. and Sourmelidis, A. and Technau, Marc}}, journal = {{Math. Ann.}}, pages = {{291–320}}, title = {{{Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums}}}, doi = {{10.1007/s00208-022-02452-2}}, volume = {{387}}, 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{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with real-valued function spaces and direct limits of Sobolev-Lie groups }}}, volume = {{33}}, year = {{2023}}, } @unpublished{55575, author = {{Jakob, Johanna}}, title = {{{Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen}}}, year = {{2023}}, } @inproceedings{42163, abstract = {{The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.}}, author = {{Offen, Christian and Ober-Blöbaum, Sina}}, booktitle = {{Geometric Science of Information}}, editor = {{Nielsen, F and Barbaresco, F}}, keywords = {{System identification, discrete Lagrangians, travelling waves}}, location = {{Saint-Malo, Palais du Grand Large, France}}, pages = {{569--579}}, publisher = {{Springer, Cham.}}, title = {{{Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}}}, doi = {{10.1007/978-3-031-38271-0_57}}, volume = {{14071}}, year = {{2023}}, } @book{37469, editor = {{Biehler, Rolf and Liebendörfer, Michael and Gueudet, Ghislaine and Rasmussen, Chris and Winsløw, Carl}}, isbn = {{9783031141744}}, issn = {{1869-4918}}, publisher = {{Springer International Publishing}}, title = {{{Practice-Oriented Research in Tertiary Mathematics Education}}}, doi = {{10.1007/978-3-031-14175-1}}, year = {{2023}}, } @article{34814, author = {{Hanusch, Maximilian}}, issn = {{0008-414X}}, journal = {{Canadian Journal of Mathematics}}, keywords = {{extension of differentiable maps}}, number = {{1}}, pages = {{170--201}}, publisher = {{Canadian Mathematical Society}}, title = {{{A $C^k$-seeley-extension-theorem for Bastiani’s differential calculus}}}, doi = {{10.4153/s0008414x21000596}}, volume = {{75}}, year = {{2023}}, } @article{27426, abstract = {{Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression and machine learning. Since the choice of the regularization parameter is crucial but often difficult, path-following methods are used to approximate the entire regularization path, i.e., the set of all possible solutions for all regularization parameters. Due to their nature, the development of these methods requires structural results about the regularization path. The goal of this article is to derive these results for the case of a smooth objective function which is penalized by a piecewise differentiable regularization term. We do this by treating regularization as a multiobjective optimization problem. Our results suggest that even in this general case, the regularization path is piecewise smooth. Moreover, our theory allows for a classification of the nonsmooth features that occur in between smooth parts. This is demonstrated in two applications, namely support-vector machines and exact penalty methods.}}, author = {{Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}}, journal = {{Journal of Global Optimization}}, number = {{3}}, pages = {{709--741}}, title = {{{On the structure of regularization paths for piecewise differentiable regularization terms}}}, doi = {{10.1007/s10898-022-01223-2}}, volume = {{85}}, year = {{2023}}, } @inproceedings{31849, author = {{Hoffmann, Max and Biehler, Rolf}}, booktitle = {{Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}}, editor = {{Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}}, keywords = {{Teaching and learning of specific topics in university mathematics, Transition to, across and from university mathematics, Student Teachers, Geometry, Congruence, Double Discontinuity.}}, publisher = {{University of Hannover and INDRUM.}}, title = {{{Student Teachers ’ Knowledge of Congruence before a University Course on Geometry}}}, year = {{2023}}, } @inproceedings{43097, author = {{Florensa, Ignasio and Hoffmann, Max and Romo Vázquez, Avenilde and Zandieh, Michelle and Martínez-Planell, Rafael}}, booktitle = {{Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2022, 19-22 October 2022)}}, editor = {{Trigueros, Marı́a and Barquero, Berta and Hochmuth, Reinhard and Peters, Jana}}, title = {{{Innovations in university teaching based on mathematic education research}}}, year = {{2023}}, } @article{43105, author = {{Black, Tobias and Fuest, Mario and Lankeit, Johannes and Mizukami, Masaaki}}, issn = {{1468-1218}}, journal = {{Nonlinear Analysis: Real World Applications}}, keywords = {{Applied Mathematics, Computational Mathematics, General Economics, Econometrics and Finance, General Engineering, General Medicine, Analysis}}, publisher = {{Elsevier BV}}, title = {{{Possible points of blow-up in chemotaxis systems with spatially heterogeneous logistic source}}}, doi = {{10.1016/j.nonrwa.2023.103868}}, volume = {{73}}, year = {{2023}}, } @inbook{43227, author = {{Vitt, Vivian and Häsel-Weide, Uta}}, booktitle = {{Mathematica Didactica, 46}}, title = {{{Reziprokes Peer-Tutoring zur Förderung von Schüler*innen mit Schwierigkeiten beim Mathematiklernen.}}}, doi = {{https://doi.org/10.18716/ojs/md/2023.1671}}, year = {{2023}}, } @article{34832, author = {{Hanusch, Maximilian}}, journal = {{Annals of Global Analysis and Geometry}}, keywords = {{Lax equation, generalized Baker-Campbell-Dynkin-Hausdorff formula, regularity of Lie groups}}, number = {{21}}, title = {{{The Lax Equation and Weak Regularity of Asymptotic Estimate Lie Groups}}}, doi = {{10.1007/s10455-023-09888-y}}, volume = {{63}}, year = {{2023}}, } @article{44857, abstract = {{Ancestral reconstruction is a classic task in comparative genomics. Here, we study the genome median problem, a related computational problem which, given a set of three or more genomes, asks to find a new genome that minimizes the sum of pairwise distances between it and the given genomes. The distance stands for the amount of evolution observed at the genome level, for which we determine the minimum number of rearrangement operations necessary to transform one genome into the other. For almost all rearrangement operations the median problem is NP-hard, with the exception of the breakpoint median that can be constructed efficiently for multichromosomal circular and mixed genomes. In this work, we study the median problem under a restricted rearrangement measure called c4-distance, which is closely related to the breakpoint and the DCJ distance. We identify tight bounds and decomposers of the c4-median and develop algorithms for its construction, one exact ILP-based and three combinatorial heuristics. Subsequently, we perform experiments on simulated data sets. Our results suggest that the c4-distance is useful for the study the genome median problem, from theoretical and practical perspectives.}}, author = {{Silva, Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr, Daniel and Martinez, Fábio V.}}, issn = {{0399-0559}}, journal = {{RAIRO - Operations Research}}, keywords = {{Management Science and Operations Research, Computer Science Applications, Theoretical Computer Science}}, number = {{3}}, pages = {{1045--1058}}, publisher = {{EDP Sciences}}, title = {{{Algorithms for the genome median under a restricted measure of rearrangement}}}, doi = {{10.1051/ro/2023052}}, volume = {{57}}, year = {{2023}}, } @unpublished{44859, author = {{Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}}, booktitle = {{arXiv:2305.08619}}, title = {{{Sets of r-graphs that color all r-graphs}}}, year = {{2023}}, } @article{34833, author = {{Hanusch, Maximilian}}, journal = {{Indagationes Mathematicae.}}, keywords = {{Lie group actions and analytic 1-submanifolds}}, number = {{4}}, pages = {{752--811}}, title = {{{Decompositions of Analytic 1-Manifolds}}}, doi = {{10.1016/j.indag.2023.02.003}}, volume = {{34}}, year = {{2023}}, } @unpublished{45498, abstract = {{We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic expansion for an embedding of the perturbed invariant torus, as well as for the reduced phase dynamics in local coordinates. Both can be determined to arbitrary degrees of accuracy, and we show that the phase dynamics may directly be obtained in normal form. We apply the method to predict remote synchronisation in a chain of coupled Stuart-Landau oscillators.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, booktitle = {{arXiv:2306.03320}}, pages = {{29}}, title = {{{A parametrisation method for high-order phase reduction in coupled oscillator networks}}}, year = {{2023}}, } @article{45712, author = {{Häsel-Weide, Uta}}, journal = {{Die Grundschulzeitschrift}}, number = {{339}}, pages = {{6--11}}, publisher = {{Friedrich Verlag}}, title = {{{ Inklusiver Mathematikunterricht. Mathematiklernen in Vielfalt von Kompetenzen, Wegen und Lernsituationen}}}, year = {{2023}}, }