@inbook{35681, author = {{Liebendörfer, Michael and Büdenbender-Kuklinski, Christiane and Lankeit, Elisa and Schürmann, Mirko and Biehler, Rolf and Schaper, Niclas}}, booktitle = {{Practice-Oriented Research in Tertiary Mathematics Education}}, isbn = {{9783031141744}}, issn = {{1869-4918}}, pages = {{91--117}}, publisher = {{Springer International Publishing}}, title = {{{Framing Goals of Mathematics Support Measures}}}, doi = {{10.1007/978-3-031-14175-1_5}}, 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{36294, author = {{Brennecken, Dominik and Rösler, Margit}}, journal = {{Transaction of the American Mathematical Society}}, publisher = {{ American Mathematical Society}}, title = {{{The Dunkl-Laplace transform and Macdonald’s hypergeometric series}}}, doi = {{10.1090/tran/8860}}, 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{43504, author = {{Biehler, Rolf and Liebendörfer, Michael and Schmitz, A.}}, journal = {{Mitteilungen der Gesellschaft für Didaktik der Mathematik}}, pages = {{8--12}}, title = {{{Lernvideos und ihre Erstellung - Das Projekt studiVEMINTvideos}}}, volume = {{114}}, 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}}, } @inbook{43226, author = {{Häsel-Weide, Uta and Nührenbörger, M.}}, booktitle = {{Mathematica Didactica, 46}}, title = {{{Inklusive Praktiken unterrichtsintegrierter Förderung im Mathematikunterricht.}}}, doi = {{https://doi.org/10.18716/ojs/md/2023.1670}}, 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}}, } @unpublished{44501, abstract = {{Extending the notion of maxcut, the study of the frustration index of signed graphs is one of the basic questions in the theory of signed graphs. Recently two of the authors initiated the study of critically frustrated signed graphs. That is a signed graph whose frustration index decreases with the removal of any edge. The main focus of this study is on critical signed graphs which are not edge-disjoint unions of critically frustrated signed graphs (namely non-decomposable signed graphs) and which are not built from other critically frustrated signed graphs by subdivision. We conjecture that for any given k there are only finitely many critically k-frustrated signed graphs of this kind. Providing support for this conjecture we show that there are only two of such critically 3-frustrated signed graphs where there is no pair of edge-disjoint negative cycles. Similarly, we show that there are exactly ten critically 3-frustrated signed planar graphs that are neither decomposable nor subdivisions of other critically frustrated signed graphs. We present a method for building non-decomposable critically frustrated signed graphs based on two given such signed graphs. We also show that the condition of being non-decomposable is necessary for our conjecture. }}, author = {{Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}}, booktitle = {{arXiv:2304.10243}}, title = {{{Critically 3-frustrated signed graphs}}}, 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}}, } @article{45713, author = {{Graf, Lara Marie and Wienhues, Inga and Häsel-Weide, Uta}}, journal = {{Die Grundschulzeitschrift}}, number = {{339}}, pages = {{20--23}}, publisher = {{Friedrich Verlag}}, title = {{{Addition und Subtraktion verstehen}}}, year = {{2023}}, } @article{45786, abstract = {{Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “interface ePortfolio” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibility of implementing the design principle of profession orientation. In the article, we theoretically clarify what we understand by this principle and locate our innovative concept against this theoretical background. We empirically investigate the extent to which counteraction against the second discontinuity is successful by analyzing reflection texts created in the interface ePortfolio, focusing on PSTs’ perspectives. Our qualitative content analysis shows that most of them perceive the innovation as helpful in the intended sense and indicates that the course concept, in general, and the interface ePortfolio, in particular, have helped establish relevant links between the course content and their later work as teachers.}}, author = {{Hoffmann, Max and Biehler, Rolf}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, keywords = {{General Mathematics, Education}}, publisher = {{Springer}}, title = {{{Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course}}}, doi = {{10.1007/s11858-023-01505-3}}, year = {{2023}}, }