[{"author":[{"id":"32202","full_name":"Hoffmann, Max","first_name":"Max","orcid":"0000-0002-6964-7123","last_name":"Hoffmann"},{"id":"220","last_name":"Hilgert","first_name":"Joachim","full_name":"Hilgert, Joachim"},{"full_name":"Weich, Tobias","first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178"}],"publication_identifier":{"isbn":["9783662673560","9783662673577"]},"year":"2024","status":"public","title":"Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik","publication_status":"published","date_updated":"2024-08-08T08:05:30Z","_id":"55193","publisher":"Springer Berlin Heidelberg","language":[{"iso":"ger"}],"user_id":"220","doi":"10.1007/978-3-662-67357-7","citation":{"ama":"Hoffmann M, Hilgert J, Weich T. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg; 2024. doi:<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>","bibtex":"@book{Hoffmann_Hilgert_Weich_2024, place={Berlin, Heidelberg}, title={Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>}, publisher={Springer Berlin Heidelberg}, author={Hoffmann, Max and Hilgert, Joachim and Weich, Tobias}, year={2024} }","mla":"Hoffmann, Max, et al. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg, 2024, doi:<a href=\"https://doi.org/10.1007/978-3-662-67357-7\">10.1007/978-3-662-67357-7</a>.","short":"M. Hoffmann, J. Hilgert, T. Weich, Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik, Springer Berlin Heidelberg, Berlin, Heidelberg, 2024.","chicago":"Hoffmann, Max, Joachim Hilgert, and Tobias Weich. <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. <a href=\"https://doi.org/10.1007/978-3-662-67357-7\">https://doi.org/10.1007/978-3-662-67357-7</a>.","apa":"Hoffmann, M., Hilgert, J., &#38; Weich, T. (2024). <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-67357-7\">https://doi.org/10.1007/978-3-662-67357-7</a>","ieee":"M. Hoffmann, J. Hilgert, and T. Weich, <i>Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024."},"date_created":"2024-07-12T08:36:42Z","place":"Berlin, Heidelberg","department":[{"_id":"97"},{"_id":"643"},{"_id":"548"}],"type":"book"},{"oa":"1","external_id":{"arxiv":["2308.05082 "]},"quality_controlled":"1","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"file_date_updated":"2024-01-09T11:19:49Z","citation":{"bibtex":"@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of variational PDEs from data}, volume={34}, DOI={<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>}, number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2024} }","ama":"Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. <i>Chaos</i>. 2024;34(1). doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i>, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>.","short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i> 34, no. 1 (2024). <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>.","ieee":"C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” <i>Chaos</i>, vol. 34, no. 1, Art. no. 013104, 2024, doi: <a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. <i>Chaos</i>, <i>34</i>(1), Article 013104. <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>"},"ddc":["510"],"user_id":"85279","volume":34,"publisher":"AIP Publishing","_id":"46469","has_accepted_license":"1","status":"public","type":"journal_article","department":[{"_id":"636"}],"file":[{"date_created":"2024-01-09T10:48:38Z","creator":"coffen","title":"Accepted Manuscript Chaos","file_id":"50376","content_type":"application/pdf","relation":"main_file","date_updated":"2024-01-09T10:48:38Z","file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf","access_level":"open_access","file_size":13222105},{"creator":"coffen","description":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train\na neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent\nwith the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian\ndensities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for\nthe training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers\nguarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical\nsimulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory\nsuch as travelling waves. This is possible even when travelling waves are not present in the training data. This is\ncompared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces\ncontaining structurally simple solutions when these are not present in the training data. Ideas are demonstrated on\nexamples based on the wave equation and the Schrödinger equation.","date_created":"2024-01-09T11:19:49Z","relation":"main_file","date_updated":"2024-01-09T11:19:49Z","file_name":"LDensityPDE_AIP.pdf","file_size":12960884,"access_level":"open_access","title":"Learning of discrete models of variational PDEs from data","file_id":"50390","content_type":"application/pdf"}],"date_created":"2023-08-10T08:24:48Z","related_material":{"link":[{"description":"GitHub","url":"https://github.com/Christian-Offen/DLNN_pde","relation":"software"}]},"abstract":[{"lang":"eng","text":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are consistent with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory such as travelling waves. This is possible even when travelling waves are not present in the training data. This is compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger equation. "}],"issue":"1","publication":"Chaos","doi":"10.1063/5.0172287","article_number":"013104","language":[{"iso":"eng"}],"date_updated":"2024-08-12T13:45:43Z","publication_status":"published","intvolume":"        34","article_type":"original","year":"2024","title":"Learning of discrete models of variational PDEs from data","publication_identifier":{"issn":["1054-1500"]},"author":[{"id":"85279","full_name":"Offen, Christian","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"}]},{"_id":"55159","page":"28","ddc":["510"],"user_id":"85279","status":"public","has_accepted_license":"1","external_id":{"arxiv":["2407.07642"]},"oa":"1","citation":{"mla":"Offen, Christian. <i>Machine Learning of Discrete Field Theories with Guaranteed Convergence and Uncertainty Quantification</i>.","ama":"Offen C. Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification.","bibtex":"@article{Offen, title={Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification}, author={Offen, Christian} }","apa":"Offen, C. (n.d.). <i>Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification</i>.","ieee":"C. Offen, “Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification.” .","chicago":"Offen, Christian. “Machine Learning of Discrete Field Theories with Guaranteed Convergence and Uncertainty Quantification,” n.d.","short":"C. Offen, (n.d.)."},"file_date_updated":"2024-07-10T13:39:32Z","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"language":[{"iso":"eng"}],"author":[{"id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian"}],"title":"Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification","year":"2024","date_updated":"2024-08-12T13:43:32Z","publication_status":"submitted","date_created":"2024-07-10T13:43:50Z","file":[{"content_type":"application/pdf","file_id":"55160","title":"Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification","access_level":"open_access","file_size":4569314,"file_name":"L_Collocation.pdf","date_updated":"2024-07-10T13:39:32Z","relation":"main_file","date_created":"2024-07-10T13:39:32Z","description":"We introduce a method based on Gaussian process regression to identify discrete\nvariational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design.\nWe provide a rigorous convergence statement of the method.\nThe proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.\nMoreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory.\nThis is illustrated on the example of the discrete wave equation and Schrödinger equation.\nThe article constitutes an extension of our previous article for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.","creator":"coffen"}],"department":[{"_id":"636"}],"type":"preprint","keyword":["System identification","inverse problem of variational calculus","Gaussian process","Lagrangian learning","physics informed machine learning","geometry aware learning"],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/Lagrangian_GP_PDE","description":"GitHub"}]},"abstract":[{"text":"We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design. We provide a rigorous convergence statement of the method. The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.\r\nMoreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory. This is illustrated on the example of the discrete wave equation and Schrödinger equation.\r\nThe article constitutes an extension of our previous article  arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.","lang":"eng"}]},{"date_created":"2024-08-21T09:59:33Z","department":[{"_id":"363"}],"type":"journal_article","issue":"1","publication":"Statistics Education Research Journal","abstract":[{"text":"<jats:p>This study investigates how 11- to 12-year-old students construct data-based decision trees using data cards for classification purposes. We examine the students' heuristics and reasoning during this process. The research is based on an eight-week teaching unit during which students labeled data, built decision trees, and assessed them using test data. They learned to manually construct decision trees to classify food items as recommendable or not. They utilized data cards with a heuristic that is a simplified form of a machine learning algorithm. We report on evidence that this topic is teachable to middle school students, along with insights for refining our teaching approach and broader implications for teaching machine learning at the school level.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"article_number":"3","main_file_link":[{"open_access":"1","url":"https://doi.org/10.52041/serj.v23i1.450"}],"doi":"10.52041/serj.v23i1.450","publication_identifier":{"issn":["1570-1824"]},"author":[{"id":"42660","full_name":"Fleischer, Franz Yannik","first_name":"Franz Yannik","last_name":"Fleischer","orcid":"https://orcid.org/0000-0003-0318-0329"},{"full_name":"Podworny, Susanne","first_name":"Susanne","last_name":"Podworny","orcid":"0000-0002-6313-5987","id":"30619"},{"full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler","id":"16274"}],"year":"2024","title":"Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards as the First Introduction to Machine Learning in Middle School","intvolume":"        23","publication_status":"published","date_updated":"2024-08-21T10:02:38Z","oa":"1","citation":{"short":"F.Y. 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Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards as the First Introduction to Machine Learning in Middle School. <i>Statistics Education Research Journal</i>, <i>23</i>(1), Article 3. <a href=\"https://doi.org/10.52041/serj.v23i1.450\">https://doi.org/10.52041/serj.v23i1.450</a>","bibtex":"@article{Fleischer_Podworny_Biehler_2024, title={Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards as the First Introduction to Machine Learning in Middle School}, volume={23}, DOI={<a href=\"https://doi.org/10.52041/serj.v23i1.450\">10.52041/serj.v23i1.450</a>}, number={13}, journal={Statistics Education Research Journal}, publisher={International Association for Statistical Education}, author={Fleischer, Franz Yannik and Podworny, Susanne and Biehler, Rolf}, year={2024} }","ama":"Fleischer FY, Podworny S, Biehler R. Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards as the First Introduction to Machine Learning in Middle School. <i>Statistics Education Research Journal</i>. 2024;23(1). doi:<a href=\"https://doi.org/10.52041/serj.v23i1.450\">10.52041/serj.v23i1.450</a>","mla":"Fleischer, Franz Yannik, et al. “Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards as the First Introduction to Machine Learning in Middle School.” <i>Statistics Education Research Journal</i>, vol. 23, no. 1, 3, International Association for Statistical Education, 2024, doi:<a href=\"https://doi.org/10.52041/serj.v23i1.450\">10.52041/serj.v23i1.450</a>."},"_id":"55667","publisher":"International Association for Statistical Education","volume":23,"user_id":"37888","status":"public"},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/978-3-658-43964-4_13"}],"_id":"55756","publisher":"Springer Fachmedien Wiesbaden","language":[{"iso":"ger"}],"doi":"10.1007/978-3-658-43964-4_13","user_id":"37888","year":"2024","title":"Eine inklusive Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der Primarstufe","status":"public","publication_identifier":{"isbn":["9783658439637","9783658439644"]},"author":[{"first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf","id":"16274"},{"first_name":"Daniel","last_name":"Frischemeier","full_name":"Frischemeier, Daniel"}],"date_updated":"2024-08-26T09:33:50Z","publication_status":"published","place":"Wiesbaden","date_created":"2024-08-26T09:18:57Z","type":"book_chapter","oa":"1","department":[{"_id":"363"}],"publication":"Inklusives Lehren und Lernen von Mathematik","citation":{"short":"R. 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Frischemeier, “Eine inklusive Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der Primarstufe,” in <i>Inklusives Lehren und Lernen von Mathematik</i>, Wiesbaden: Springer Fachmedien Wiesbaden, 2024.","ama":"Biehler R, Frischemeier D. Eine inklusive Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der Primarstufe. In: <i>Inklusives Lehren und Lernen von Mathematik</i>. 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Klett Kallmeyer; 2024."},"date_created":"2024-08-26T09:38:05Z","type":"book","department":[{"_id":"363"}]},{"language":[{"iso":"eng"}],"_id":"45972","page":"A645--A669","volume":46,"user_id":"100441","doi":"10.1137/22M1531919","author":[{"orcid":"0000-0001-9872-3474","first_name":"Balázs","last_name":"Kovács","full_name":"Kovács, Balázs","id":"100441"}],"status":"public","title":"Numerical surgery for mean curvature flow of surfaces","year":"2024","intvolume":"        46","date_updated":"2024-08-27T07:42:56Z","date_created":"2023-07-10T12:32:34Z","department":[{"_id":"841"}],"type":"journal_article","citation":{"ama":"Kovács B. Numerical surgery for mean curvature flow of surfaces. <i>SIAM Journal on Scientific Computing</i>. 2024;46(2):A645--A669. doi:<a href=\"https://doi.org/10.1137/22M1531919\">10.1137/22M1531919</a>","bibtex":"@article{Kovács_2024, title={Numerical surgery for mean curvature flow of surfaces}, volume={46}, DOI={<a href=\"https://doi.org/10.1137/22M1531919\">10.1137/22M1531919</a>}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Kovács, Balázs}, year={2024}, pages={A645--A669} }","mla":"Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.” <i>SIAM Journal on Scientific Computing</i>, vol. 46, no. 2, 2024, pp. A645--A669, doi:<a href=\"https://doi.org/10.1137/22M1531919\">10.1137/22M1531919</a>.","short":"B. 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Kovács, “Numerical surgery for mean curvature flow of surfaces,” <i>SIAM Journal on Scientific Computing</i>, vol. 46, no. 2, pp. A645--A669, 2024, doi: <a href=\"https://doi.org/10.1137/22M1531919\">10.1137/22M1531919</a>."},"issue":"2","publication":"SIAM Journal on Scientific Computing","extern":"1"},{"date_created":"2024-04-05T13:55:33Z","department":[{"_id":"555"}],"type":"journal_article","keyword":["Applied Mathematics","Analysis"],"issue":"2","publication":"Journal of Mathematical Analysis and Applications","language":[{"iso":"eng"}],"article_number":"128125","doi":"10.1016/j.jmaa.2024.128125","publication_identifier":{"issn":["0022-247X"]},"author":[{"full_name":"Brennecken, Dominik","last_name":"Brennecken","first_name":"Dominik","id":"55911"}],"title":"Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting","year":"2024","intvolume":"       535","date_updated":"2024-09-03T14:40:46Z","publication_status":"published","citation":{"mla":"Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions in the Dunkl Setting.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 535, no. 2, 128125, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">10.1016/j.jmaa.2024.128125</a>.","bibtex":"@article{Brennecken_2024, title={Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting}, volume={535}, DOI={<a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">10.1016/j.jmaa.2024.128125</a>}, number={2128125}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Brennecken, Dominik}, year={2024} }","ama":"Brennecken D. Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting. <i>Journal of Mathematical Analysis and Applications</i>. 2024;535(2). doi:<a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">10.1016/j.jmaa.2024.128125</a>","ieee":"D. Brennecken, “Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 535, no. 2, Art. no. 128125, 2024, doi: <a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">10.1016/j.jmaa.2024.128125</a>.","apa":"Brennecken, D. (2024). Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting. <i>Journal of Mathematical Analysis and Applications</i>, <i>535</i>(2), Article 128125. <a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">https://doi.org/10.1016/j.jmaa.2024.128125</a>","short":"D. Brennecken, Journal of Mathematical Analysis and Applications 535 (2024).","chicago":"Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions in the Dunkl Setting.” <i>Journal of Mathematical Analysis and Applications</i> 535, no. 2 (2024). <a href=\"https://doi.org/10.1016/j.jmaa.2024.128125\">https://doi.org/10.1016/j.jmaa.2024.128125</a>."},"_id":"53300","publisher":"Elsevier BV","volume":535,"user_id":"55911","status":"public"},{"oa":"1","citation":{"bibtex":"@article{Hoffmann_Biehler_2024, title={Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures}, DOI={<a href=\"https://doi.org/10.1007/s11858-024-01633-4\">10.1007/s11858-024-01633-4</a>}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Hoffmann, Max and Biehler, Rolf}, year={2024} }","ama":"Hoffmann M, Biehler R. Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures. <i>ZDM – Mathematics Education</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s11858-024-01633-4\">10.1007/s11858-024-01633-4</a>","mla":"Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge When Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about Rotationally Symmetric Figures.” <i>ZDM – Mathematics Education</i>, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s11858-024-01633-4\">10.1007/s11858-024-01633-4</a>.","short":"M. Hoffmann, R. 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Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures. <i>ZDM – Mathematics Education</i>. <a href=\"https://doi.org/10.1007/s11858-024-01633-4\">https://doi.org/10.1007/s11858-024-01633-4</a>"},"quality_controlled":"1","publisher":"Springer Science and Business Media LLC","_id":"56016","user_id":"32202","status":"public","date_created":"2024-09-04T09:32:26Z","department":[{"_id":"97"},{"_id":"643"}],"type":"journal_article","publication":"ZDM – Mathematics Education","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Special tasks for pre-service teachers (PSTs) in university mathematics courses (“interface tasks”) are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and skills in a professionally relevant way. In this paper, we analyze answers that PSTs have created to an interface task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical perspective and then give a suitable elementarized answer. We situate these two steps theoretically and reconstruct the mathematical reasoning in PSTs' answers. Through qualitative content analysis, we examined how PSTs justify figures' symmetries from a university mathematics perspective and when responding to the fictitious student. The scenario of a student questioning the existence of 100° rotationally symmetrical figures elicited rich and varied responses, proving suitable for an interface task. We compared PSTs' reasoning related to mathematical clarification with the reasoning related to elementarization. In many cases, this revealed a productive use of course content. An interesting result is that there is no uniform picture as to whether the arguments are more detailed in the mathematical clarification or in the elementarization.</jats:p>"}],"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s11858-024-01633-4.pdf","open_access":"1"}],"doi":"10.1007/s11858-024-01633-4","publication_identifier":{"issn":["1863-9690","1863-9704"]},"author":[{"id":"32202","last_name":"Hoffmann","first_name":"Max","orcid":"0000-0002-6964-7123","full_name":"Hoffmann, Max"},{"full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler","id":"16274"}],"title":"Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures","year":"2024","article_type":"original","date_updated":"2024-09-04T09:33:45Z","publication_status":"published"},{"author":[{"id":"55911","last_name":"Brennecken","first_name":"Dominik","full_name":"Brennecken, Dominik"},{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"}],"publication_identifier":{"isbn":["978-3-031-57004-9"]},"year":"2024","title":"The Laplace transform in Dunkl theory","intvolume":"         5","publication_status":"published","date_updated":"2024-09-05T06:58:54Z","series_title":"Trends in Mathematics: Research Perspectives Ghent Analysis and PDE Cente","language":[{"iso":"eng"}],"publication":"Women in Analysis and PDE","date_created":"2024-09-03T15:31:27Z","department":[{"_id":"555"}],"type":"book_chapter","status":"public","_id":"56001","publisher":"Birkhäuser Cham","page":"425","volume":5,"editor":[{"last_name":"Chatzakou","first_name":"Marianna","full_name":"Chatzakou, Marianna"},{"first_name":"Michael","last_name":"Ruzhansky","full_name":"Ruzhansky, Michael"},{"full_name":"Stoeva, Diana","last_name":"Stoeva","first_name":"Diana"}],"user_id":"82981","citation":{"ieee":"D. Brennecken and M. Rösler, “The Laplace transform in Dunkl theory,” in <i>Women in Analysis and PDE</i>, vol. 5, M. Chatzakou, M. Ruzhansky, and D. Stoeva, Eds. Birkhäuser Cham, 2024, p. 425.","apa":"Brennecken, D., &#38; Rösler, M. (2024). The Laplace transform in Dunkl theory. In M. Chatzakou, M. Ruzhansky, &#38; D. Stoeva (Eds.), <i>Women in Analysis and PDE</i> (Vol. 5, p. 425). 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By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and skills in a professionally relevant way. In this paper, we analyze answers that PSTs have created to an interface task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical perspective and then give a suitable elementarized answer. We situate these two steps theoretically and reconstruct the mathematical reasoning in PSTs' answers. Through qualitative content analysis, we examined how PSTs justify figures' symmetries from a university mathematics perspective and when responding to the fictitious student. The scenario of a student questioning the existence of 100° rotationally symmetrical figures elicited rich and varied responses, proving suitable for an interface task. We compared PSTs' reasoning related to mathematical clarification with the reasoning related to elementarization. In many cases, this revealed a productive use of course content. An interesting result is that there is no uniform picture as to whether the arguments are more detailed in the mathematical clarification or in the elementarization.</jats:p>","lang":"eng"}],"publication":"ZDM – Mathematics Education","citation":{"chicago":"Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge When Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about Rotationally Symmetric Figures.” <i>ZDM – Mathematics Education</i>, 2024. <a href=\"https://doi.org/10.1007/s11858-024-01633-4\">https://doi.org/10.1007/s11858-024-01633-4</a>.","short":"M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2024).","ieee":"M. Hoffmann and R. Biehler, “Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures,” <i>ZDM – Mathematics Education</i>, 2024, doi: <a href=\"https://doi.org/10.1007/s11858-024-01633-4\">10.1007/s11858-024-01633-4</a>.","apa":"Hoffmann, M., &#38; Biehler, R. (2024). Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures. <i>ZDM – Mathematics Education</i>. <a href=\"https://doi.org/10.1007/s11858-024-01633-4\">https://doi.org/10.1007/s11858-024-01633-4</a>","bibtex":"@article{Hoffmann_Biehler_2024, title={Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures}, DOI={<a href=\"https://doi.org/10.1007/s11858-024-01633-4\">10.1007/s11858-024-01633-4</a>}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Hoffmann, Max and Biehler, Rolf}, year={2024} }","ama":"Hoffmann M, Biehler R. Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures. <i>ZDM – Mathematics Education</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1007/s11858-024-01633-4\">10.1007/s11858-024-01633-4</a>","mla":"Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge When Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about Rotationally Symmetric Figures.” <i>ZDM – Mathematics Education</i>, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s11858-024-01633-4\">10.1007/s11858-024-01633-4</a>."}},{"language":[{"iso":"eng"}],"_id":"56114","user_id":"178","status":"public","title":"Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups","year":"2024","author":[{"full_name":"Pinaud, Matthieu","first_name":"Matthieu","last_name":"Pinaud"}],"date_updated":"2024-09-11T22:45:02Z","external_id":{"arxiv":["2409.06512"]},"date_created":"2024-09-11T22:40:37Z","type":"preprint","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"citation":{"mla":"Pinaud, Matthieu. <i>Manifolds of Absolutely Continuous Functions with Values in an Infinite-Dimensional Manifold and Regularity Properties of Half-Lie Groups</i>. 2024.","ama":"Pinaud M. Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups. Published online 2024.","bibtex":"@article{Pinaud_2024, title={Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups}, author={Pinaud, Matthieu}, year={2024} }","apa":"Pinaud, M. (2024). <i>Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups</i>.","ieee":"M. Pinaud, “Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups.” 2024.","chicago":"Pinaud, Matthieu. “Manifolds of Absolutely Continuous Functions with Values in an Infinite-Dimensional Manifold and Regularity Properties of Half-Lie Groups,” 2024.","short":"M. Pinaud, (2024)."}},{"title":"Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln","status":"public","year":"2024","publication_status":"published","date_updated":"2024-09-25T08:26:10Z","_id":"56199","language":[{"iso":"ger"}],"main_file_link":[{"url":"https://kobra.uni-kassel.de/handle/123456789/15993"}],"editor":[{"last_name":"Liebendörfer","orcid":"0000-0001-9887-2074","first_name":"Michael","full_name":"Liebendörfer, Michael","id":"30933"},{"full_name":"Schmitz, Angelika","last_name":"Schmitz","first_name":"Angelika"},{"last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf","id":"16274"}],"user_id":"37888","citation":{"chicago":"Liebendörfer, Michael, Angelika Schmitz, and Rolf Biehler, eds. <i>Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln</i>, 2024.","short":"M. Liebendörfer, A. Schmitz, R. Biehler, eds., Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln, 2024.","ieee":"M. Liebendörfer, A. Schmitz, and R. Biehler, Eds., <i>Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln</i>. 2024.","apa":"Liebendörfer, M., Schmitz, A., &#38; Biehler, R. (Eds.). (2024). <i>Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln</i>.","bibtex":"@book{Liebendörfer_Schmitz_Biehler_2024, title={Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln}, year={2024} }","ama":"Liebendörfer M, Schmitz A, Biehler R, eds. <i>Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln</i>.; 2024.","mla":"Liebendörfer, Michael, et al., editors. <i>Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn und der TH Köln</i>. 2024."},"date_created":"2024-09-23T07:42:26Z","department":[{"_id":"363"}],"type":"book_editor"},{"publication_identifier":{"issn":["0025-584X","1522-2616"]},"author":[{"id":"55911","first_name":"Dominik","last_name":"Brennecken","full_name":"Brennecken, Dominik"}],"status":"public","year":"2024","title":"Dunkl convolution and elliptic regularity for Dunkl operators","publication_status":"published","date_updated":"2024-10-07T11:46:15Z","_id":"56366","publisher":"Wiley","language":[{"iso":"eng"}],"user_id":"55911","doi":"10.1002/mana.202300370","citation":{"chicago":"Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.” <i>Mathematische Nachrichten</i>, 2024. <a href=\"https://doi.org/10.1002/mana.202300370\">https://doi.org/10.1002/mana.202300370</a>.","short":"D. Brennecken, Mathematische Nachrichten (2024).","apa":"Brennecken, D. (2024). Dunkl convolution and elliptic regularity for Dunkl operators. <i>Mathematische Nachrichten</i>. <a href=\"https://doi.org/10.1002/mana.202300370\">https://doi.org/10.1002/mana.202300370</a>","ieee":"D. Brennecken, “Dunkl convolution and elliptic regularity for Dunkl operators,” <i>Mathematische Nachrichten</i>, 2024, doi: <a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>.","ama":"Brennecken D. Dunkl convolution and elliptic regularity for Dunkl operators. <i>Mathematische Nachrichten</i>. Published online 2024. doi:<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>","bibtex":"@article{Brennecken_2024, title={Dunkl convolution and elliptic regularity for Dunkl operators}, DOI={<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>}, journal={Mathematische Nachrichten}, publisher={Wiley}, author={Brennecken, Dominik}, year={2024} }","mla":"Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.” <i>Mathematische Nachrichten</i>, Wiley, 2024, doi:<a href=\"https://doi.org/10.1002/mana.202300370\">10.1002/mana.202300370</a>."},"publication":"Mathematische Nachrichten","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We discuss in which cases the Dunkl convolution  of distributions , possibly both with non‐compact support, can be defined and study its analytic properties. We prove results on the (singular‐)support of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic regularity for a certain class of Dunkl operators, called elliptic Dunkl operators. Finally, for the root system  we consider the Riesz distributions  and prove that their Dunkl convolution exists and that  holds.</jats:p>","lang":"eng"}],"date_created":"2024-10-07T11:44:00Z","department":[{"_id":"555"}],"type":"journal_article"},{"issue":"1","publication":"Discrete Mathematics","date_created":"2024-10-10T12:27:11Z","department":[{"_id":"542"}],"type":"journal_article","publication_identifier":{"issn":["0012-365X"]},"author":[{"last_name":"Cappello","first_name":"Chiara","full_name":"Cappello, Chiara"},{"full_name":"Naserasr, Reza","last_name":"Naserasr","first_name":"Reza"},{"full_name":"Steffen, Eckhard","first_name":"Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen","id":"15548"},{"first_name":"Zhouningxin","last_name":"Wang","full_name":"Wang, Zhouningxin"}],"title":"Critically 3-frustrated signed graphs","year":"2024","intvolume":"       348","publication_status":"published","date_updated":"2024-10-10T12:28:13Z","language":[{"iso":"eng"}],"article_number":"114258","doi":"10.1016/j.disc.2024.114258","citation":{"bibtex":"@article{Cappello_Naserasr_Steffen_Wang_2024, title={Critically 3-frustrated signed graphs}, volume={348}, DOI={<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>}, number={1114258}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2024} }","ama":"Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. <i>Discrete Mathematics</i>. 2024;348(1). doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>","mla":"Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” <i>Discrete Mathematics</i>, vol. 348, no. 1, 114258, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>.","short":"C. Cappello, R. Naserasr, E. Steffen, Z. Wang, Discrete Mathematics 348 (2024).","chicago":"Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” <i>Discrete Mathematics</i> 348, no. 1 (2024). <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">https://doi.org/10.1016/j.disc.2024.114258</a>.","ieee":"C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated signed graphs,” <i>Discrete Mathematics</i>, vol. 348, no. 1, Art. no. 114258, 2024, doi: <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>.","apa":"Cappello, C., Naserasr, R., Steffen, E., &#38; Wang, Z. (2024). Critically 3-frustrated signed graphs. <i>Discrete Mathematics</i>, <i>348</i>(1), Article 114258. <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">https://doi.org/10.1016/j.disc.2024.114258</a>"},"status":"public","_id":"56497","publisher":"Elsevier BV","volume":348,"user_id":"15540"},{"_id":"56584","language":[{"iso":"eng"}],"page":"105109","main_file_link":[{"url":"https://doi.org/10.1016/j.geomphys.2024.105109"}],"volume":198,"user_id":"178","author":[{"first_name":"Ali","last_name":"Suri","full_name":"Suri, Ali"}],"title":"Curvature and stability of quasi-geostrophic motion","status":"public","year":"2024","intvolume":"       198","date_updated":"2024-10-10T16:00:50Z","date_created":"2024-10-10T15:59:49Z","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"journal_article","citation":{"apa":"Suri, A. (2024). Curvature and stability of quasi-geostrophic motion. <i>Journal of Geometry and Physics</i>, <i>198</i>, 105109.","ieee":"A. Suri, “Curvature and stability of quasi-geostrophic motion,” <i>Journal of Geometry and Physics</i>, vol. 198, p. 105109, 2024.","short":"A. Suri, Journal of Geometry and Physics 198 (2024) 105109.","chicago":"Suri, Ali. “Curvature and Stability of Quasi-Geostrophic Motion.” <i>Journal of Geometry and Physics</i> 198 (2024): 105109.","mla":"Suri, Ali. “Curvature and Stability of Quasi-Geostrophic Motion.” <i>Journal of Geometry and Physics</i>, vol. 198, 2024, p. 105109.","ama":"Suri A. Curvature and stability of quasi-geostrophic motion. <i>Journal of Geometry and Physics</i>. 2024;198:105109.","bibtex":"@article{Suri_2024, title={Curvature and stability of quasi-geostrophic motion}, volume={198}, journal={Journal of Geometry and Physics}, author={Suri, Ali}, year={2024}, pages={105109} }"},"publication":"Journal of Geometry and Physics","quality_controlled":"1"},{"date_updated":"2024-10-10T16:05:47Z","intvolume":"       206","title":"Conjugate points along spherical harmonics","year":"2024","status":"public","author":[{"full_name":"Suri, Ali","first_name":"Ali","last_name":"Suri"}],"user_id":"178","volume":206,"page":"105333","main_file_link":[{"url":"https://doi.org/10.1016/j.geomphys.2024.105333"}],"language":[{"iso":"eng"}],"_id":"56585","quality_controlled":"1","publication":"Journal of Geometry and Physics","citation":{"short":"A. Suri, Journal of Geometry and Physics 206 (2024) 105333.","chicago":"Suri, Ali. “Conjugate Points along Spherical Harmonics.” <i>Journal of Geometry and Physics</i> 206 (2024): 105333.","apa":"Suri, A. (2024). Conjugate points along spherical harmonics. <i>Journal of Geometry and Physics</i>, <i>206</i>, 105333.","ieee":"A. Suri, “Conjugate points along spherical harmonics,” <i>Journal of Geometry and Physics</i>, vol. 206, p. 105333, 2024.","ama":"Suri A. Conjugate points along spherical harmonics. <i>Journal of Geometry and Physics</i>. 2024;206:105333.","bibtex":"@article{Suri_2024, title={Conjugate points along spherical harmonics}, volume={206}, journal={Journal of Geometry and Physics}, author={Suri, Ali}, year={2024}, pages={105333} }","mla":"Suri, Ali. “Conjugate Points along Spherical Harmonics.” <i>Journal of Geometry and Physics</i>, vol. 206, 2024, p. 105333."},"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"date_created":"2024-10-10T16:05:18Z"},{"date_created":"2024-10-10T15:49:15Z","external_id":{"arxiv":["2410.02909"]},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"preprint","citation":{"apa":"Glöckner, H., &#38; Suri, A. (2024). <i>L^1-regularity of strong ILB-Lie groups</i>.","ieee":"H. Glöckner and A. Suri, “L^1-regularity of strong ILB-Lie groups.” 2024.","short":"H. Glöckner, A. Suri, (2024).","chicago":"Glöckner, Helge, and Ali Suri. “L^1-Regularity of Strong ILB-Lie Groups,” 2024.","mla":"Glöckner, Helge, and Ali Suri. <i>L^1-Regularity of Strong ILB-Lie Groups</i>. 2024.","ama":"Glöckner H, Suri A. L^1-regularity of strong ILB-Lie groups. Published online 2024.","bibtex":"@article{Glöckner_Suri_2024, title={L^1-regularity of strong ILB-Lie groups}, author={Glöckner, Helge and Suri, Ali}, year={2024} }"},"_id":"56583","language":[{"iso":"eng"}],"user_id":"178","author":[{"id":"178","last_name":"Glöckner","first_name":"Helge","full_name":"Glöckner, Helge"},{"first_name":"Ali","last_name":"Suri","full_name":"Suri, Ali"}],"year":"2024","title":"L^1-regularity of strong ILB-Lie groups","status":"public","date_updated":"2024-10-10T15:51:43Z"}]