[{"language":[{"iso":"eng"}],"date_updated":"2023-08-10T08:44:55Z","doi":"10.3934/jgm.2022014","oa":"1","department":[{"_id":"636"}],"publication_status":"published","external_id":{"arxiv":["2006.14172"]},"title":"Backward error analysis for variational discretisations of partial differential equations","related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/multisymplectic"}]},"page":"447 - 471","citation":{"bibtex":"@article{McLachlan_Offen_2022, title={Backward error analysis for variational discretisations of partial differential equations}, volume={14}, DOI={10.3934/jgm.2022014}, number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan, Robert I and Offen, Christian}, year={2022}, pages={447–471} }","mla":"McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial Differential Equations.” Journal of Geometric Mechanics, vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:10.3934/jgm.2022014.","ama":"McLachlan RI, Offen C. Backward error analysis for variational discretisations of partial differential equations. Journal of Geometric Mechanics. 2022;14(3):447-471. doi:10.3934/jgm.2022014","apa":"McLachlan, R. I., & Offen, C. (2022). Backward error analysis for variational discretisations of partial differential equations. Journal of Geometric Mechanics, 14(3), 447–471. https://doi.org/10.3934/jgm.2022014","chicago":"McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial Differential Equations.” Journal of Geometric Mechanics 14, no. 3 (2022): 447–71. https://doi.org/10.3934/jgm.2022014.","ieee":"R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations of partial differential equations,” Journal of Geometric Mechanics, vol. 14, no. 3, pp. 447–471, 2022, doi: 10.3934/jgm.2022014.","short":"R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471."},"year":"2022","type":"journal_article","_id":"19941","intvolume":" 14","issue":"3","file_date_updated":"2022-06-13T09:11:38Z","publication":"Journal of Geometric Mechanics","publisher":"AIMS","author":[{"last_name":"McLachlan","first_name":"Robert I","full_name":"McLachlan, Robert I"},{"last_name":"Offen","id":"85279","first_name":"Christian","full_name":"Offen, Christian","orcid":"https://orcid.org/0000-0002-5940-8057"}],"file":[{"creator":"coffen","file_id":"31859","description":"In backward error analysis, an approximate solution to an equa-\ntion is compared to the exact solution to a nearby ‘modified’ equation. In\nnumerical ordinary differential equations, the two agree up to any power of\nthe step size. If the differential equation has a geometric property then the\nmodified equation may share it. In this way, known properties of differential\nequations can be applied to the approximation. But for partial differential\nequations, the known modified equations are of higher order, limiting appli-\ncability of the theory. Therefore, we study symmetric solutions of discretized\npartial differential equations that arise from a discrete variational principle.\nThese symmetric solutions obey infinite-dimensional functional equations. We\nshow that these equations admit second-order modified equations which are\nHamiltonian and also possess first-order Lagrangians in modified coordinates.\nThe modified equation and its associated structures are computed explicitly\nfor the case of rotating travelling waves in the nonlinear wave equation.","relation":"main_file","content_type":"application/pdf","date_updated":"2022-06-13T09:11:38Z","date_created":"2022-06-13T09:11:38Z","file_name":"2_BlendedBEASymmPDE.pdf","access_level":"open_access","title":"Backward error analysis for variational discretisations of PDEs","file_size":1507248}],"volume":14,"date_created":"2020-10-06T16:33:19Z","has_accepted_license":"1","status":"public","abstract":[{"text":"In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized\r\npartial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation.","lang":"eng"}],"article_type":"original","ddc":["510"],"user_id":"85279"},{"_id":"23382","main_file_link":[{"url":"https://aip.scitation.org/doi/abs/10.1063/5.0065913","open_access":"1"}],"year":"2022","type":"journal_article","citation":{"chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022). https://doi.org/10.1063/5.0065913.","apa":"Offen, C., & Ober-Blöbaum, S. (2022). Symplectic integration of learned Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(1). https://doi.org/10.1063/5.0065913","ama":"Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2022;32(1). doi:10.1063/5.0065913","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 32(1), AIP, 2022, doi:10.1063/5.0065913.","bibtex":"@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned Hamiltonian systems}, volume={32(1)}, DOI={10.1063/5.0065913}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }","short":"C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022).","ieee":"C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 32(1), 2022, doi: 10.1063/5.0065913."},"article_type":"original","abstract":[{"lang":"eng","text":"Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes."}],"user_id":"85279","ddc":["510"],"file":[{"access_level":"open_access","date_created":"2021-12-13T14:56:15Z","file_name":"SymplecticShadowIntegration_AIP.pdf","relation":"main_file","content_type":"application/pdf","date_updated":"2021-12-13T14:56:15Z","creator":"coffen","file_id":"28734","file_size":2285059}],"publisher":"AIP","quality_controlled":"1","author":[{"id":"85279","last_name":"Offen","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","id":"16494"}],"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","file_date_updated":"2021-12-13T14:56:15Z","status":"public","has_accepted_license":"1","date_created":"2021-08-11T08:24:02Z","volume":"32(1)","date_updated":"2023-08-10T08:48:14Z","oa":"1","doi":"10.1063/5.0065913","language":[{"iso":"eng"}],"external_id":{"arxiv":["2108.02492"]},"related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/Christian-Offen/symplectic-shadow-integration"}]},"title":"Symplectic integration of learned Hamiltonian systems","department":[{"_id":"636"}],"publication_status":"published"},{"date_updated":"2023-08-15T06:04:03Z","_id":"40613","language":[{"iso":"eng"}],"citation":{"mla":"Dröse, Jennifer. “Verstehensgrundlagen Diagnostizieren - Diagnostisches Denken von Drei Professionalisierungsgruppen.” Beiträge Zum Mathematikunterricht, 2022.","bibtex":"@inproceedings{Dröse_2022, title={Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen}, booktitle={Beiträge zum Mathematikunterricht}, author={Dröse, Jennifer}, year={2022} }","chicago":"Dröse, Jennifer. “Verstehensgrundlagen Diagnostizieren - Diagnostisches Denken von Drei Professionalisierungsgruppen.” In Beiträge Zum Mathematikunterricht, 2022.","ama":"Dröse J. Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen. In: Beiträge Zum Mathematikunterricht. ; 2022.","apa":"Dröse, J. (2022). Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen. Beiträge Zum Mathematikunterricht.","ieee":"J. Dröse, “Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen,” 2022.","short":"J. Dröse, in: Beiträge Zum Mathematikunterricht, 2022."},"type":"conference","year":"2022","user_id":"85820","title":"Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen","author":[{"last_name":"Dröse","id":"85820","first_name":"Jennifer","full_name":"Dröse, Jennifer"}],"department":[{"_id":"98"}],"publication":"Beiträge zum Mathematikunterricht","status":"public","date_created":"2023-01-27T19:00:01Z"},{"publication":"Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","department":[{"_id":"543"}],"author":[{"first_name":"Lara Marie","full_name":"Graf, Lara Marie","last_name":"Graf","id":"89837"},{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"},{"first_name":"Marcus","full_name":"Nührenbörger, Marcus","last_name":"Nührenbörger"},{"last_name":"Höveler","full_name":"Höveler, Karina","first_name":"Karina"}],"date_created":"2023-09-27T10:01:52Z","status":"public","user_id":"44184","title":"Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen","language":[{"iso":"eng"}],"page":"773-776","citation":{"ieee":"L. M. Graf, U. Häsel-Weide, M. Nührenbörger, and K. Höveler, “Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen,” in Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Frankfurt am Main, 2022, pp. 773–776.","short":"L.M. Graf, U. Häsel-Weide, M. Nührenbörger, K. Höveler, in: IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, 2022, pp. 773–776.","mla":"Graf, Lara Marie, et al. “Lernwege von Fachfremd Unterrichtenden Lehrkräften Zur Ablösung Vom Zählenden Rechnen.” Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfurt, 2022, pp. 773–76.","bibtex":"@inproceedings{Graf_Häsel-Weide_Nührenbörger_Höveler_2022, title={Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen}, booktitle={Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, author={Graf, Lara Marie and Häsel-Weide, Uta and Nührenbörger, Marcus and Höveler, Karina}, editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2022}, pages={773–776} }","chicago":"Graf, Lara Marie, Uta Häsel-Weide, Marcus Nührenbörger, and Karina Höveler. “Lernwege von Fachfremd Unterrichtenden Lehrkräften Zur Ablösung Vom Zählenden Rechnen.” In Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfurt, 773–76, 2022.","apa":"Graf, L. M., Häsel-Weide, U., Nührenbörger, M., & Höveler, K. (2022). Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 773–776).","ama":"Graf LM, Häsel-Weide U, Nührenbörger M, Höveler K. Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen. In: IDMI-Primar Goethe-Universität Frankfurt, ed. Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik. ; 2022:773-776."},"type":"conference","year":"2022","conference":{"start_date":"29.08.2022","name":"56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","location":"Frankfurt am Main","end_date":"02.09.2022"},"date_updated":"2023-09-27T10:02:12Z","_id":"47520","corporate_editor":["IDMI-Primar Goethe-Universität Frankfurt"]},{"author":[{"last_name":"Schwerin","id":"48912","first_name":"Imke","full_name":"Schwerin, Imke"}],"department":[{"_id":"543"}],"publication":"Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","status":"public","date_created":"2023-09-27T09:53:36Z","title":"Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis","user_id":"44184","type":"conference","year":"2022","citation":{"short":"I. Schwerin, in: IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, 2022, pp. 401–404.","ieee":"I. Schwerin, “Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis,” in Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Frankfurt am Main, 2022, pp. 401–404.","chicago":"Schwerin, Imke. “Verdoppeln Und Halbieren Im 2. Schuljahr - Vorgehensweisen Und Verständnis.” In Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfurt, 401–4, 2022.","ama":"Schwerin I. Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis. In: IDMI-Primar Goethe-Universität Frankfurt, ed. Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik. ; 2022:401-404.","apa":"Schwerin, I. (2022). Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 401–404).","bibtex":"@inproceedings{Schwerin_2022, title={Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis}, booktitle={Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, author={Schwerin, Imke}, editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2022}, pages={401–404} }","mla":"Schwerin, Imke. “Verdoppeln Und Halbieren Im 2. Schuljahr - Vorgehensweisen Und Verständnis.” Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität Frankfurt, 2022, pp. 401–04."},"page":"401-404","language":[{"iso":"eng"}],"_id":"47519","date_updated":"2023-09-27T09:54:00Z","conference":{"start_date":"29.08.2022","name":"56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","location":"Frankfurt am Main","end_date":"02.09.2022"},"corporate_editor":["IDMI-Primar Goethe-Universität Frankfurt"]},{"place":"Boston","title":"Pre-service Teachers' Professional Development: Relating Abstract Algebra and School Algebra","user_id":"37888","author":[{"last_name":"Dellori","full_name":"Dellori, Anna","first_name":"Anna"},{"id":"85190","last_name":"Wessel","full_name":"Wessel, Lena","first_name":"Lena"}],"publisher":"MA","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"643"}],"publication":"Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education","editor":[{"full_name":"Karunakaran, S.S.","first_name":"S.S.","last_name":"Karunakaran"},{"last_name":"Higgins","first_name":"A.","full_name":"Higgins, A."}],"status":"public","date_created":"2023-10-24T07:28:19Z","_id":"48407","date_updated":"2023-10-24T07:28:22Z","type":"book_chapter","citation":{"short":"A. Dellori, L. Wessel, in: S.S. Karunakaran, A. Higgins (Eds.), Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education, MA, Boston, 2022, p. 1177.","ieee":"A. Dellori and L. Wessel, “Pre-service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra,” in Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education, S. S. Karunakaran and A. Higgins, Eds. Boston: MA, 2022, p. 1177.","chicago":"Dellori, Anna, and Lena Wessel. “Pre-Service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra.” In Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education, edited by S.S. Karunakaran and A. Higgins, 1177. Boston: MA, 2022.","ama":"Dellori A, Wessel L. Pre-service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra. In: Karunakaran SS, Higgins A, eds. Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education. MA; 2022:1177.","apa":"Dellori, A., & Wessel, L. (2022). Pre-service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra. In S. S. Karunakaran & A. Higgins (Eds.), Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education (p. 1177). MA.","bibtex":"@inbook{Dellori_Wessel_2022, place={Boston}, title={Pre-service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra}, booktitle={Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education}, publisher={MA}, author={Dellori, Anna and Wessel, Lena}, editor={Karunakaran, S.S. and Higgins, A.}, year={2022}, pages={1177} }","mla":"Dellori, Anna, and Lena Wessel. “Pre-Service Teachers’ Professional Development: Relating Abstract Algebra and School Algebra.” Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education, edited by S.S. Karunakaran and A. Higgins, MA, 2022, p. 1177."},"year":"2022","page":"1177","language":[{"iso":"eng"}]},{"user_id":"37888","title":"Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten","publication":"mathematik lehren","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"643"}],"author":[{"id":"85190","last_name":"Wessel","full_name":"Wessel, Lena","first_name":"Lena"},{"id":"85820","last_name":"Dröse","full_name":"Dröse, Jennifer","first_name":"Jennifer"}],"date_created":"2023-10-24T07:33:17Z","status":"public","volume":233,"_id":"48408","intvolume":" 233","date_updated":"2023-10-24T07:33:22Z","language":[{"iso":"ger"}],"page":"33-36","year":"2022","citation":{"bibtex":"@article{Wessel_Dröse_2022, title={Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten}, volume={233}, journal={mathematik lehren}, author={Wessel, Lena and Dröse, Jennifer}, year={2022}, pages={33–36} }","mla":"Wessel, Lena, and Jennifer Dröse. “Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten.” mathematik lehren, vol. 233, 2022, pp. 33–36.","chicago":"Wessel, Lena, and Jennifer Dröse. “Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten.” mathematik lehren 233 (2022): 33–36.","ama":"Wessel L, Dröse J. Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten. mathematik lehren. 2022;233:33-36.","apa":"Wessel, L., & Dröse, J. (2022). Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten. mathematik lehren, 233, 33–36.","ieee":"L. Wessel and J. Dröse, “Schreiben will gelernt sein: Schreiblerngelegenheiten adaptiv gestalten,” mathematik lehren, vol. 233, pp. 33–36, 2022.","short":"L. Wessel, J. Dröse, mathematik lehren 233 (2022) 33–36."},"type":"journal_article"},{"user_id":"37888","title":"Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory","place":"Cham","status":"public","date_created":"2023-07-26T10:34:02Z","editor":[{"full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"},{"full_name":"Liebendörfer, Michael","first_name":"Michael","last_name":"Liebendörfer"},{"last_name":"Gueudet","full_name":"Gueudet, G.","first_name":"G."},{"last_name":"Rasmussen","first_name":"C.","full_name":"Rasmussen, C."},{"first_name":"C.","full_name":"Winslow, C.","last_name":"Winslow"}],"publication_identifier":{"isbn":["9783031141744","9783031141751"],"issn":["1869-4918","1869-4926"]},"publication_status":"published","publisher":"Springer International Publishing","author":[{"last_name":"Wessel","id":"85190","first_name":"Lena","full_name":"Wessel, Lena"},{"last_name":"Leuders","full_name":"Leuders, Timo","first_name":"Timo"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"643"}],"publication":"Practice-Oriented Research in Tertiary Mathematics Education","doi":"10.1007/978-3-031-14175-1_17","_id":"46160","date_updated":"2023-10-30T09:00:53Z","language":[{"iso":"eng"}],"type":"book_chapter","citation":{"mla":"Wessel, Lena, and Timo Leuders. “Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory.” Practice-Oriented Research in Tertiary Mathematics Education, edited by Rolf Biehler et al., Springer International Publishing, 2022, pp. 349–68, doi:10.1007/978-3-031-14175-1_17.","bibtex":"@inbook{Wessel_Leuders_2022, place={Cham}, title={Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory}, DOI={10.1007/978-3-031-14175-1_17}, booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer International Publishing}, author={Wessel, Lena and Leuders, Timo}, editor={Biehler, Rolf and Liebendörfer, Michael and Gueudet, G. and Rasmussen, C. and Winslow, C.}, year={2022}, pages={349–368} }","ama":"Wessel L, Leuders T. Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory. In: Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winslow C, eds. Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2022:349-368. doi:10.1007/978-3-031-14175-1_17","apa":"Wessel, L., & Leuders, T. (2022). Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory. In R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, & C. Winslow (Eds.), Practice-Oriented Research in Tertiary Mathematics Education (pp. 349–368). Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1_17","chicago":"Wessel, Lena, and Timo Leuders. “Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory.” In Practice-Oriented Research in Tertiary Mathematics Education, edited by Rolf Biehler, Michael Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winslow, 349–68. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-031-14175-1_17.","ieee":"L. Wessel and T. Leuders, “Profession-Specific Curriculum Design in Mathematics Teacher Education: Connecting Disciplinary Practice to the Learning of Group Theory,” in Practice-Oriented Research in Tertiary Mathematics Education, R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winslow, Eds. Cham: Springer International Publishing, 2022, pp. 349–368.","short":"L. Wessel, T. Leuders, in: R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winslow (Eds.), Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2022, pp. 349–368."},"year":"2022","page":"349-368"},{"author":[{"first_name":"Anna","full_name":"Dellori, Anna","last_name":"Dellori"},{"full_name":"Wessel, Lena","first_name":"Lena","id":"85190","last_name":"Wessel"}],"publisher":"LibreCat University","publication":"Beiträge zum Mathematikunterricht 2022","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"643"}],"status":"public","date_created":"2023-10-19T09:37:24Z","user_id":"37888","title":"Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra","main_file_link":[{"url":"http://dx.doi.org/10.17877/DE290R-23598"}],"language":[{"iso":"ger"}],"citation":{"mla":"Dellori, Anna, and Lena Wessel. “Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra.” Beiträge zum Mathematikunterricht 2022, LibreCat University, 2022, pp. 665–68, doi:10.17877/DE290R-23598.","bibtex":"@article{Dellori_Wessel_2022, title={Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra}, DOI={10.17877/DE290R-23598}, journal={Beiträge zum Mathematikunterricht 2022}, publisher={LibreCat University}, author={Dellori, Anna and Wessel, Lena}, year={2022}, pages={665–668} }","chicago":"Dellori, Anna, and Lena Wessel. “Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra.” Beiträge zum Mathematikunterricht 2022, 2022, 665–68. https://doi.org/10.17877/DE290R-23598.","apa":"Dellori, A., & Wessel, L. (2022). Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra. Beiträge zum Mathematikunterricht 2022, 665–668. https://doi.org/10.17877/DE290R-23598","ama":"Dellori A, Wessel L. Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra. Beiträge zum Mathematikunterricht 2022. Published online 2022:665-668. doi:10.17877/DE290R-23598","ieee":"A. Dellori and L. Wessel, “Entwicklung und Erprobung von professionsorientierten Lernumgebungen zur Wissensvernetzung in der Algebra,” Beiträge zum Mathematikunterricht 2022, pp. 665–668, 2022, doi: 10.17877/DE290R-23598.","short":"A. Dellori, L. Wessel, Beiträge zum Mathematikunterricht 2022 (2022) 665–668."},"type":"journal_article","year":"2022","page":"665-668","_id":"48325","date_updated":"2023-10-31T09:32:18Z","doi":"10.17877/DE290R-23598"},{"editor":[{"first_name":"P.","full_name":"Kleine, P.","last_name":"Kleine"},{"full_name":"Graulich, N.","first_name":"N.","last_name":"Graulich"},{"last_name":"Kuhn","first_name":"J.","full_name":"Kuhn, J."},{"full_name":"Schindler, M.","first_name":"M.","last_name":"Schindler"}],"status":"public","date_created":"2023-05-31T06:22:21Z","author":[{"first_name":"Jennifer","full_name":"Dröse, Jennifer","last_name":"Dröse","id":"85820"},{"full_name":"Neugebauer, P.","first_name":"P.","last_name":"Neugebauer"},{"last_name":"Delucchi Danhier","full_name":"Delucchi Danhier, R.","first_name":"R."},{"last_name":"Mertins","full_name":"Mertins, B.","first_name":"B."}],"quality_controlled":"1","department":[{"_id":"98"}],"publication":"Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis","title":"Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen","user_id":"85820","year":"2022","type":"book_chapter","citation":{"apa":"Dröse, J., Neugebauer, P., Delucchi Danhier, R., & Mertins, B. (2022). Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen. In P. Kleine, N. Graulich, J. Kuhn, & M. Schindler (Eds.), Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis (pp. 209–225). https://doi.org/10.1007/978-3-662-63214-7","ama":"Dröse J, Neugebauer P, Delucchi Danhier R, Mertins B. Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen. In: Kleine P, Graulich N, Kuhn J, Schindler M, eds. Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis. ; 2022:209-225. doi:https://doi.org/10.1007/978-3-662-63214-7","chicago":"Dröse, Jennifer, P. Neugebauer, R. Delucchi Danhier, and B. Mertins. “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen.” In Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, edited by P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, 209–25, 2022. https://doi.org/10.1007/978-3-662-63214-7.","mla":"Dröse, Jennifer, et al. “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen.” Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, edited by P. Kleine et al., 2022, pp. 209–25, doi:https://doi.org/10.1007/978-3-662-63214-7.","bibtex":"@inbook{Dröse_Neugebauer_Delucchi Danhier_Mertins_2022, title={Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen}, DOI={https://doi.org/10.1007/978-3-662-63214-7}, booktitle={Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis}, author={Dröse, Jennifer and Neugebauer, P. and Delucchi Danhier, R. and Mertins, B.}, editor={Kleine, P. and Graulich, N. and Kuhn, J. and Schindler, M.}, year={2022}, pages={209–225} }","short":"J. Dröse, P. Neugebauer, R. Delucchi Danhier, B. Mertins, in: P. Kleine, N. Graulich, J. Kuhn, M. Schindler (Eds.), Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, 2022, pp. 209–225.","ieee":"J. Dröse, P. Neugebauer, R. Delucchi Danhier, and B. Mertins, “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen,” in Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, Eds. 2022, pp. 209–225."},"page":"209-225","language":[{"iso":"ger"}],"doi":"https://doi.org/10.1007/978-3-662-63214-7","date_updated":"2023-11-02T08:07:31Z","_id":"45373"},{"status":"public","date_created":"2023-05-31T06:27:51Z","author":[{"first_name":"S.","full_name":"Prediger, S.","last_name":"Prediger"},{"id":"85820","last_name":"Dröse","full_name":"Dröse, Jennifer","first_name":"Jennifer"},{"last_name":"Stahnke","first_name":"R.","full_name":"Stahnke, R."},{"last_name":"Ademmer","first_name":"C.","full_name":"Ademmer, C."}],"quality_controlled":"1","publication":"Journal of Mathematics Teacher Education","department":[{"_id":"98"}],"user_id":"85820","title":"Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth","language":[{"iso":"eng"}],"type":"journal_article","year":"2022","citation":{"chicago":"Prediger, S., Jennifer Dröse, R. Stahnke, and C. Ademmer. “Teacher Expertise for Fostering At-Risk Students’ Understanding of Basic Concepts: Conceptual Model and Evidence for Growth.” Journal of Mathematics Teacher Education, 2022. https://doi.org/10.1007/s10857-022-09538-3.","apa":"Prediger, S., Dröse, J., Stahnke, R., & Ademmer, C. (2022). Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-022-09538-3","ama":"Prediger S, Dröse J, Stahnke R, Ademmer C. Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth. Journal of Mathematics Teacher Education. Published online 2022. doi:https://doi.org/10.1007/s10857-022-09538-3","bibtex":"@article{Prediger_Dröse_Stahnke_Ademmer_2022, title={Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth}, DOI={https://doi.org/10.1007/s10857-022-09538-3}, journal={Journal of Mathematics Teacher Education}, author={Prediger, S. and Dröse, Jennifer and Stahnke, R. and Ademmer, C.}, year={2022} }","mla":"Prediger, S., et al. “Teacher Expertise for Fostering At-Risk Students’ Understanding of Basic Concepts: Conceptual Model and Evidence for Growth.” Journal of Mathematics Teacher Education, 2022, doi:https://doi.org/10.1007/s10857-022-09538-3.","short":"S. Prediger, J. Dröse, R. Stahnke, C. Ademmer, Journal of Mathematics Teacher Education (2022).","ieee":"S. Prediger, J. Dröse, R. Stahnke, and C. Ademmer, “Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth,” Journal of Mathematics Teacher Education, 2022, doi: https://doi.org/10.1007/s10857-022-09538-3."},"doi":"https://doi.org/10.1007/s10857-022-09538-3","date_updated":"2023-11-02T08:07:42Z","_id":"45374"},{"date_updated":"2023-11-02T08:05:43Z","_id":"45379","type":"conference","year":"2022","citation":{"chicago":"Dröse, Jennifer, B. Griese, and Lena Wessel. “Prosepctive Teachers‘ Diagnostic Judgements on Students’ under- Standing of Conditional Probabilities.” In Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). Bozen-Bolzano, Italy, 2022.","apa":"Dröse, J., Griese, B., & Wessel, L. (2022). Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12).","ama":"Dröse J, Griese B, Wessel L. Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities. In: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). ; 2022.","mla":"Dröse, Jennifer, et al. “Prosepctive Teachers‘ Diagnostic Judgements on Students’ under- Standing of Conditional Probabilities.” Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2022.","bibtex":"@inproceedings{Dröse_Griese_Wessel_2022, place={Bozen-Bolzano, Italy}, title={Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities}, booktitle={Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)}, author={Dröse, Jennifer and Griese, B. and Wessel, Lena}, year={2022} }","short":"J. Dröse, B. Griese, L. Wessel, in: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Bozen-Bolzano, Italy, 2022.","ieee":"J. Dröse, B. Griese, and L. Wessel, “Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities,” 2022."},"language":[{"iso":"eng"}],"place":"Bozen-Bolzano, Italy","title":"Prosepctive teachers‘ diagnostic judgements on students’ under- standing of conditional probabilities","user_id":"85820","quality_controlled":"1","author":[{"last_name":"Dröse","id":"85820","first_name":"Jennifer","full_name":"Dröse, Jennifer"},{"last_name":"Griese","first_name":"B.","full_name":"Griese, B."},{"first_name":"Lena","full_name":"Wessel, Lena","last_name":"Wessel","id":"85190"}],"department":[{"_id":"98"}],"publication":"Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)","status":"public","date_created":"2023-05-31T06:59:15Z"},{"has_accepted_license":"1","status":"public","date_created":"2022-03-31T11:14:13Z","author":[{"first_name":"Nikolaus","full_name":"Vertovec, Nikolaus","last_name":"Vertovec","id":"93930"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","id":"16494"},{"last_name":"Margellos","first_name":"Kostas","full_name":"Margellos, Kostas"}],"department":[{"_id":"636"}],"title":"Verification of safety critical control policies using kernel methods","ddc":["510"],"user_id":"15694","abstract":[{"lang":"eng","text":"Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example."}],"type":"conference","citation":{"mla":"Vertovec, Nikolaus, et al. Verification of Safety Critical Control Policies Using Kernel Methods. 2022, pp. 1870–75.","bibtex":"@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875} }","chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.","apa":"Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (2022). Verification of safety critical control policies using kernel methods. 1870–1875.","ama":"Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control policies using kernel methods. In: ; 2022:1870-1875.","ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical control policies using kernel methods,” London, 2022, pp. 1870–1875.","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875."},"year":"2022","page":"1870-1875","language":[{"iso":"eng"}],"_id":"30733","date_updated":"2023-11-29T10:00:18Z","conference":{"end_date":"2022-07-15","start_date":"2022-07-12","name":"2022 European Control Conference (ECC)","location":"London"}},{"author":[{"last_name":"Dellori","full_name":"Dellori, Anna","first_name":"Anna"},{"id":"85190","last_name":"Wessel","full_name":"Wessel, Lena","first_name":"Lena"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"643"}],"publication":"Proceedings of INDRUM2022","status":"public","date_created":"2023-10-23T09:40:30Z","editor":[{"full_name":"Trigueros, M.","first_name":"M.","last_name":"Trigueros"},{"first_name":"B.","full_name":"Barquero, B.","last_name":"Barquero"},{"first_name":"R.","full_name":"Hochmuth, R.","last_name":"Hochmuth"},{"last_name":"Peters","full_name":"Peters, J.","first_name":"J."}],"user_id":"37888","title":"Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra","language":[{"iso":"eng"}],"type":"book_chapter","year":"2022","citation":{"ieee":"A. Dellori and L. Wessel, “Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra,” in Proceedings of INDRUM2022, M. Trigueros, B. Barquero, R. Hochmuth, and J. Peters, Eds. 2022, pp. 572–573.","short":"A. Dellori, L. Wessel, in: M. Trigueros, B. Barquero, R. Hochmuth, J. Peters (Eds.), Proceedings of INDRUM2022, 2022, pp. 572–573.","bibtex":"@inbook{Dellori_Wessel_2022, title={Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra}, booktitle={Proceedings of INDRUM2022}, author={Dellori, Anna and Wessel, Lena}, editor={Trigueros, M. and Barquero, B. and Hochmuth, R. and Peters, J.}, year={2022}, pages={572–573} }","mla":"Dellori, Anna, and Lena Wessel. “Design Principles for Intertwining Local and Nonlocal Mathematics - The Case of Relating Registers and Representations in Abstract Algebra.” Proceedings of INDRUM2022, edited by M. Trigueros et al., 2022, pp. 572–73.","apa":"Dellori, A., & Wessel, L. (2022). Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra. In M. Trigueros, B. Barquero, R. Hochmuth, & J. Peters (Eds.), Proceedings of INDRUM2022 (pp. 572–573).","ama":"Dellori A, Wessel L. Design principles for intertwining local and nonlocal mathematics - The case of relating registers and representations in abstract algebra. In: Trigueros M, Barquero B, Hochmuth R, Peters J, eds. Proceedings of INDRUM2022. ; 2022:572-573.","chicago":"Dellori, Anna, and Lena Wessel. “Design Principles for Intertwining Local and Nonlocal Mathematics - The Case of Relating Registers and Representations in Abstract Algebra.” In Proceedings of INDRUM2022, edited by M. Trigueros, B. Barquero, R. Hochmuth, and J. Peters, 572–73, 2022."},"page":"572-573","_id":"48385","date_updated":"2023-10-23T09:43:48Z"},{"publication_status":"published","publication_identifier":{"issn":["0173-5322","1869-2699"]},"date_created":"2023-01-27T18:47:24Z","status":"public","publication":"Journal für Mathematik-Didaktik","keyword":["Education","General Mathematics"],"department":[{"_id":"98"}],"publisher":"Springer Science and Business Media LLC","quality_controlled":"1","author":[{"last_name":"Dröse","first_name":"Jennifer","full_name":"Dröse, Jennifer"},{"first_name":"Susanne","full_name":"Prediger, Susanne","last_name":"Prediger"}],"title":"Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements","user_id":"85820","abstract":[{"text":"AbstractTeachers’ in-depth diagnostic thinking has been shown to be crucial for student-centered teaching as they need to perceive and interpret students’ understanding for well-informed decision-making on adaptive teaching practices. The paper presents a content-related approach to analyzing diagnostic thinking processes with respect to the mathematical knowledge elements that prospective teachers identify as students’ resources and obstacles. Prospective teachers’ challenge is that some relevant knowledge elements first have to be unpacked, because compact concepts (such as the place value concept) or procedures (such as for multi-digit multiplication) comprise several smaller knowledge elements (such as the positional property) that have to be made explicit for students to foster their learning processes adequately. Our study examines what knowledge elements prospective teachers perceive and interpret in a transcript vignettes on multi-digit multiplication (of decimal and natural numbers) and its underlying basic arithmetic concepts (place value understanding and meaning of multiplication) in written diagnostic judgments on students’ resources and obstacles (N = 196). A comparative design within the vignette is used to investigate how far the process of perceiving can be supported by thematic cues. The analysis reveals that those knowledge elements cued in the vignette by being already unpacked and explicitly addressed are perceived and interpreted more often (but with lower correctness) than those that are uncued and therefore have to be unpacked by the prospective teachers themselves. This confirms the need to prepare prospective teachers for unpacking mathematical concepts themselves.","lang":"eng"}],"citation":{"short":"J. Dröse, S. Prediger, Journal Für Mathematik-Didaktik (2022).","ieee":"J. Dröse and S. Prediger, “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements,” Journal für Mathematik-Didaktik, 2022, doi: 10.1007/s13138-022-00214-w.","ama":"Dröse J, Prediger S. Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements. Journal für Mathematik-Didaktik. Published online 2022. doi:10.1007/s13138-022-00214-w","apa":"Dröse, J., & Prediger, S. (2022). Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements. Journal Für Mathematik-Didaktik. https://doi.org/10.1007/s13138-022-00214-w","chicago":"Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik, 2022. https://doi.org/10.1007/s13138-022-00214-w.","bibtex":"@article{Dröse_Prediger_2022, title={Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements}, DOI={10.1007/s13138-022-00214-w}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science and Business Media LLC}, author={Dröse, Jennifer and Prediger, Susanne}, year={2022} }","mla":"Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik, Springer Science and Business Media LLC, 2022, doi:10.1007/s13138-022-00214-w."},"type":"journal_article","year":"2022","language":[{"iso":"eng"}],"doi":"10.1007/s13138-022-00214-w","date_updated":"2023-11-02T08:05:14Z","_id":"40607"},{"year":"2022","citation":{"apa":"Dröse, J., Griese, B., & Wessel, L. (2022). Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). TwelfthCongressoftheEuropeanSocietyforResearchin Mathematics Education(CERME12), Bozen-Bolzano,Italy.","ama":"Dröse J, Griese B, Wessel L. Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities. In: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). ; 2022.","chicago":"Dröse, Jennifer, Birgit Griese, and Lena Wessel. “Prospective Teachers’ Diagnostic Judgments on Students’ Understanding of Conditional Probabilities.” In Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2022.","bibtex":"@inproceedings{Dröse_Griese_Wessel_2022, title={Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities}, booktitle={Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)}, author={Dröse, Jennifer and Griese, Birgit and Wessel, Lena}, year={2022} }","mla":"Dröse, Jennifer, et al. “Prospective Teachers’ Diagnostic Judgments on Students’ Understanding of Conditional Probabilities.” Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2022.","short":"J. Dröse, B. Griese, L. Wessel, in: Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), 2022.","ieee":"J. Dröse, B. Griese, and L. Wessel, “Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities,” presented at the TwelfthCongressoftheEuropeanSocietyforResearchin Mathematics Education(CERME12), Bozen-Bolzano,Italy, 2022."},"type":"conference","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://hal.science/hal-03744585/"}],"_id":"48389","date_updated":"2023-11-02T08:04:55Z","conference":{"name":"TwelfthCongressoftheEuropeanSocietyforResearchin Mathematics Education(CERME12)","start_date":"Feb2022","location":"Bozen-Bolzano,Italy"},"status":"public","date_created":"2023-10-23T10:56:02Z","quality_controlled":"1","author":[{"full_name":"Dröse, Jennifer","first_name":"Jennifer","id":"85820","last_name":"Dröse"},{"last_name":"Griese","full_name":"Griese, Birgit","first_name":"Birgit"},{"last_name":"Wessel","id":"85190","first_name":"Lena","full_name":"Wessel, Lena"}],"publication":"Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"643"}],"title":"Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities","user_id":"85820"},{"date_created":"2023-05-31T06:54:24Z","status":"public","editor":[{"full_name":"Fernandez, C.","first_name":"C.","last_name":"Fernandez"},{"last_name":"Llinares","first_name":"S.","full_name":"Llinares, S."},{"last_name":"Gutiérrez","first_name":"A.","full_name":"Gutiérrez, A."},{"last_name":"Planas","full_name":"Planas, N.","first_name":"N."}],"department":[{"_id":"98"}],"publication":"Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME","author":[{"first_name":"Jennifer","full_name":"Dröse, Jennifer","last_name":"Dröse","id":"85820"},{"first_name":"Lena","full_name":"Wessel, Lena","last_name":"Wessel","id":"85190"}],"quality_controlled":"1","user_id":"85820","title":"Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task","language":[{"iso":"eng"}],"citation":{"mla":"Dröse, Jennifer, and Lena Wessel. “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task.” Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME, edited by C. Fernandez et al., 2022.","bibtex":"@inproceedings{Dröse_Wessel_2022, title={Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task}, booktitle={Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME}, author={Dröse, Jennifer and Wessel, Lena}, editor={Fernandez, C. and Llinares, S. and Gutiérrez, A. and Planas, N.}, year={2022} }","ama":"Dröse J, Wessel L. Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task. In: Fernandez C, Llinares S, Gutiérrez A, Planas N, eds. Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME. ; 2022.","apa":"Dröse, J., & Wessel, L. (2022). Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task. In C. Fernandez, S. Llinares, A. Gutiérrez, & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME.","chicago":"Dröse, Jennifer, and Lena Wessel. “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task.” In Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME, edited by C. Fernandez, S. Llinares, A. Gutiérrez, and N. Planas, 2022.","ieee":"J. Dröse and L. Wessel, “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task,” in Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME, 2022.","short":"J. Dröse, L. Wessel, in: C. Fernandez, S. Llinares, A. Gutiérrez, N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME, 2022."},"year":"2022","type":"conference","_id":"45378","date_updated":"2023-11-02T08:05:31Z"},{"external_id":{"arxiv":["2201.04892"]},"title":"Semiclassical formulae For Wigner distributions","department":[{"_id":"623"},{"_id":"548"},{"_id":"10"}],"date_updated":"2024-02-06T20:40:45Z","doi":"10.1088/1751-8121/ac6d2b","language":[{"iso":"eng"}],"abstract":[{"text":"In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.","lang":"eng"}],"article_type":"review","user_id":"49178","publication":"Journal of Physics A: Mathematical and Theoretical","publisher":"IOP Publishing Ltd","author":[{"last_name":"Barkhofen","id":"48188","first_name":"Sonja","full_name":"Barkhofen, Sonja"},{"first_name":"Philipp","full_name":"Schütte, Philipp","last_name":"Schütte","id":"50168"},{"full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","first_name":"Tobias","id":"49178","last_name":"Weich"}],"date_created":"2022-05-04T12:23:11Z","status":"public","volume":55,"_id":"31057","intvolume":" 55","issue":"24","article_number":"244007","year":"2022","citation":{"bibtex":"@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For Wigner distributions}, volume={55}, DOI={10.1088/1751-8121/ac6d2b}, number={24244007}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd}, author={Barkhofen, Sonja and Schütte, Philipp and Weich, Tobias}, year={2022} }","mla":"Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, 244007, IOP Publishing Ltd, 2022, doi:10.1088/1751-8121/ac6d2b.","apa":"Barkhofen, S., Schütte, P., & Weich, T. (2022). Semiclassical formulae For Wigner distributions. Journal of Physics A: Mathematical and Theoretical, 55(24), Article 244007. https://doi.org/10.1088/1751-8121/ac6d2b","ama":"Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions. Journal of Physics A: Mathematical and Theoretical. 2022;55(24). doi:10.1088/1751-8121/ac6d2b","chicago":"Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical 55, no. 24 (2022). https://doi.org/10.1088/1751-8121/ac6d2b.","ieee":"S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner distributions,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, Art. no. 244007, 2022, doi: 10.1088/1751-8121/ac6d2b.","short":"S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022)."},"type":"journal_article"},{"language":[{"iso":"eng"}],"supervisor":[{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler"},{"id":"220","last_name":"Hilgert","full_name":"Hilgert, Joachim","first_name":"Joachim"}],"page":"410","citation":{"bibtex":"@book{Hoffmann_2022, title={Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende}, DOI={10.17619/UNIPB/1-1313}, author={Hoffmann, Max}, year={2022} }","mla":"Hoffmann, Max. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende. 2022, doi:10.17619/UNIPB/1-1313.","chicago":"Hoffmann, Max. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende, 2022. https://doi.org/10.17619/UNIPB/1-1313.","apa":"Hoffmann, M. (2022). Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende. https://doi.org/10.17619/UNIPB/1-1313","ama":"Hoffmann M. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende.; 2022. doi:10.17619/UNIPB/1-1313","ieee":"M. Hoffmann, Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende. 2022.","short":"M. Hoffmann, Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende, 2022."},"type":"dissertation","year":"2022","main_file_link":[{"url":"https://digital.ub.uni-paderborn.de/hs/content/titleinfo/6503170","open_access":"1"}],"oa":"1","doi":"10.17619/UNIPB/1-1313","date_updated":"2024-02-19T06:28:58Z","_id":"31363","date_created":"2022-05-22T10:56:47Z","status":"public","department":[{"_id":"97"}],"author":[{"last_name":"Hoffmann","id":"32202","first_name":"Max","full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123"}],"user_id":"49063","title":"Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende","abstract":[{"lang":"eng","text":"Vorgestellt wird ein Entwicklungsforschungsprojekt zur Konzeption und Durchführung einer Veranstaltung \"Geometrie für Lehramtsstudierende\". Die Schwerpunkte des Projekts sind zum einen die inhaltliche Gestaltung der Veranstaltung und zum anderen die Umsetzung von Professionsorientierung. Bezogen auf den inhaltlichen Aufbau wird das auf metrischen Räumen aufbauende Axiomensystem der \"Saccheri-Ebene\" vorgestellt und mit alternativen axiomatischen Zugängen zur ebenen Geometrie verglichen. Die Frage nach der Umsetzung von Professionsorientierung in Fachveranstaltungen ist eng mit der Problematik der zweiten Diskontinuität verbunden. In der Arbeit wird dieses Problem auf Grundlage der Synthese von theoretischen Hintergründen zur Bedeutung von mathematischem Wissen und Können für professionelle Handlungskompetenz von Mathematiklehrkräften diskutiert und darauf aufbauend werden theoriebasierte Entwurfsprinzipien für professionsorientierte Fachveranstaltungen entworfen. Zentrale Elemente der methodischen Gestaltung sind die sogenannten \"Schnittstellenwochen\" zu den Themen Kongruenz und Symmetrie sowie das begleitende Schnittstellen-ePortfolio. Das zentrale Ergebnis der Arbeit ist ein theoretisch fundiertes und empirisch evaluiertes ganzheitliches Veranstaltungskonzept für eine professionsorientierte Geometrie-Veranstaltung für Lehramtsstudierende, dessen Konzeption auf andere Fachveranstaltungen übertragbar ist. Darüber hinaus ergeben sich im Rahmen der durchgeführten Entwicklungsforschung verschiedene neue Beiträge zur Geometriedidaktik in Schule- und Hochschule."},{"text":"This thesis presents a design research project on the conception and implementation of a course \"Geometry for Student Teachers\". The focal points of the project are, on the one hand, the content structure of the course and, on the other hand, the implementation of professional orientation. With regard to the content structure, the axiom system of the \"Saccheri plane\", which is based on metric spaces, is presented and compared with alternative axiomatic approaches to plane geometry. The question of implementing professional orientation in mathematics courses is closely connected to the problem of the second discontinuity. In the paper, this problem is discussed on the basis of the synthesis of theoretical backgrounds on the importance of mathematical knowledge and skills for professional competence of mathematics teachers. Building on this, theory-based design principles for profession-oriented subject courses are developed. Central elements of the methodological design are the so-called \"interface weeks\" on the topics of congruence and symmetry and an accompanying interface ePortfolio. The central result of the thesis is a theoretically founded and empirically evaluated holistic course concept for a profession-oriented geometry course for student teachers, the conception of which is transferable to other subject events. In addition, various new contributions to the didactics of geometry in schools and universities result from the desing research.","lang":"eng"}]},{"date_updated":"2024-02-19T06:28:12Z","doi":"10.4171/jst/414","language":[{"iso":"eng"}],"title":"Poisson transforms for trees of bounded degree","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"publication_status":"published","publication_identifier":{"issn":["1664-039X"]},"_id":"35322","intvolume":" 12","issue":"2","page":"659-681","year":"2022","citation":{"short":"K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.","ieee":"K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded degree,” Journal of Spectral Theory, vol. 12, no. 2, pp. 659–681, 2022, doi: 10.4171/jst/414.","apa":"Bux, K.-U., Hilgert, J., & Weich, T. (2022). Poisson transforms for trees of bounded degree. Journal of Spectral Theory, 12(2), 659–681. https://doi.org/10.4171/jst/414","ama":"Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree. 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Hilgert, T. Weich, K.-U. Bux, J. of Spectral Theory 12 (2022) 659–681.","ieee":"J. Hilgert, T. Weich, and K.-U. Bux, “Poisson transforms for trees of bounded degree,” J. of Spectral Theory, vol. 12, pp. 659–681, 2022.","apa":"Hilgert, J., Weich, T., & Bux, K.-U. (2022). Poisson transforms for trees of bounded degree. J. of Spectral Theory, 12, 659–681.","ama":"Hilgert J, Weich T, Bux K-U. Poisson transforms for trees of bounded degree. J of Spectral Theory. 2022;12:659-681.","chicago":"Hilgert, Joachim, Tobias Weich, and K.-U. Bux. “Poisson Transforms for Trees of Bounded Degree.” J. of Spectral Theory 12 (2022): 659–81.","bibtex":"@article{Hilgert_Weich_Bux_2022, title={Poisson transforms for trees of bounded degree}, volume={12}, journal={J. of Spectral Theory}, author={Hilgert, Joachim and Weich, Tobias and Bux, K.-U.}, year={2022}, pages={659–681} }","mla":"Hilgert, Joachim, et al. “Poisson Transforms for Trees of Bounded Degree.” J. of Spectral Theory, vol. 12, 2022, pp. 659–81."},"page":"659-681","intvolume":" 12","_id":"51385","date_updated":"2024-02-19T06:36:21Z","status":"public","date_created":"2024-02-19T06:36:17Z","volume":12,"publication_status":"published","author":[{"full_name":"Hilgert, Joachim","first_name":"Joachim","id":"220","last_name":"Hilgert"},{"orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","first_name":"Tobias","id":"49178","last_name":"Weich"},{"last_name":"Bux","full_name":"Bux, K.-U.","first_name":"K.-U."}],"publication":"J. of Spectral Theory","department":[{"_id":"91"}],"user_id":"49063","title":"Poisson transforms for trees of bounded degree"},{"publication":"Mathematische Semesterberichte","department":[{"_id":"91"}],"author":[{"first_name":"Joachim","full_name":"Hilgert, Joachim","last_name":"Hilgert","id":"220"}],"date_created":"2024-02-20T09:49:04Z","status":"public","volume":69,"publication_status":"published","user_id":"49063","title":"Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021","language":[{"iso":"eng"}],"page":"151–153","year":"2022","citation":{"ieee":"J. Hilgert, “Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021,” Mathematische Semesterberichte, vol. 69. pp. 151–153, 2022, doi: 10.1007/s00591-021-00314-7.","short":"J. Hilgert, Mathematische Semesterberichte 69 (2022) 151–153.","bibtex":"@article{Hilgert_2022, title={Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021}, volume={69}, DOI={10.1007/s00591-021-00314-7}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2022}, pages={151–153} }","mla":"Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021.” Mathematische Semesterberichte, vol. 69, 2022, pp. 151–153, doi:10.1007/s00591-021-00314-7.","chicago":"Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021.” Mathematische Semesterberichte, 2022. https://doi.org/10.1007/s00591-021-00314-7.","ama":"Hilgert J. Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021. Mathematische Semesterberichte. 2022;69:151–153. doi:10.1007/s00591-021-00314-7","apa":"Hilgert, J. (2022). Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021. In Mathematische Semesterberichte (Vol. 69, pp. 151–153). https://doi.org/10.1007/s00591-021-00314-7"},"type":"review","_id":"51554","date_updated":"2024-02-20T09:52:53Z","intvolume":" 69","doi":"10.1007/s00591-021-00314-7"},{"conference":{"end_date":"2022-09-02","location":"Frankfurt am. Main","name":"56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","start_date":"2022-08-29"},"_id":"52574","date_updated":"2024-03-14T11:19:43Z","doi":"https://doi.org/10.37626/GA9783959872089.0","language":[{"iso":"ger"}],"citation":{"short":"G. Werth, in: Beiträge zum Mathematikunterricht, WTM, Münster, 2022.","ieee":"G. Werth, “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings,” presented at the 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Frankfurt am. Main, 2022, doi: https://doi.org/10.37626/GA9783959872089.0.","ama":"Werth G. Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings. In: Beiträge zum Mathematikunterricht. WTM; 2022. doi:https://doi.org/10.37626/GA9783959872089.0","apa":"Werth, G. (2022). Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings. Beiträge zum Mathematikunterricht. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, Frankfurt am. Main. https://doi.org/10.37626/GA9783959872089.0","chicago":"Werth, Gerda. “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings.” In Beiträge zum Mathematikunterricht. Münster: WTM, 2022. https://doi.org/10.37626/GA9783959872089.0.","bibtex":"@inproceedings{Werth_2022, place={Münster}, title={Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings}, DOI={https://doi.org/10.37626/GA9783959872089.0}, booktitle={Beiträge zum Mathematikunterricht}, publisher={WTM}, author={Werth, Gerda}, year={2022} }","mla":"Werth, Gerda. “Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings.” Beiträge zum Mathematikunterricht, WTM, 2022, doi:https://doi.org/10.37626/GA9783959872089.0."},"year":"2022","type":"conference","place":"Münster","user_id":"578","title":"Neue Wege im mathematischen Unterricht - Auf den Spuren Mathilde Vaertings","publication":"Beiträge zum Mathematikunterricht","department":[{"_id":"98"}],"author":[{"full_name":"Werth, Gerda","first_name":"Gerda","id":"578","last_name":"Werth"}],"publisher":"WTM","date_created":"2024-03-14T11:17:56Z","status":"public","publication_status":"published"},{"user_id":"81513","title":"Tensor-based computation of metastable and coherent sets","department":[{"_id":"101"}],"publication":"Physica D: Nonlinear Phenomena","author":[{"first_name":"Feliks","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","last_name":"Nüske","id":"81513"},{"full_name":"Gelß, Patrick","first_name":"Patrick","last_name":"Gelß"},{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"last_name":"Clementi","first_name":"Cecilia","full_name":"Clementi, Cecilia"}],"date_created":"2021-09-12T08:51:24Z","status":"public","publication_status":"published","publication_identifier":{"issn":["0167-2789"]},"_id":"24169","date_updated":"2022-01-06T06:56:08Z","doi":"10.1016/j.physd.2021.133018","article_number":"133018","language":[{"iso":"eng"}],"year":"2021","citation":{"ieee":"F. Nüske, P. Gelß, S. Klus, and C. Clementi, “Tensor-based computation of metastable and coherent sets,” Physica D: Nonlinear Phenomena, Art. no. 133018, 2021, doi: 10.1016/j.physd.2021.133018.","short":"F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena (2021).","mla":"Nüske, Feliks, et al. “Tensor-Based Computation of Metastable and Coherent Sets.” Physica D: Nonlinear Phenomena, 133018, 2021, doi:10.1016/j.physd.2021.133018.","bibtex":"@article{Nüske_Gelß_Klus_Clementi_2021, title={Tensor-based computation of metastable and coherent sets}, DOI={10.1016/j.physd.2021.133018}, number={133018}, journal={Physica D: Nonlinear Phenomena}, author={Nüske, Feliks and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia}, year={2021} }","chicago":"Nüske, Feliks, Patrick Gelß, Stefan Klus, and Cecilia Clementi. “Tensor-Based Computation of Metastable and Coherent Sets.” Physica D: Nonlinear Phenomena, 2021. https://doi.org/10.1016/j.physd.2021.133018.","apa":"Nüske, F., Gelß, P., Klus, S., & Clementi, C. (2021). Tensor-based computation of metastable and coherent sets. Physica D: Nonlinear Phenomena, Article 133018. https://doi.org/10.1016/j.physd.2021.133018","ama":"Nüske F, Gelß P, Klus S, Clementi C. Tensor-based computation of metastable and coherent sets. Physica D: Nonlinear Phenomena. Published online 2021. doi:10.1016/j.physd.2021.133018"},"type":"journal_article"},{"user_id":"81513","title":"Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry","department":[{"_id":"101"}],"publication":"Machine Learning: Science and Technology","author":[{"first_name":"Stefan","full_name":"Klus, Stefan","last_name":"Klus"},{"last_name":"Gelß","full_name":"Gelß, Patrick","first_name":"Patrick"},{"last_name":"Nüske","id":"81513","first_name":"Feliks","full_name":"Nüske, Feliks","orcid":"0000-0003-2444-7889"},{"first_name":"Frank","full_name":"Noé, Frank","last_name":"Noé"}],"date_created":"2021-09-12T08:52:57Z","status":"public","publication_identifier":{"issn":["2632-2153"]},"publication_status":"published","_id":"24170","date_updated":"2022-01-06T06:56:08Z","doi":"10.1088/2632-2153/ac14ad","article_number":"045016","language":[{"iso":"eng"}],"citation":{"ieee":"S. Klus, P. Gelß, F. Nüske, and F. Noé, “Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry,” Machine Learning: Science and Technology, Art. no. 045016, 2021, doi: 10.1088/2632-2153/ac14ad.","short":"S. Klus, P. Gelß, F. Nüske, F. Noé, Machine Learning: Science and Technology (2021).","bibtex":"@article{Klus_Gelß_Nüske_Noé_2021, title={Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry}, DOI={10.1088/2632-2153/ac14ad}, number={045016}, journal={Machine Learning: Science and Technology}, author={Klus, Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank}, year={2021} }","mla":"Klus, Stefan, et al. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” Machine Learning: Science and Technology, 045016, 2021, doi:10.1088/2632-2153/ac14ad.","chicago":"Klus, Stefan, Patrick Gelß, Feliks Nüske, and Frank Noé. “Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.” Machine Learning: Science and Technology, 2021. https://doi.org/10.1088/2632-2153/ac14ad.","apa":"Klus, S., Gelß, P., Nüske, F., & Noé, F. (2021). Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. Machine Learning: Science and Technology, Article 045016. https://doi.org/10.1088/2632-2153/ac14ad","ama":"Klus S, Gelß P, Nüske F, Noé F. Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry. Machine Learning: Science and Technology. Published online 2021. doi:10.1088/2632-2153/ac14ad"},"type":"journal_article","year":"2021"},{"_id":"21195","date_updated":"2022-01-06T06:54:49Z","doi":"10.1007/s11571-020-09656-9","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s11571-020-09656-9.pdf"}],"citation":{"chicago":"Goelz, Christian, Karin Mora, Julia Kristin Stroehlein, Franziska Katharina Haase, Michael Dellnitz, Claus Reinsberger, and Solveig Vieluf. “Electrophysiological Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.” Cognitive Neurodynamics, 2021. https://doi.org/10.1007/s11571-020-09656-9.","ama":"Goelz C, Mora K, Stroehlein JK, et al. Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. Cognitive Neurodynamics. 2021. doi:10.1007/s11571-020-09656-9","apa":"Goelz, C., Mora, K., Stroehlein, J. K., Haase, F. K., Dellnitz, M., Reinsberger, C., & Vieluf, S. (2021). Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults. Cognitive Neurodynamics. https://doi.org/10.1007/s11571-020-09656-9","mla":"Goelz, Christian, et al. “Electrophysiological Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.” Cognitive Neurodynamics, 2021, doi:10.1007/s11571-020-09656-9.","bibtex":"@article{Goelz_Mora_Stroehlein_Haase_Dellnitz_Reinsberger_Vieluf_2021, title={Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults}, DOI={10.1007/s11571-020-09656-9}, journal={Cognitive Neurodynamics}, author={Goelz, Christian and Mora, Karin and Stroehlein, Julia Kristin and Haase, Franziska Katharina and Dellnitz, Michael and Reinsberger, Claus and Vieluf, Solveig}, year={2021} }","short":"C. Goelz, K. Mora, J.K. Stroehlein, F.K. Haase, M. Dellnitz, C. Reinsberger, S. Vieluf, Cognitive Neurodynamics (2021).","ieee":"C. Goelz et al., “Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults,” Cognitive Neurodynamics, 2021."},"year":"2021","type":"journal_article","language":[{"iso":"eng"}],"title":"Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults","user_id":"32643","author":[{"full_name":"Goelz, Christian","first_name":"Christian","last_name":"Goelz"},{"last_name":"Mora","first_name":"Karin","full_name":"Mora, Karin"},{"last_name":"Stroehlein","first_name":"Julia Kristin","full_name":"Stroehlein, Julia Kristin"},{"last_name":"Haase","first_name":"Franziska Katharina","full_name":"Haase, Franziska Katharina"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Reinsberger","first_name":"Claus","full_name":"Reinsberger, Claus"},{"full_name":"Vieluf, Solveig","first_name":"Solveig","last_name":"Vieluf"}],"publication":"Cognitive Neurodynamics","department":[{"_id":"101"}],"status":"public","date_created":"2021-02-08T13:16:07Z"},{"main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/2297-8747/26/2/31/pdf"}],"year":"2021","type":"journal_article","citation":{"ama":"Berkemeier MB, Peitz S. Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models. Mathematical and Computational Applications. 2021;26(2). doi:10.3390/mca26020031","apa":"Berkemeier, M. B., & Peitz, S. (2021). Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models. Mathematical and Computational Applications, 26(2). https://doi.org/10.3390/mca26020031","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical and Computational Applications 26, no. 2 (2021). https://doi.org/10.3390/mca26020031.","mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical and Computational Applications, vol. 26, no. 2, 31, 2021, doi:10.3390/mca26020031.","bibtex":"@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models}, volume={26}, DOI={10.3390/mca26020031}, number={231}, journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2021} }","short":"M.B. Berkemeier, S. Peitz, Mathematical and Computational Applications 26 (2021).","ieee":"M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models,” Mathematical and Computational Applications, vol. 26, no. 2, 2021."},"intvolume":" 26","_id":"21337","article_number":"31","issue":"2","author":[{"full_name":"Berkemeier, Manuel Bastian","first_name":"Manuel Bastian","id":"51701","last_name":"Berkemeier"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"publication":"Mathematical and Computational Applications","volume":26,"status":"public","date_created":"2021-03-01T10:46:48Z","abstract":[{"lang":"eng","text":"We present a flexible trust region descend algorithm for unconstrained and\r\nconvexly constrained multiobjective optimization problems. It is targeted at\r\nheterogeneous and expensive problems, i.e., problems that have at least one\r\nobjective function that is computationally expensive. The method is\r\nderivative-free in the sense that neither need derivative information be\r\navailable for the expensive objectives nor are gradients approximated using\r\nrepeated function evaluations as is the case in finite-difference methods.\r\nInstead, a multiobjective trust region approach is used that works similarly to\r\nits well-known scalar pendants. Local surrogate models constructed from\r\nevaluation data of the true objective functions are employed to compute\r\npossible descent directions. In contrast to existing multiobjective trust\r\nregion algorithms, these surrogates are not polynomial but carefully\r\nconstructed radial basis function networks. This has the important advantage\r\nthat the number of data points scales linearly with the parameter space\r\ndimension. The local models qualify as fully linear and the corresponding\r\ngeneral scalar framework is adapted for problems with multiple objectives.\r\nConvergence to Pareto critical points is proven and numerical examples\r\nillustrate our findings."}],"user_id":"47427","language":[{"iso":"eng"}],"date_updated":"2022-01-06T06:54:55Z","doi":"10.3390/mca26020031","oa":"1","department":[{"_id":"101"},{"_id":"655"}],"publication_identifier":{"eissn":["2297-8747"]},"publication_status":"published","title":"Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models"},{"user_id":"81513","title":"Spectral Properties of Effective Dynamics from Conditional Expectations","abstract":[{"lang":"eng","text":"The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting."}],"status":"public","date_created":"2021-04-28T18:07:56Z","publication_identifier":{"issn":["1099-4300"]},"publication_status":"published","author":[{"id":"81513","last_name":"Nüske","orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","first_name":"Feliks"},{"last_name":"Koltai","full_name":"Koltai, Péter","first_name":"Péter"},{"full_name":"Boninsegna, Lorenzo","first_name":"Lorenzo","last_name":"Boninsegna"},{"last_name":"Clementi","first_name":"Cecilia","full_name":"Clementi, Cecilia"}],"publication":"Entropy","department":[{"_id":"101"}],"oa":"1","article_number":"134","doi":"10.3390/e23020134","_id":"21820","date_updated":"2022-01-06T06:55:16Z","language":[{"iso":"eng"}],"type":"journal_article","citation":{"ama":"Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective Dynamics from Conditional Expectations. Entropy. 2021. doi:10.3390/e23020134","apa":"Nüske, F., Koltai, P., Boninsegna, L., & Clementi, C. (2021). Spectral Properties of Effective Dynamics from Conditional Expectations. Entropy. https://doi.org/10.3390/e23020134","chicago":"Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi. “Spectral Properties of Effective Dynamics from Conditional Expectations.” Entropy, 2021. https://doi.org/10.3390/e23020134.","bibtex":"@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties of Effective Dynamics from Conditional Expectations}, DOI={10.3390/e23020134}, number={134}, journal={Entropy}, author={Nüske, Feliks and Koltai, Péter and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2021} }","mla":"Nüske, Feliks, et al. “Spectral Properties of Effective Dynamics from Conditional Expectations.” Entropy, 134, 2021, doi:10.3390/e23020134.","short":"F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).","ieee":"F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties of Effective Dynamics from Conditional Expectations,” Entropy, 2021."},"year":"2021","main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/1099-4300/23/2/134"}]},{"user_id":"47427","abstract":[{"lang":"eng","text":"In this article, we present an efficient descent method for locally Lipschitz\r\ncontinuous multiobjective optimization problems (MOPs). The method is realized\r\nby combining a theoretical result regarding the computation of descent\r\ndirections for nonsmooth MOPs with a practical method to approximate the\r\nsubdifferentials of the objective functions. We show convergence to points\r\nwhich satisfy a necessary condition for Pareto optimality. Using a set of test\r\nproblems, we compare our method to the multiobjective proximal bundle method by\r\nM\\\"akel\\\"a. The results indicate that our method is competitive while being\r\neasier to implement. While the number of objective function evaluations is\r\nlarger, the overall number of subgradient evaluations is lower. Finally, we\r\nshow that our method can be combined with a subdivision algorithm to compute\r\nentire Pareto sets of nonsmooth MOPs."}],"status":"public","date_created":"2020-04-27T09:11:22Z","volume":188,"author":[{"id":"32643","last_name":"Gebken","full_name":"Gebken, Bennet","first_name":"Bennet"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian","id":"47427","last_name":"Peitz"}],"publication":"Journal of Optimization Theory and Applications","intvolume":" 188","_id":"16867","citation":{"short":"B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188 (2021) 696–723.","ieee":"B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz multiobjective optimization problems,” Journal of Optimization Theory and Applications, vol. 188, pp. 696–723, 2021.","chicago":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications 188 (2021): 696–723. https://doi.org/10.1007/s10957-020-01803-w.","ama":"Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications. 2021;188:696-723. doi:10.1007/s10957-020-01803-w","apa":"Gebken, B., & Peitz, S. (2021). An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications, 188, 696–723. https://doi.org/10.1007/s10957-020-01803-w","bibtex":"@article{Gebken_Peitz_2021, title={An efficient descent method for locally Lipschitz multiobjective optimization problems}, volume={188}, DOI={10.1007/s10957-020-01803-w}, journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={696–723} }","mla":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications, vol. 188, 2021, pp. 696–723, doi:10.1007/s10957-020-01803-w."},"year":"2021","type":"journal_article","page":"696-723","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf"}],"title":"An efficient descent method for locally Lipschitz multiobjective optimization problems","publication_status":"published","department":[{"_id":"101"}],"oa":"1","doi":"10.1007/s10957-020-01803-w","date_updated":"2022-01-06T06:52:57Z","language":[{"iso":"eng"}]},{"title":"Inverse multiobjective optimization: Inferring decision criteria from data","department":[{"_id":"101"}],"oa":"1","doi":"10.1007/s10898-020-00983-z","date_updated":"2022-01-06T06:52:48Z","language":[{"iso":"eng"}],"user_id":"47427","abstract":[{"lang":"eng","text":"It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs."}],"status":"public","date_created":"2020-03-13T12:45:05Z","volume":80,"publisher":"Springer","author":[{"id":"32643","last_name":"Gebken","full_name":"Gebken, Bennet","first_name":"Bennet"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427"}],"publication":"Journal of Global Optimization","_id":"16295","intvolume":" 80","year":"2021","type":"journal_article","citation":{"short":"B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29.","ieee":"B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision criteria from data,” Journal of Global Optimization, vol. 80, pp. 3–29, 2021.","apa":"Gebken, B., & Peitz, S. (2021). Inverse multiobjective optimization: Inferring decision criteria from data. Journal of Global Optimization, 80, 3–29. https://doi.org/10.1007/s10898-020-00983-z","ama":"Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision criteria from data. Journal of Global Optimization. 2021;80:3-29. doi:10.1007/s10898-020-00983-z","chicago":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” Journal of Global Optimization 80 (2021): 3–29. https://doi.org/10.1007/s10898-020-00983-z.","bibtex":"@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization: Inferring decision criteria from data}, volume={80}, DOI={10.1007/s10898-020-00983-z}, journal={Journal of Global Optimization}, publisher={Springer}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={3–29} }","mla":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” Journal of Global Optimization, vol. 80, Springer, 2021, pp. 3–29, doi:10.1007/s10898-020-00983-z."},"page":"3-29","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf","open_access":"1"}]},{"date_created":"2022-06-20T09:54:24Z","status":"public","department":[{"_id":"101"}],"author":[{"last_name":"Gerlach","id":"32655","first_name":"Raphael","full_name":"Gerlach, Raphael"}],"title":"The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems","user_id":"32643","abstract":[{"lang":"ger","text":"Ein zentraler Aspekt bei der Untersuchung dynamischer Systeme ist die Analyse ihrer invarianten Mengen wie des globalen Attraktors und (in)stabiler Mannigfaltigkeiten. Insbesondere wenn das zugrunde liegende System von einem Parameter abhängt, ist es entscheidend, sie im Bezug auf diesen Parameter effizient zu verfolgen. Für die Berechnung invarianter Mengen stützen wir uns für ihre Approximation auf numerische Algorithmen. Typischerweise können diese Methoden jedoch nur auf endlich-dimensionale dynamische Systeme angewendet werden. In dieser Arbeit präsentieren wir daher einen numerischen Rahmen für die globale dynamische Analyse unendlich-dimensionaler Systeme. Wir werden Einbettungstechniken verwenden, um das core dynamical system (CDS) zu definieren, welches ein dynamisch äquivalentes endlich-dimensionales System ist.Das CDS wird dann verwendet, um eingebettete invariante Mengen, also eins-zu-eins Bilder, mittels Mengen-orientierten numerischen Methoden zu approximieren. Bei der Konstruktion des CDS ist es entscheidend, eine geeignete Beobachtungsabbildung auszuwählen und die geeignete inverse Abbildung zu entwerfen. Dazu werden wir geeignete numerische Implementierungen des CDS für DDEs und PDEs vorstellen. Für eine nachfolgende geometrische Analyse der eingebetteten invarianten Menge betrachten wir eine Lerntechnik namens diffusion maps, die ihre intrinsische Geometrie enthüllt sowie ihre Dimension schätzt. Schließlich wenden wir unsere entwickelten numerischen Methoden an einigen bekannten unendlich-dimensionale dynamischen Systeme an, wie die Mackey-Glass-Gleichung, die Kuramoto-Sivashinsky-Gleichung und die Navier-Stokes-Gleichung."},{"lang":"eng","text":"One central aspect in the study of dynamical systems is the analysis of its invariant sets such as the global attractor and (un)stable manifolds. In particular, when the underlying system depends on a parameter it is crucial to efficiently track those set with respect to this parameter. For the computation of invariant sets we rely on numerical algorithms for their approximation but typically those tools can only be applied to finite-dimensional dynamical systems. Thus, in thesis we present a numerical framework for the global dynamical analysis of infinite-dimensional systems. We will use embedding techniques for the definition of the core dynamical system (CDS) which is a dynamically equivalent finite-dimensional system. The CDS is then used for the approximation of related embedded invariant sets, i.e, one-to-one images, by set-oriented numerical methods. For the construction of the CDS it is crucial to choose an appropriate observation map and to design its corresponding inverse. Therefore, we will present suitable numerical realizations of the CDS for DDEs and PDEs. For a subsequent geometric analysis of the embedded invariant set we will consider a manifold learning technique called diffusion maps which reveals its intrinsic geometry and estimates its dimension. Finally, we apply our develop numerical tools on some well-known infinite-dimensional dynamical systems such as the Mackey-Glass equation, the Kuramoto-Sivashinsky equation and the Navier-Stokes equation."}],"citation":{"apa":"Gerlach, R. (2021). The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems. https://doi.org/10.17619/UNIPB/1-1278","ama":"Gerlach R. The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems.; 2021. doi:10.17619/UNIPB/1-1278","chicago":"Gerlach, Raphael. The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems, 2021. https://doi.org/10.17619/UNIPB/1-1278.","bibtex":"@book{Gerlach_2021, title={The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems}, DOI={10.17619/UNIPB/1-1278}, author={Gerlach, Raphael}, year={2021} }","mla":"Gerlach, Raphael. The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems. 2021, doi:10.17619/UNIPB/1-1278.","short":"R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems, 2021.","ieee":"R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems. 2021."},"type":"dissertation","year":"2021","language":[{"iso":"eng"}],"supervisor":[{"last_name":"Dellnitz ","full_name":"Dellnitz , Michael","first_name":"Michael"},{"full_name":"Koltai, Péter","first_name":"Péter","last_name":"Koltai"}],"main_file_link":[{"open_access":"1","url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/6214949"}],"doi":"10.17619/UNIPB/1-1278","oa":"1","date_updated":"2022-06-20T13:40:30Z","_id":"32057"},{"date_updated":"2022-06-21T11:54:50Z","doi":"10.4310/JSG.2021.v19.n6.a1","language":[{"iso":"eng"}],"title":"Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions","department":[{"_id":"548"}],"publication_status":"published","publication_identifier":{"unknown":["1540-2347","1527-5256"]},"intvolume":" 19","_id":"32016","issue":"6","page":"1281 - 1337","year":"2021","type":"journal_article","citation":{"mla":"Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” Journal of Symplectic Geometry, vol. 19, no. 6, 2021, pp. 1281–337, doi:10.4310/JSG.2021.v19.n6.a1.","bibtex":"@article{Delarue_Ramacher_2021, title={Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions}, volume={19}, DOI={10.4310/JSG.2021.v19.n6.a1}, number={6}, journal={Journal of Symplectic Geometry}, author={Delarue, Benjamin and Ramacher, Pablo}, year={2021}, pages={1281–1337} }","ama":"Delarue B, Ramacher P. Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. Journal of Symplectic Geometry. 2021;19(6):1281-1337. doi:10.4310/JSG.2021.v19.n6.a1","apa":"Delarue, B., & Ramacher, P. (2021). Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. Journal of Symplectic Geometry, 19(6), 1281–1337. https://doi.org/10.4310/JSG.2021.v19.n6.a1","chicago":"Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” Journal of Symplectic Geometry 19, no. 6 (2021): 1281–1337. https://doi.org/10.4310/JSG.2021.v19.n6.a1.","ieee":"B. Delarue and P. Ramacher, “Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions,” Journal of Symplectic Geometry, vol. 19, no. 6, pp. 1281–1337, 2021, doi: 10.4310/JSG.2021.v19.n6.a1.","short":"B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337."},"article_type":"original","user_id":"70575","publication":"Journal of Symplectic Geometry","author":[{"last_name":"Delarue","id":"70575","first_name":"Benjamin","full_name":"Delarue, Benjamin"},{"last_name":"Ramacher","full_name":"Ramacher, Pablo","first_name":"Pablo"}],"volume":19,"date_created":"2022-06-20T08:46:56Z","status":"public"},{"type":"journal_article","citation":{"ieee":"J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, and C.-Q. Zhang, “Nowhere-zero 3-flows in toroidal graphs,” Journal of Combinatorial Theory, Series B, vol. 153, pp. 61–80, 2021, doi: 10.1016/j.jctb.2021.11.001.","bibtex":"@article{Li_Ma_Miao_Shi_Wang_Zhang_2021, title={Nowhere-zero 3-flows in toroidal graphs}, volume={153}, DOI={10.1016/j.jctb.2021.11.001}, journal={Journal of Combinatorial Theory, Series B}, publisher={Elsevier BV}, author={Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang, Weifan and Zhang, Cun-Quan}, year={2021}, pages={61–80} }","mla":"Li, Jiaao, et al. “Nowhere-Zero 3-Flows in Toroidal Graphs.” Journal of Combinatorial Theory, Series B, vol. 153, Elsevier BV, 2021, pp. 61–80, doi:10.1016/j.jctb.2021.11.001.","apa":"Li, J., Ma, Y., Miao, Z., Shi, Y., Wang, W., & Zhang, C.-Q. (2021). Nowhere-zero 3-flows in toroidal graphs. Journal of Combinatorial Theory, Series B, 153, 61–80. https://doi.org/10.1016/j.jctb.2021.11.001","ama":"Li J, Ma Y, Miao Z, Shi Y, Wang W, Zhang C-Q. Nowhere-zero 3-flows in toroidal graphs. Journal of Combinatorial Theory, Series B. 2021;153:61-80. doi:10.1016/j.jctb.2021.11.001","short":"J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, C.-Q. Zhang, Journal of Combinatorial Theory, Series B 153 (2021) 61–80.","chicago":"Li, Jiaao, Yulai Ma, Zhengke Miao, Yongtang Shi, Weifan Wang, and Cun-Quan Zhang. “Nowhere-Zero 3-Flows in Toroidal Graphs.” Journal of Combinatorial Theory, Series B 153 (2021): 61–80. https://doi.org/10.1016/j.jctb.2021.11.001."},"year":"2021","page":"61-80","_id":"34042","intvolume":" 153","publisher":"Elsevier BV","author":[{"last_name":"Li","first_name":"Jiaao","full_name":"Li, Jiaao"},{"full_name":"Ma, Yulai","first_name":"Yulai","id":"92748","last_name":"Ma"},{"last_name":"Miao","first_name":"Zhengke","full_name":"Miao, Zhengke"},{"last_name":"Shi","first_name":"Yongtang","full_name":"Shi, Yongtang"},{"last_name":"Wang","first_name":"Weifan","full_name":"Wang, Weifan"},{"first_name":"Cun-Quan","full_name":"Zhang, Cun-Quan","last_name":"Zhang"}],"publication":"Journal of Combinatorial Theory, Series B","keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"volume":153,"status":"public","date_created":"2022-11-09T08:43:55Z","user_id":"15540","language":[{"iso":"eng"}],"date_updated":"2022-11-09T08:44:37Z","doi":"10.1016/j.jctb.2021.11.001","department":[{"_id":"542"}],"publication_status":"published","publication_identifier":{"issn":["0095-8956"]},"title":"Nowhere-zero 3-flows in toroidal graphs"},{"doi":"https://doi.org/10.1016/j.jalgebra.2020.11.007","date_updated":"2022-12-21T18:58:44Z","language":[{"iso":"eng"}],"title":"Decompositions of locally compact contraction groups, series and extensions","publication_identifier":{"issn":["0021-8693"]},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34786","intvolume":" 570","page":"164-214","year":"2021","citation":{"bibtex":"@article{Glöckner_Willis_2021, title={Decompositions of locally compact contraction groups, series and extensions}, volume={570}, DOI={https://doi.org/10.1016/j.jalgebra.2020.11.007}, journal={Journal of Algebra}, author={Glöckner, Helge and Willis, George A.}, year={2021}, pages={164–214} }","mla":"Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction Groups, Series and Extensions.” Journal of Algebra, vol. 570, 2021, pp. 164–214, doi:https://doi.org/10.1016/j.jalgebra.2020.11.007.","chicago":"Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction Groups, Series and Extensions.” Journal of Algebra 570 (2021): 164–214. https://doi.org/10.1016/j.jalgebra.2020.11.007.","apa":"Glöckner, H., & Willis, G. A. (2021). Decompositions of locally compact contraction groups, series and extensions. Journal of Algebra, 570, 164–214. https://doi.org/10.1016/j.jalgebra.2020.11.007","ama":"Glöckner H, Willis GA. Decompositions of locally compact contraction groups, series and extensions. Journal of Algebra. 2021;570:164-214. doi:https://doi.org/10.1016/j.jalgebra.2020.11.007","ieee":"H. Glöckner and G. A. Willis, “Decompositions of locally compact contraction groups, series and extensions,” Journal of Algebra, vol. 570, pp. 164–214, 2021, doi: https://doi.org/10.1016/j.jalgebra.2020.11.007.","short":"H. Glöckner, G.A. Willis, Journal of Algebra 570 (2021) 164–214."},"type":"journal_article","user_id":"178","abstract":[{"text":"A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups.","lang":"eng"}],"article_type":"original","volume":570,"date_created":"2022-12-21T18:43:08Z","status":"public","publication":"Journal of Algebra","keyword":["Contraction group","Torsion group","Extension","Cocycle","Section","Equivariant cohomology","Abelian group","Nilpotent group","Isomorphism types"],"author":[{"full_name":"Glöckner, Helge","first_name":"Helge","id":"178","last_name":"Glöckner"},{"last_name":"Willis","first_name":"George A.","full_name":"Willis, George A."}],"quality_controlled":"1"},{"status":"public","date_created":"2022-12-21T19:17:28Z","volume":781,"quality_controlled":"1","author":[{"full_name":"Glöckner, Helge","first_name":"Helge","id":"178","last_name":"Glöckner"},{"full_name":"Willis, George A.","first_name":"George A.","last_name":"Willis"}],"keyword":["22D05","22A05","20E18"],"publication":"J. Reine Angew. Math.","user_id":"178","article_type":"original","citation":{"ieee":"H. Glöckner and G. A. Willis, “Locally pro-p contraction groups are nilpotent,” J. Reine Angew. Math., vol. 781, pp. 85–103, 2021, doi: 10.1515/crelle-2021-0050.","short":"H. Glöckner, G.A. Willis, J. Reine Angew. Math. 781 (2021) 85–103.","bibtex":"@article{Glöckner_Willis_2021, title={Locally pro-p contraction groups are nilpotent}, volume={781}, DOI={10.1515/crelle-2021-0050}, journal={J. Reine Angew. Math.}, author={Glöckner, Helge and Willis, George A.}, year={2021}, pages={85–103} }","mla":"Glöckner, Helge, and George A. Willis. “Locally Pro-p Contraction Groups Are Nilpotent.” J. Reine Angew. Math., vol. 781, 2021, pp. 85–103, doi:10.1515/crelle-2021-0050.","chicago":"Glöckner, Helge, and George A. Willis. “Locally Pro-p Contraction Groups Are Nilpotent.” J. Reine Angew. Math. 781 (2021): 85–103. https://doi.org/10.1515/crelle-2021-0050.","apa":"Glöckner, H., & Willis, G. A. (2021). Locally pro-p contraction groups are nilpotent. J. Reine Angew. Math., 781, 85–103. https://doi.org/10.1515/crelle-2021-0050","ama":"Glöckner H, Willis GA. Locally pro-p contraction groups are nilpotent. J Reine Angew Math. 2021;781:85–103. doi:10.1515/crelle-2021-0050"},"year":"2021","type":"journal_article","page":"85–103","intvolume":" 781","_id":"34790","publication_identifier":{"issn":["0075-4102"]},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"title":"Locally pro-p contraction groups are nilpotent","language":[{"iso":"eng"}],"doi":"10.1515/crelle-2021-0050","date_updated":"2022-12-21T19:23:15Z"},{"issue":"1","intvolume":" 294","_id":"34795","page":"74–81","type":"journal_article","citation":{"short":"H. Glöckner, Mathematische Nachrichten 294 (2021) 74–81.","ieee":"H. Glöckner, “Direct limits of regular Lie groups,” Mathematische Nachrichten, vol. 294, no. 1, pp. 74–81, 2021, doi: 10.1002/mana.201900073.","chicago":"Glöckner, Helge. “Direct Limits of Regular Lie Groups.” Mathematische Nachrichten 294, no. 1 (2021): 74–81. https://doi.org/10.1002/mana.201900073.","apa":"Glöckner, H. (2021). Direct limits of regular Lie groups. Mathematische Nachrichten, 294(1), 74–81. https://doi.org/10.1002/mana.201900073","ama":"Glöckner H. Direct limits of regular Lie groups. Mathematische Nachrichten. 2021;294(1):74–81. doi:10.1002/mana.201900073","bibtex":"@article{Glöckner_2021, title={Direct limits of regular Lie groups}, volume={294}, DOI={10.1002/mana.201900073}, number={1}, journal={Mathematische Nachrichten}, author={Glöckner, Helge}, year={2021}, pages={74–81} }","mla":"Glöckner, Helge. “Direct Limits of Regular Lie Groups.” Mathematische Nachrichten, vol. 294, no. 1, 2021, pp. 74–81, doi:10.1002/mana.201900073."},"year":"2021","user_id":"178","article_type":"original","date_created":"2022-12-21T19:57:32Z","status":"public","volume":294,"publication":"Mathematische Nachrichten","quality_controlled":"1","author":[{"last_name":"Glöckner","id":"178","first_name":"Helge","full_name":"Glöckner, Helge"}],"doi":"10.1002/mana.201900073","date_updated":"2022-12-21T20:00:29Z","language":[{"iso":"eng"}],"title":"Direct limits of regular Lie groups","publication_identifier":{"issn":["0025-584X"]},"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}]},{"abstract":[{"lang":"eng","text":"Let $G$ be a Lie group over a totally disconnected local field and $\\alpha$\r\nbe an analytic endomorphism of $G$. The contraction group of $\\alpha$ ist the\r\nset of all $x\\in G$ such that $\\alpha^n(x)\\to e$ as $n\\to\\infty$. Call sequence\r\n$(x_{-n})_{n\\geq 0}$ in $G$ an $\\alpha$-regressive trajectory for $x\\in G$ if\r\n$\\alpha(x_{-n})=x_{-n+1}$ for all $n\\geq 1$ and $x_0=x$. The anti-contraction\r\ngroup of $\\alpha$ is the set of all $x\\in G$ admitting an $\\alpha$-regressive\r\ntrajectory $(x_{-n})_{n\\geq 0}$ such that $x_{-n}\\to e$ as $n\\to\\infty$. The\r\nLevi subgroup is the set of all $x\\in G$ whose $\\alpha$-orbit is relatively\r\ncompact, and such that $x$ admits an $\\alpha$-regressive trajectory\r\n$(x_{-n})_{n\\geq 0}$ such that $\\{x_{-n}\\colon n\\geq 0\\}$ is relatively\r\ncompact. The big cell associated to $\\alpha$ is the set $\\Omega$ of all all\r\nproducts $xyz$ with $x$ in the contraction group, $y$ in the Levi subgroup and\r\n$z$ in the anti-contraction group. Let $\\pi$ be the mapping from the cartesian\r\nproduct of the contraction group, Levi subgroup and anti-contraction group to\r\n$\\Omega$ which maps $(x,y,z)$ to $xyz$. We show: $\\Omega$ is open in $G$ and\r\n$\\pi$ is \\'{e}tale for suitable immersed Lie subgroup structures on the three\r\nsubgroups just mentioned. Moreover, we study group-theoretic properties of\r\ncontraction groups and anti-contraction groups."}],"external_id":{"arxiv":["2101.02981"]},"title":"Contraction groups and the big cell for endomorphisms of Lie groups over local fields","user_id":"178","author":[{"first_name":"Helge","full_name":"Glöckner, Helge","last_name":"Glöckner","id":"178"}],"department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"publication":"arXiv:2101.02981","status":"public","date_created":"2022-12-22T07:47:35Z","date_updated":"2022-12-22T07:48:29Z","_id":"34806","citation":{"chicago":"Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms of Lie Groups over Local Fields.” ArXiv:2101.02981, 2021.","apa":"Glöckner, H. (2021). Contraction groups and the big cell for endomorphisms of Lie groups over local fields. In arXiv:2101.02981.","ama":"Glöckner H. Contraction groups and the big cell for endomorphisms of Lie groups over local fields. arXiv:210102981. Published online 2021.","mla":"Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms of Lie Groups over Local Fields.” ArXiv:2101.02981, 2021.","bibtex":"@article{Glöckner_2021, title={Contraction groups and the big cell for endomorphisms of Lie groups over local fields}, journal={arXiv:2101.02981}, author={Glöckner, Helge}, year={2021} }","short":"H. Glöckner, ArXiv:2101.02981 (2021).","ieee":"H. Glöckner, “Contraction groups and the big cell for endomorphisms of Lie groups over local fields,” arXiv:2101.02981. 2021."},"type":"preprint","year":"2021","language":[{"iso":"eng"}]},{"page":"327-333","type":"conference","citation":{"short":"S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.","ieee":"S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational integrators,” in 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, vol. 54(19), pp. 327–333.","ama":"Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators. In: IFAC-PapersOnLine, ed. 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC. Vol 54(19). ; 2021:327-333.","apa":"Ober-Blöbaum, S., & Vermeeren, M. (2021). Superconvergence of galerkin variational integrators. In IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19) (pp. 327–333).","chicago":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” In 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.","bibtex":"@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum, Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333} }","mla":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp. 327–33."},"year":"2021","language":[{"iso":"eng"}],"corporate_editor":["IFAC-PapersOnLine"],"date_updated":"2022-01-21T13:36:53Z","_id":"29421","volume":"54(19)","date_created":"2022-01-18T14:27:56Z","status":"public","department":[{"_id":"636"}],"publication":"7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC","author":[{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","id":"16494"},{"first_name":"M.","full_name":"Vermeeren, M.","last_name":"Vermeeren"}],"title":"Superconvergence of galerkin variational integrators","user_id":"15694"},{"abstract":[{"text":"Model predictive control is a prominent approach to construct a feedback\r\ncontrol loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge in MPC is to solve model-based optimal control problems in a very\r\nshort amount of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit formulation where the underlying optimization problems are\r\nsolved a priori in an offline phase. In this article, we present an extension\r\nof this concept in two significant ways. We consider nonlinear problems and -\r\nmore importantly - problems with multiple conflicting objective functions. In\r\nthe offline phase, we build a library of Pareto optimal solutions from which we\r\nthen obtain a valid compromise solution in the online phase according to a\r\ndecision maker's preference. Since the standard multi-parametric programming\r\napproach is no longer valid in this situation, we instead use interpolation\r\nbetween different entries of the library. To reduce the number of problems that\r\nhave to be solved in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the corresponding multiobjective optimal control problem. The\r\nresults are verified using two different examples from autonomous driving.","lang":"eng"}],"user_id":"15694","title":"Explicit multiobjective model predictive control for nonlinear systems with symmetries","author":[{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","id":"16494","last_name":"Ober-Blöbaum"},{"first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","last_name":"Peitz","id":"47427"}],"publication":"International Journal of Robust and Nonlinear Control","department":[{"_id":"101"}],"status":"public","date_created":"2020-03-13T12:44:36Z","project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"volume":"31(2)","_id":"16294","date_updated":"2022-01-24T13:27:50Z","oa":"1","doi":"10.1002/rnc.5281","main_file_link":[{"open_access":"1","url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281"}],"language":[{"iso":"eng"}],"year":"2021","citation":{"ieee":"S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems with symmetries,” International Journal of Robust and Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi: 10.1002/rnc.5281.","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","mla":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems with Symmetries.” International Journal of Robust and Nonlinear Control, vol. 31(2), 2021, pp. 380–403, doi:10.1002/rnc.5281.","bibtex":"@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems with symmetries}, volume={31(2)}, DOI={10.1002/rnc.5281}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }","apa":"Ober-Blöbaum, S., & Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems with symmetries. International Journal of Robust and Nonlinear Control, 31(2), 380–403. https://doi.org/10.1002/rnc.5281","ama":"Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems with symmetries. International Journal of Robust and Nonlinear Control. 2021;31(2):380-403. doi:10.1002/rnc.5281","chicago":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems with Symmetries.” International Journal of Robust and Nonlinear Control 31(2) (2021): 380–403. https://doi.org/10.1002/rnc.5281."},"type":"journal_article","page":"380-403"},{"user_id":"87909","keyword":["Electrical and Electronic Engineering","Control and Systems Engineering"],"publication":"Automatica","publisher":"Elsevier BV","author":[{"full_name":"Djema, Walid","first_name":"Walid","last_name":"Djema"},{"last_name":"Giraldi","full_name":"Giraldi, Laetitia","first_name":"Laetitia"},{"first_name":"Sofya","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","id":"87909"},{"first_name":"Olivier","full_name":"Bernard, Olivier","last_name":"Bernard"}],"date_created":"2022-01-26T13:13:06Z","status":"public","volume":132,"intvolume":" 132","_id":"29543","article_number":"109804","year":"2021","type":"journal_article","citation":{"ieee":"W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features in optimal selection of species represented by quota models,” Automatica, vol. 132, Art. no. 109804, 2021, doi: 10.1016/j.automatica.2021.109804.","short":"W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).","bibtex":"@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features in optimal selection of species represented by quota models}, volume={132}, DOI={10.1016/j.automatica.2021.109804}, number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema, Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021} }","mla":"Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” Automatica, vol. 132, 109804, Elsevier BV, 2021, doi:10.1016/j.automatica.2021.109804.","chicago":"Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” Automatica 132 (2021). https://doi.org/10.1016/j.automatica.2021.109804.","apa":"Djema, W., Giraldi, L., Maslovskaya, S., & Bernard, O. (2021). Turnpike features in optimal selection of species represented by quota models. Automatica, 132, Article 109804. https://doi.org/10.1016/j.automatica.2021.109804","ama":"Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal selection of species represented by quota models. Automatica. 2021;132. doi:10.1016/j.automatica.2021.109804"},"title":"Turnpike features in optimal selection of species represented by quota models","department":[{"_id":"636"}],"publication_status":"published","publication_identifier":{"issn":["0005-1098"]},"date_updated":"2022-01-26T13:15:33Z","doi":"10.1016/j.automatica.2021.109804","language":[{"iso":"eng"}]},{"date_updated":"2022-05-17T12:05:52Z","_id":"31058","language":[{"iso":"eng"}],"year":"2021","citation":{"short":"P. Schütte, T. Weich, B. Delarue, (2021).","ieee":"P. Schütte, T. Weich, and B. Delarue, “Resonances and weighted zeta functions for obstacle scattering via smooth models.” 2021.","chicago":"Schütte, Philipp, Tobias Weich, and Benjamin Delarue. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” 2021.","ama":"Schütte P, Weich T, Delarue B. Resonances and weighted zeta functions for obstacle scattering via smooth models. Published online 2021.","apa":"Schütte, P., Weich, T., & Delarue, B. (2021). Resonances and weighted zeta functions for obstacle scattering via smooth models.","bibtex":"@article{Schütte_Weich_Delarue_2021, title={Resonances and weighted zeta functions for obstacle scattering via smooth models}, author={Schütte, Philipp and Weich, Tobias and Delarue, Benjamin}, year={2021} }","mla":"Schütte, Philipp, et al. Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. 2021."},"type":"preprint","abstract":[{"lang":"eng","text":"We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane."}],"external_id":{"arxiv":["2109.05907"]},"user_id":"50168","title":"Resonances and weighted zeta functions for obstacle scattering via smooth models","department":[{"_id":"10"},{"_id":"548"}],"author":[{"full_name":"Schütte, Philipp","first_name":"Philipp","id":"50168","last_name":"Schütte"},{"first_name":"Tobias","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178"},{"first_name":"Benjamin","full_name":"Delarue, Benjamin","last_name":"Delarue"}],"date_created":"2022-05-04T12:25:58Z","status":"public"},{"title":"Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie","user_id":"32202","publication_status":"published","volume":68,"date_created":"2022-05-22T15:20:46Z","status":"public","department":[{"_id":"97"}],"publication":"Mathematische Semesterberichte","author":[{"full_name":"Hoffmann, Max","first_name":"Max","id":"32202","last_name":"Hoffmann"}],"doi":"10.1007/s00591-021-00299-3","oa":"1","_id":"31385","date_updated":"2022-05-22T15:58:33Z","intvolume":" 68","page":"295–297","type":"review","citation":{"ieee":"M. Hoffmann, “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie,” Mathematische Semesterberichte, vol. 68. pp. 295–297, 2021, doi: 10.1007/s00591-021-00299-3.","short":"M. Hoffmann, Mathematische Semesterberichte 68 (2021) 295–297.","bibtex":"@article{Hoffmann_2021, title={Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie}, volume={68}, DOI={10.1007/s00591-021-00299-3}, journal={Mathematische Semesterberichte}, author={Hoffmann, Max}, year={2021}, pages={295–297} }","mla":"Hoffmann, Max. “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie.” Mathematische Semesterberichte, vol. 68, 2021, pp. 295–297, doi:10.1007/s00591-021-00299-3.","chicago":"Hoffmann, Max. “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie.” Mathematische Semesterberichte, 2021. https://doi.org/10.1007/s00591-021-00299-3.","apa":"Hoffmann, M. (2021). Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie. In Mathematische Semesterberichte (Vol. 68, pp. 295–297). https://doi.org/10.1007/s00591-021-00299-3","ama":"Hoffmann M. Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie. Mathematische Semesterberichte. 2021;68:295–297. doi:10.1007/s00591-021-00299-3"},"year":"2021","language":[{"iso":"ger"}],"main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00591-021-00299-3","open_access":"1"}]},{"doi":"10.1007/978-3-662-62854-6_9","date_updated":"2022-05-24T13:18:09Z","language":[{"iso":"ger"}],"title":"Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn","place":"Berlin, Heidelberg","publication_identifier":{"isbn":["9783662628539","9783662628546"],"issn":["2197-8751","2197-876X"]},"publication_status":"published","editor":[{"last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"full_name":"Eichler, Andreas","first_name":"Andreas","last_name":"Eichler"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"last_name":"Rach","first_name":"Stefanie","full_name":"Rach, Stefanie"},{"first_name":"Niclas","full_name":"Schaper, Niclas","last_name":"Schaper"}],"department":[{"_id":"97"}],"_id":"31364","page":"179–204","year":"2021","type":"book_chapter","citation":{"short":"M. Hoffmann, in: R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper (Eds.), Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert, Springer Berlin Heidelberg, Berlin, Heidelberg, 2021, pp. 179–204.","ieee":"M. Hoffmann, “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn,” in Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert, R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2021, pp. 179–204.","chicago":"Hoffmann, Max. “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn.” In Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert, edited by Rolf Biehler, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and Niclas Schaper, 179–204. Berlin, Heidelberg: Springer Berlin Heidelberg, 2021. https://doi.org/10.1007/978-3-662-62854-6_9.","ama":"Hoffmann M. Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn. In: Biehler R, Eichler A, Hochmuth R, Rach S, Schaper N, eds. Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert. Springer Berlin Heidelberg; 2021:179–204. doi:10.1007/978-3-662-62854-6_9","apa":"Hoffmann, M. (2021). Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn. In R. Biehler, A. Eichler, R. Hochmuth, S. Rach, & N. Schaper (Eds.), Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert (pp. 179–204). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-62854-6_9","bibtex":"@inbook{Hoffmann_2021, place={Berlin, Heidelberg}, title={Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn}, DOI={10.1007/978-3-662-62854-6_9}, booktitle={ Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert}, publisher={Springer Berlin Heidelberg}, author={Hoffmann, Max}, editor={Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}, year={2021}, pages={179–204} }","mla":"Hoffmann, Max. “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn.” Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert, edited by Rolf Biehler et al., Springer Berlin Heidelberg, 2021, pp. 179–204, doi:10.1007/978-3-662-62854-6_9."},"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-662-62854-6_9"}],"user_id":"32202","date_created":"2022-05-22T13:56:39Z","status":"public","publication":" Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert","publisher":"Springer Berlin Heidelberg","quality_controlled":"1","author":[{"first_name":"Max","full_name":"Hoffmann, Max","last_name":"Hoffmann","id":"32202"}]},{"issue":"11","_id":"31261","intvolume":" 2021","page":"8225-8296","citation":{"chicago":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” International Mathematics Research Notices 2021, no. 11 (2021): 8225–96. https://doi.org/10.1093/imrn/rnz068.","apa":"Küster, B., & Weich, T. (2021). Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. International Mathematics Research Notices, 2021(11), 8225–8296. https://doi.org/10.1093/imrn/rnz068","ama":"Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. International Mathematics Research Notices. 2021;2021(11):8225-8296. doi:10.1093/imrn/rnz068","mla":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” International Mathematics Research Notices, vol. 2021, no. 11, Oxford University Press (OUP), 2021, pp. 8225–96, doi:10.1093/imrn/rnz068.","bibtex":"@article{Küster_Weich_2021, title={Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={10.1093/imrn/rnz068}, number={11}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2021}, pages={8225–8296} }","short":"B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021) 8225–8296.","ieee":"B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces,” International Mathematics Research Notices, vol. 2021, no. 11, pp. 8225–8296, 2021, doi: 10.1093/imrn/rnz068."},"year":"2021","type":"journal_article","user_id":"49178","abstract":[{"text":"Abstract\r\n For a compact Riemannian locally symmetric space $\\mathcal M$ of rank 1 and an associated vector bundle $\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\\sigma )$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$ over $\\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau }$ and $\\mathbf W_{\\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory and Lie theory.","lang":"eng"}],"volume":2021,"date_created":"2022-05-17T12:00:36Z","status":"public","keyword":["General Mathematics"],"publication":"International Mathematics Research Notices","publisher":"Oxford University Press (OUP)","author":[{"full_name":"Küster, Benjamin","first_name":"Benjamin","last_name":"Küster"},{"last_name":"Weich","first_name":"Tobias","full_name":"Weich, Tobias"}],"doi":"10.1093/imrn/rnz068","date_updated":"2022-05-25T06:42:01Z","language":[{"iso":"eng"}],"title":"Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces","external_id":{"arxiv":["1710.04625"]},"publication_identifier":{"issn":["1073-7928","1687-0247"]},"publication_status":"published","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}]},{"_id":"31576","date_updated":"2022-06-02T08:04:19Z","issue":"14","citation":{"ieee":"U. Häsel-Weide and M. Nührenbürger, “Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.,” Zeitschrift für Grundschulforschung (ZfG), no. 14, pp. 49–65, 2021.","short":"U. Häsel-Weide, M. Nührenbürger, Zeitschrift für Grundschulforschung (ZfG) (2021) 49–65.","bibtex":"@article{Häsel-Weide_Nührenbürger_2021, title={Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.}, number={14}, journal={Zeitschrift für Grundschulforschung (ZfG)}, publisher={Springer}, author={Häsel-Weide, Uta and Nührenbürger, Marcus}, year={2021}, pages={49–65} }","mla":"Häsel-Weide, Uta, and Marcus Nührenbürger. “Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.” Zeitschrift für Grundschulforschung (ZfG), no. 14, Springer, 2021, pp. 49–65.","chicago":"Häsel-Weide, Uta, and Marcus Nührenbürger. “Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.” Zeitschrift für Grundschulforschung (ZfG), no. 14 (2021): 49–65.","ama":"Häsel-Weide U, Nührenbürger M. Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. Zeitschrift für Grundschulforschung (ZfG). 2021;(14):49-65.","apa":"Häsel-Weide, U., & Nührenbürger, M. (2021). Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. Zeitschrift für Grundschulforschung (ZfG), 14, 49–65."},"type":"journal_article","year":"2021","page":"49-65","language":[{"iso":"ger"}],"title":"Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.","related_material":{"link":[{"url":"https://link.springer.com/content/pdf/10.1007/s42278-020-00097-1.pdf","relation":"contains"}]},"user_id":"85821","publisher":"Springer","author":[{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"},{"last_name":"Nührenbürger","full_name":"Nührenbürger, Marcus","first_name":"Marcus"}],"department":[{"_id":"98"},{"_id":"543"}],"publication":"Zeitschrift für Grundschulforschung (ZfG)","publication_status":"published","status":"public","date_created":"2022-06-02T08:04:02Z"},{"language":[{"iso":"ger"}],"type":"journal_article","year":"2021","citation":{"ieee":"U. Häsel-Weide and C. Schöttler, “Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen,” Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP), no. 2, 2021.","short":"U. Häsel-Weide, C. Schöttler, Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP) (2021).","mla":"Häsel-Weide, Uta, and Christian Schöttler. “Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen.” Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP), no. 2, 2021.","bibtex":"@article{Häsel-Weide_Schöttler_2021, title={Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen}, number={2}, journal={Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP)}, author={Häsel-Weide, Uta and Schöttler, Christian}, year={2021} }","apa":"Häsel-Weide, U., & Schöttler, C. (2021). Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen. Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP), 2.","ama":"Häsel-Weide U, Schöttler C. Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen. Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP). 2021;(2).","chicago":"Häsel-Weide, Uta, and Christian Schöttler. “Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen.” Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP), no. 2 (2021)."},"_id":"31577","date_updated":"2022-06-02T09:05:00Z","issue":"2","department":[{"_id":"98"},{"_id":"543"}],"publication":"Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP)","author":[{"first_name":"Uta","full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","id":"60267"},{"last_name":"Schöttler","first_name":"Christian","full_name":"Schöttler, Christian"}],"date_created":"2022-06-02T08:09:31Z","status":"public","publication_identifier":{"issn":[" 2701-9012"]},"publication_status":"published","related_material":{"link":[{"url":"https://zmfp.de/fileadmin/user_upload/veroeffentlichungen/ZMFP_2021_Ha__sel-Weide_Scho__ttler_Dezimalsystem_ISSN.pdf","relation":"contains"}]},"user_id":"85821","title":"Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen"},{"volume":100,"date_created":"2022-08-15T09:35:02Z","status":"public","publication":"European Journal of Combinatorics","keyword":["Discrete Mathematics and Combinatorics"],"publisher":"Elsevier BV","author":[{"last_name":"Li","full_name":"Li, Jiaao","first_name":"Jiaao"},{"full_name":"Ma, Yulai","first_name":"Yulai","id":"92748","last_name":"Ma"},{"last_name":"Shi","first_name":"Yongtang","full_name":"Shi, Yongtang"},{"last_name":"Wang","full_name":"Wang, Weifan","first_name":"Weifan"},{"last_name":"Wu","full_name":"Wu, Yezhou","first_name":"Yezhou"}],"user_id":"15540","year":"2021","type":"journal_article","citation":{"ieee":"J. Li, Y. Ma, Y. Shi, W. Wang, and Y. Wu, “On 3-flow-critical graphs,” European Journal of Combinatorics, vol. 100, Art. no. 103451, 2021, doi: 10.1016/j.ejc.2021.103451.","short":"J. Li, Y. Ma, Y. Shi, W. Wang, Y. Wu, European Journal of Combinatorics 100 (2021).","bibtex":"@article{Li_Ma_Shi_Wang_Wu_2021, title={On 3-flow-critical graphs}, volume={100}, DOI={10.1016/j.ejc.2021.103451}, number={103451}, journal={European Journal of Combinatorics}, publisher={Elsevier BV}, author={Li, Jiaao and Ma, Yulai and Shi, Yongtang and Wang, Weifan and Wu, Yezhou}, year={2021} }","mla":"Li, Jiaao, et al. “On 3-Flow-Critical Graphs.” European Journal of Combinatorics, vol. 100, 103451, Elsevier BV, 2021, doi:10.1016/j.ejc.2021.103451.","chicago":"Li, Jiaao, Yulai Ma, Yongtang Shi, Weifan Wang, and Yezhou Wu. “On 3-Flow-Critical Graphs.” European Journal of Combinatorics 100 (2021). https://doi.org/10.1016/j.ejc.2021.103451.","apa":"Li, J., Ma, Y., Shi, Y., Wang, W., & Wu, Y. (2021). On 3-flow-critical graphs. European Journal of Combinatorics, 100, Article 103451. https://doi.org/10.1016/j.ejc.2021.103451","ama":"Li J, Ma Y, Shi Y, Wang W, Wu Y. On 3-flow-critical graphs. European Journal of Combinatorics. 2021;100. doi:10.1016/j.ejc.2021.103451"},"article_number":"103451","intvolume":" 100","_id":"32810","publication_status":"published","publication_identifier":{"issn":["0195-6698"]},"department":[{"_id":"542"}],"title":"On 3-flow-critical graphs","language":[{"iso":"eng"}],"doi":"10.1016/j.ejc.2021.103451","date_updated":"2022-08-15T09:35:32Z"},{"_id":"33278","intvolume":" 23","issue":"4","main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00023-021-01121-5","open_access":"1"}],"page":"1283-1296","citation":{"short":"M. Kolb, T. Weich, L. Wolf, Annales Henri Poincaré 23 (2021) 1283–1296.","ieee":"M. Kolb, T. Weich, and L. Wolf, “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature,” Annales Henri Poincaré , vol. 23, no. 4, pp. 1283–1296, 2021.","ama":"Kolb M, Weich T, Wolf L. Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. Annales Henri Poincaré . 2021;23(4):1283-1296.","apa":"Kolb, M., Weich, T., & Wolf, L. (2021). Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. Annales Henri Poincaré , 23(4), 1283–1296.","chicago":"Kolb, Martin, Tobias Weich, and Lasse Wolf. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature.” Annales Henri Poincaré 23, no. 4 (2021): 1283–96.","mla":"Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature.” Annales Henri Poincaré , vol. 23, no. 4, Springer Science + Business Media, 2021, pp. 1283–96.","bibtex":"@article{Kolb_Weich_Wolf_2021, title={Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature}, volume={23}, number={4}, journal={Annales Henri Poincaré }, publisher={Springer Science + Business Media}, author={Kolb, Martin and Weich, Tobias and Wolf, Lasse}, year={2021}, pages={1283–1296} }"},"year":"2021","type":"journal_article","abstract":[{"lang":"eng","text":"The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold."}],"user_id":"85821","publication":"Annales Henri Poincaré ","author":[{"last_name":"Kolb","id":"48880","first_name":"Martin","full_name":"Kolb, Martin"},{"first_name":"Tobias","full_name":"Weich, Tobias","last_name":"Weich"},{"full_name":"Wolf, Lasse","first_name":"Lasse","last_name":"Wolf"}],"publisher":"Springer Science + Business Media","date_created":"2022-09-07T07:05:33Z","status":"public","volume":23,"date_updated":"2022-09-08T06:06:13Z","oa":"1","language":[{"iso":"eng"}],"related_material":{"link":[{"relation":"contains","url":"https://link.springer.com/article/10.1007/s00023-021-01121-5"}]},"title":"Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature","department":[{"_id":"96"}],"publication_status":"published"},{"date_created":"2022-06-22T09:56:43Z","status":"public","has_accepted_license":"1","file_date_updated":"2022-06-22T09:56:39Z","publication":"arXiv:2103.02968v1","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"author":[{"last_name":"Weich","id":"49178","first_name":"Tobias","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias"},{"full_name":"Budde, Julia","first_name":"Julia","last_name":"Budde"}],"file":[{"file_size":978990,"creator":"weich","file_id":"32100","content_type":"application/pdf","date_updated":"2022-06-22T09:56:39Z","relation":"main_file","file_name":"2103.02968.pdf","date_created":"2022-06-22T09:56:39Z","access_level":"open_access"}],"ddc":["510"],"title":"Wave Front Sets of Nilpotent Lie Group Representations","user_id":"49178","citation":{"short":"T. Weich, J. Budde, ArXiv:2103.02968v1 (2021).","ieee":"T. Weich and J. Budde, “Wave Front Sets of Nilpotent Lie Group Representations,” arXiv:2103.02968v1. 2021.","chicago":"Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.” ArXiv:2103.02968v1, 2021.","ama":"Weich T, Budde J. Wave Front Sets of Nilpotent Lie Group Representations. arXiv:210302968v1. Published online 2021.","apa":"Weich, T., & Budde, J. (2021). Wave Front Sets of Nilpotent Lie Group Representations. In arXiv:2103.02968v1.","bibtex":"@article{Weich_Budde_2021, title={Wave Front Sets of Nilpotent Lie Group Representations}, journal={arXiv:2103.02968v1}, author={Weich, Tobias and Budde, Julia}, year={2021} }","mla":"Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.” ArXiv:2103.02968v1, 2021."},"year":"2021","type":"preprint","language":[{"iso":"eng"}],"oa":"1","date_updated":"2022-09-12T07:49:55Z","_id":"32099"},{"_id":"33481","intvolume":" 132","date_updated":"2022-09-26T06:54:06Z","doi":"https://doi.org/10.1016/j.spa.2020.10.003","language":[{"iso":"eng"}],"year":"2021","type":"journal_article","citation":{"chicago":"Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement of Particles in 2D Gibbsian Particle Systems.” Stochastic Processes and Their Applications 132 (2021): 1–32. https://doi.org/10.1016/j.spa.2020.10.003.","apa":"Richthammer, T., & Fiedler, M. (2021). A lower bound on the displacement of particles in 2D Gibbsian particle systems. Stochastic Processes and Their Applications, 132, 1–32. https://doi.org/10.1016/j.spa.2020.10.003","ama":"Richthammer T, Fiedler M. A lower bound on the displacement of particles in 2D Gibbsian particle systems. Stochastic Processes and their Applications. 2021;132:1-32. doi:https://doi.org/10.1016/j.spa.2020.10.003","bibtex":"@article{Richthammer_Fiedler_2021, title={A lower bound on the displacement of particles in 2D Gibbsian particle systems}, volume={132}, DOI={https://doi.org/10.1016/j.spa.2020.10.003}, journal={Stochastic Processes and their Applications}, publisher={Elsevier}, author={Richthammer, Thomas and Fiedler, Michael}, year={2021}, pages={1–32} }","mla":"Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement of Particles in 2D Gibbsian Particle Systems.” Stochastic Processes and Their Applications, vol. 132, Elsevier, 2021, pp. 1–32, doi:https://doi.org/10.1016/j.spa.2020.10.003.","short":"T. Richthammer, M. Fiedler, Stochastic Processes and Their Applications 132 (2021) 1–32.","ieee":"T. Richthammer and M. Fiedler, “A lower bound on the displacement of particles in 2D Gibbsian particle systems,” Stochastic Processes and their Applications, vol. 132, pp. 1–32, 2021, doi: https://doi.org/10.1016/j.spa.2020.10.003."},"page":"1-32","abstract":[{"lang":"eng","text":"While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction."}],"user_id":"85821","title":"A lower bound on the displacement of particles in 2D Gibbsian particle systems","publisher":"Elsevier","author":[{"last_name":"Richthammer","id":"62054","first_name":"Thomas","full_name":"Richthammer, Thomas"},{"last_name":"Fiedler","full_name":"Fiedler, Michael","first_name":"Michael"}],"publication":"Stochastic Processes and their Applications","department":[{"_id":"96"}],"status":"public","date_created":"2022-09-26T06:53:59Z","publication_status":"published","volume":132},{"year":"2021","type":"journal_article","citation":{"mla":"Hanusch, Maximilian. “Symmetries of Analytic Curves.” Differential Geometry and Its Applications, vol. 74, 101687, Elsevier BV, 2021, doi:10.1016/j.difgeo.2020.101687.","bibtex":"@article{Hanusch_2021, title={Symmetries of analytic curves}, volume={74}, DOI={10.1016/j.difgeo.2020.101687}, number={101687}, journal={Differential Geometry and its Applications}, publisher={Elsevier BV}, author={Hanusch, Maximilian}, year={2021} }","chicago":"Hanusch, Maximilian. “Symmetries of Analytic Curves.” Differential Geometry and Its Applications 74 (2021). https://doi.org/10.1016/j.difgeo.2020.101687.","apa":"Hanusch, M. (2021). Symmetries of analytic curves. Differential Geometry and Its Applications, 74, Article 101687. https://doi.org/10.1016/j.difgeo.2020.101687","ama":"Hanusch M. Symmetries of analytic curves. Differential Geometry and its Applications. 2021;74. doi:10.1016/j.difgeo.2020.101687","ieee":"M. Hanusch, “Symmetries of analytic curves,” Differential Geometry and its Applications, vol. 74, Art. no. 101687, 2021, doi: 10.1016/j.difgeo.2020.101687.","short":"M. Hanusch, Differential Geometry and Its Applications 74 (2021)."},"_id":"34818","intvolume":" 74","article_number":"101687","publication":"Differential Geometry and its Applications","keyword":["Geometry and Topology","Analysis"],"author":[{"full_name":"Hanusch, Maximilian","first_name":"Maximilian","id":"30905","last_name":"Hanusch"}],"publisher":"Elsevier BV","volume":74,"date_created":"2022-12-22T09:20:30Z","status":"public","extern":"1","article_type":"original","user_id":"30905","language":[{"iso":"eng"}],"date_updated":"2023-01-09T18:07:26Z","doi":"10.1016/j.difgeo.2020.101687","department":[{"_id":"93"}],"publication_identifier":{"issn":["0926-2245"]},"publication_status":"published","title":"Symmetries of analytic curves"},{"citation":{"short":"R. Biehler, in: R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper (Eds.), Lehrinnovationen in Der Hochschulmathematik . Konzepte Und Studien Zur Hochschuldidaktik Und Lehrerbildung Mathematik, Springer Spektrum, Berlin, Heidelberg, 2021, pp. 285–290.","ieee":"R. Biehler, “Mathematikvorkurse als Brücke in das Studium–Einführung,” in Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, Eds. Berlin, Heidelberg: Springer Spektrum, 2021, pp. 285–290.","apa":"Biehler, R. (2021). Mathematikvorkurse als Brücke in das Studium–Einführung. In R. Biehler, A. Eichler, R. Hochmuth, S. Rach, & N. Schaper (Eds.), Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik (pp. 285–290). Springer Spektrum. https://doi.org/10.1007/978-3-662-62854-6_13","ama":"Biehler R. Mathematikvorkurse als Brücke in das Studium–Einführung. In: Biehler R, Eichler A, Hochmuth R, Rach S, Schaper N, eds. Lehrinnovationen in Der Hochschulmathematik . Konzepte Und Studien Zur Hochschuldidaktik Und Lehrerbildung Mathematik. Springer Spektrum; 2021:285–290. doi:10.1007/978-3-662-62854-6_13","chicago":"Biehler, Rolf. “Mathematikvorkurse Als Brücke in Das Studium–Einführung.” In Lehrinnovationen in Der Hochschulmathematik . Konzepte Und Studien Zur Hochschuldidaktik Und Lehrerbildung Mathematik, edited by Rolf Biehler, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and Niclas Schaper, 285–290. Berlin, Heidelberg: Springer Spektrum, 2021. https://doi.org/10.1007/978-3-662-62854-6_13.","mla":"Biehler, Rolf. “Mathematikvorkurse Als Brücke in Das Studium–Einführung.” Lehrinnovationen in Der Hochschulmathematik . Konzepte Und Studien Zur Hochschuldidaktik Und Lehrerbildung Mathematik, edited by Rolf Biehler et al., Springer Spektrum, 2021, pp. 285–290, doi:10.1007/978-3-662-62854-6_13.","bibtex":"@inbook{Biehler_2021, place={Berlin, Heidelberg}, title={Mathematikvorkurse als Brücke in das Studium–Einführung}, DOI={10.1007/978-3-662-62854-6_13}, booktitle={Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}, publisher={Springer Spektrum}, author={Biehler, Rolf}, editor={Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}, year={2021}, pages={285–290} }"},"type":"book_chapter","year":"2021","page":"285–290","language":[{"iso":"eng"}],"doi":"10.1007/978-3-662-62854-6_13","date_updated":"2023-01-11T09:50:48Z","_id":"35720","editor":[{"last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"last_name":"Eichler","full_name":"Eichler, Andreas","first_name":"Andreas"},{"full_name":"Hochmuth, Reinhard","first_name":"Reinhard","last_name":"Hochmuth"},{"full_name":"Rach, Stefanie","first_name":"Stefanie","last_name":"Rach"},{"full_name":"Schaper, Niclas","first_name":"Niclas","last_name":"Schaper"}],"publication_identifier":{"eisbn":["978-3-662-62854-6"]},"status":"public","date_created":"2023-01-10T09:30:05Z","author":[{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"}],"publisher":"Springer Spektrum","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication":"Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik","title":"Mathematikvorkurse als Brücke in das Studium–Einführung","user_id":"37888","place":"Berlin, Heidelberg"},{"date_updated":"2023-01-11T10:00:33Z","_id":"35730","doi":"10.1007/978-3-662-62854-6_1","page":"1-6","type":"book_chapter","citation":{"bibtex":"@inbook{Biehler_Eichler_Hochmuth_Rach_Schaper_2021, place={Berlin, Heidelberg}, title={Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert}, DOI={10.1007/978-3-662-62854-6_1}, booktitle={Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}, publisher={Springer Spektrum}, author={Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}, editor={Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}, year={2021}, pages={1–6} }","mla":"Biehler, Rolf, et al. “Einführung: Lehrinnovationen in Der Hochschulmathematik – Praxisrelevant – Didaktisch Fundiert – Forschungsbasiert.” Lehrinnovationen in Der Hochschulmathematik . Konzepte Und Studien Zur Hochschuldidaktik Und Lehrerbildung Mathematik, edited by Rolf Biehler et al., Springer Spektrum, 2021, pp. 1–6, doi:10.1007/978-3-662-62854-6_1.","ama":"Biehler R, Eichler A, Hochmuth R, Rach S, Schaper N. Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert. In: Biehler R, Eichler A, Hochmuth R, Rach S, Schaper N, eds. Lehrinnovationen in Der Hochschulmathematik . 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Konzepte Und Studien Zur Hochschuldidaktik Und Lehrerbildung Mathematik, edited by Rolf Biehler, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and Niclas Schaper, 1–6. Berlin, Heidelberg: Springer Spektrum, 2021. https://doi.org/10.1007/978-3-662-62854-6_1.","ieee":"R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, “Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert,” in Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, Eds. Berlin, Heidelberg: Springer Spektrum, 2021, pp. 1–6.","short":"R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper, in: R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper (Eds.), Lehrinnovationen in Der Hochschulmathematik . Konzepte Und Studien Zur Hochschuldidaktik Und Lehrerbildung Mathematik, Springer Spektrum, Berlin, Heidelberg, 2021, pp. 1–6."},"year":"2021","language":[{"iso":"eng"}],"place":"Berlin, Heidelberg","title":"Einführung: Lehrinnovationen in der Hochschulmathematik – praxisrelevant – didaktisch fundiert – forschungsbasiert","user_id":"37888","publication":"Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publisher":"Springer Spektrum","author":[{"full_name":"Biehler, Rolf","first_name":"Rolf","id":"16274","last_name":"Biehler"},{"last_name":"Eichler","full_name":"Eichler, Andreas","first_name":"Andreas"},{"full_name":"Hochmuth, Reinhard","first_name":"Reinhard","last_name":"Hochmuth"},{"first_name":"Stefanie","full_name":"Rach, Stefanie","last_name":"Rach"},{"last_name":"Schaper","full_name":"Schaper, Niclas","first_name":"Niclas"}],"publication_identifier":{"isbn":["9783662628539","9783662628546"],"issn":["2197-8751","2197-876X"]},"publication_status":"published","editor":[{"last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"first_name":"Andreas","full_name":"Eichler, Andreas","last_name":"Eichler"},{"last_name":"Hochmuth","full_name":"Hochmuth, Reinhard","first_name":"Reinhard"},{"last_name":"Rach","full_name":"Rach, Stefanie","first_name":"Stefanie"},{"full_name":"Schaper, Niclas","first_name":"Niclas","last_name":"Schaper"}],"date_created":"2023-01-10T09:58:01Z","status":"public"},{"_id":"35737","intvolume":" 43","type":"journal_article","citation":{"apa":"Biehler, R., & Fleischer, Y. (2021). Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks. Teaching Statistics, 43, S133–S142. https://doi.org/10.1111/test.12279","ama":"Biehler R, Fleischer Y. Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks. Teaching Statistics. 2021;43:S133-S142. doi:10.1111/test.12279","chicago":"Biehler, Rolf, and Yannik Fleischer. “Introducing Students to Machine Learning with Decision Trees Using CODAP and Jupyter Notebooks.” Teaching Statistics 43 (2021): S133–42. https://doi.org/10.1111/test.12279.","bibtex":"@article{Biehler_Fleischer_2021, title={Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks}, volume={43}, DOI={10.1111/test.12279}, journal={Teaching Statistics}, publisher={Wiley}, author={Biehler, Rolf and Fleischer, Yannik}, year={2021}, pages={S133–S142} }","mla":"Biehler, Rolf, and Yannik Fleischer. “Introducing Students to Machine Learning with Decision Trees Using CODAP and Jupyter Notebooks.” Teaching Statistics, vol. 43, Wiley, 2021, pp. S133–42, doi:10.1111/test.12279.","short":"R. Biehler, Y. Fleischer, Teaching Statistics 43 (2021) S133–S142.","ieee":"R. Biehler and Y. Fleischer, “Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks,” Teaching Statistics, vol. 43, pp. S133–S142, 2021, doi: 10.1111/test.12279."},"year":"2021","page":"S133-S142","user_id":"37888","author":[{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"first_name":"Yannik","full_name":"Fleischer, Yannik","last_name":"Fleischer"}],"publisher":"Wiley","keyword":["Education","Statistics and Probability"],"publication":"Teaching Statistics","status":"public","date_created":"2023-01-10T10:08:32Z","volume":43,"date_updated":"2023-01-11T10:05:36Z","doi":"10.1111/test.12279","language":[{"iso":"eng"}],"title":"Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication_identifier":{"issn":["0141-982X","1467-9639"]},"publication_status":"published"},{"date_updated":"2023-01-11T10:04:16Z","_id":"35734","doi":"10.1007/978-3-662-62854-6","language":[{"iso":"eng"}],"type":"book_editor","year":"2021","citation":{"ama":"Biehler R, Eichler A, Hochmuth R, Rach S, Schaper N, eds. Lehrinnovationen in Der Hochschulmathematik. Springer Spektrum; 2021. doi:10.1007/978-3-662-62854-6","apa":"Biehler, R., Eichler, A., Hochmuth, R., Rach, S., & Schaper, N. (Eds.). (2021). Lehrinnovationen in der Hochschulmathematik. Springer Spektrum. https://doi.org/10.1007/978-3-662-62854-6","chicago":"Biehler, Rolf, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and Niclas Schaper, eds. Lehrinnovationen in Der Hochschulmathematik. Berlin, Heidelberg: Springer Spektrum, 2021. https://doi.org/10.1007/978-3-662-62854-6.","mla":"Biehler, Rolf, et al., editors. Lehrinnovationen in Der Hochschulmathematik. Springer Spektrum, 2021, doi:10.1007/978-3-662-62854-6.","bibtex":"@book{Biehler_Eichler_Hochmuth_Rach_Schaper_2021, place={Berlin, Heidelberg}, title={Lehrinnovationen in der Hochschulmathematik}, DOI={10.1007/978-3-662-62854-6}, publisher={Springer Spektrum}, year={2021} }","short":"R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper, eds., Lehrinnovationen in Der Hochschulmathematik, Springer Spektrum, Berlin, Heidelberg, 2021.","ieee":"R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, Eds., Lehrinnovationen in der Hochschulmathematik. Berlin, Heidelberg: Springer Spektrum, 2021."},"place":"Berlin, Heidelberg","user_id":"37888","title":"Lehrinnovationen in der Hochschulmathematik","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publisher":"Springer Spektrum","date_created":"2023-01-10T10:03:34Z","status":"public","publication_status":"published","publication_identifier":{"isbn":["9783662628539","9783662628546"],"issn":["2197-8751","2197-876X"]},"editor":[{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"full_name":"Eichler, Andreas","first_name":"Andreas","last_name":"Eichler"},{"last_name":"Hochmuth","full_name":"Hochmuth, Reinhard","first_name":"Reinhard"},{"first_name":"Stefanie","full_name":"Rach, Stefanie","last_name":"Rach"},{"first_name":"Niclas","full_name":"Schaper, Niclas","last_name":"Schaper"}],"alternative_title":["praxisrelevant – didaktisch fundiert – forschungsbasiert"]},{"place":"Berlin, Heidelberg","title":"Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“","user_id":"37888","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"}],"publication":"Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik","author":[{"full_name":"Frischemeier, Daniel","first_name":"Daniel","last_name":"Frischemeier"},{"full_name":"Podworny, Susanne","first_name":"Susanne","last_name":"Podworny"},{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"}],"publisher":"Springer Spektrum","publication_identifier":{"isbn":["9783662628539","9783662628546"],"issn":["2197-8751","2197-876X"]},"publication_status":"published","editor":[{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler"},{"first_name":"Andreas","full_name":"Eichler, Andreas","last_name":"Eichler"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"full_name":"Rach, Stefanie","first_name":"Stefanie","last_name":"Rach"},{"last_name":"Schaper","full_name":"Schaper, Niclas","first_name":"Niclas"}],"date_created":"2023-01-10T10:19:01Z","status":"public","_id":"35752","date_updated":"2023-01-11T10:10:08Z","doi":"10.1007/978-3-662-62854-6_11","page":"227-249","type":"book_chapter","citation":{"bibtex":"@inbook{Frischemeier_Podworny_Biehler_2021, place={Berlin, Heidelberg}, title={Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“}, DOI={10.1007/978-3-662-62854-6_11}, booktitle={Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik}, publisher={Springer Spektrum}, author={Frischemeier, Daniel and Podworny, Susanne and Biehler, Rolf}, editor={Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}, year={2021}, pages={227–249} }","mla":"Frischemeier, Daniel, et al. “Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“.” Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik, edited by Rolf Biehler et al., Springer Spektrum, 2021, pp. 227–49, doi:10.1007/978-3-662-62854-6_11.","ama":"Frischemeier D, Podworny S, Biehler R. 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Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik (pp. 227–249). Springer Spektrum. https://doi.org/10.1007/978-3-662-62854-6_11","chicago":"Frischemeier, Daniel, Susanne Podworny, and Rolf Biehler. “Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“.” In Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik, edited by Rolf Biehler, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and Niclas Schaper, 227–49. Berlin, Heidelberg: Springer Spektrum, 2021. https://doi.org/10.1007/978-3-662-62854-6_11.","ieee":"D. Frischemeier, S. Podworny, and R. Biehler, “Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“,” in Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematikzur Hochschuldidaktik und Lehrerbildung Mathematik, R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, Eds. Berlin, Heidelberg: Springer Spektrum, 2021, pp. 227–249.","short":"D. Frischemeier, S. Podworny, R. Biehler, in: R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper (Eds.), Konzepte und Studien Lehrinnovationen in der Hochschulmathematik . 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Berlin, Heidelberg: Springer Spektrum, 2021, pp. 365–397."},"type":"book_chapter","year":"2021","page":"365-397"},{"type":"book_chapter","citation":{"short":"L. Kempen, R. Biehler, in: R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper (Eds.), Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, Springer Spektrum, Berlin, Heidelberg, 2021, pp. 477–525.","ieee":"L. Kempen and R. Biehler, “Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“,” in Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, Eds. Berlin, Heidelberg: Springer Spektrum, 2021, pp. 477–525.","chicago":"Kempen, Leander, and Rolf Biehler. “Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“.” In Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, edited by Rolf Biehler, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and Niclas Schaper, 477–525. Berlin, Heidelberg: Springer Spektrum, 2021. https://doi.org/10.1007/978-3-662-62854-6_20.","apa":"Kempen, L., & Biehler, R. (2021). Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“. In R. Biehler, A. Eichler, R. Hochmuth, S. Rach, & N. Schaper (Eds.), Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik (pp. 477–525). 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Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}, publisher={Springer Spektrum}, author={Kempen, Leander and Biehler, Rolf}, editor={Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}, year={2021}, pages={477–525} }","mla":"Kempen, Leander, and Rolf Biehler. “Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“.” Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, edited by Rolf Biehler et al., Springer Spektrum, 2021, pp. 477–525, doi:10.1007/978-3-662-62854-6_20."},"year":"2021","page":"477-525","language":[{"iso":"ger"}],"doi":"10.1007/978-3-662-62854-6_20","_id":"35776","date_updated":"2023-01-11T10:17:29Z","editor":[{"last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf"},{"last_name":"Eichler","full_name":"Eichler, Andreas","first_name":"Andreas"},{"full_name":"Hochmuth, Reinhard","first_name":"Reinhard","last_name":"Hochmuth"},{"last_name":"Rach","full_name":"Rach, Stefanie","first_name":"Stefanie"},{"last_name":"Schaper","first_name":"Niclas","full_name":"Schaper, Niclas"}],"publication_identifier":{"issn":["2197-8751","2197-876X"],"isbn":["9783662628539","9783662628546"]},"publication_status":"published","status":"public","date_created":"2023-01-10T10:40:51Z","author":[{"last_name":"Kempen","full_name":"Kempen, Leander","first_name":"Leander"},{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"}],"publisher":"Springer Spektrum","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication":"Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik","title":"Design-Based Research in der Hochschullehre am Beispiel der Lehrveranstaltung „Einführung in die Kultur der Mathematik“","user_id":"37888","place":"Berlin, Heidelberg"},{"user_id":"37888","title":"Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik","date_created":"2023-01-10T10:28:38Z","status":"public","volume":2021,"publication":"mathematik lehren","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"author":[{"first_name":"Lukas","full_name":"Höper, Lukas","last_name":"Höper"},{"full_name":"Malin, Leah","first_name":"Leah","last_name":"Malin"},{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"}],"publisher":"Friedrich Verlag","issue":"228","date_updated":"2023-01-11T10:15:23Z","_id":"35761","intvolume":" 2021","language":[{"iso":"ger"}],"page":"19–22","citation":{"bibtex":"@article{Höper_Malin_Biehler_2021, title={Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik}, volume={2021}, number={228}, journal={mathematik lehren}, publisher={Friedrich Verlag}, author={Höper, Lukas and Malin, Leah and Biehler, Rolf}, year={2021}, pages={19–22} }","mla":"Höper, Lukas, et al. “Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik.” mathematik lehren, vol. 2021, no. 228, Friedrich Verlag, 2021, pp. 19–22.","ama":"Höper L, Malin L, Biehler R. Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik. mathematik lehren. 2021;2021(228):19–22.","apa":"Höper, L., Malin, L., & Biehler, R. (2021). Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik. mathematik lehren, 2021(228), 19–22.","chicago":"Höper, Lukas, Leah Malin, and Rolf Biehler. “Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik.” mathematik lehren 2021, no. 228 (2021): 19–22.","ieee":"L. Höper, L. Malin, and R. Biehler, “Schatten von 3D-Objekten: Modellierung mit GeoGebra 3D und Anwendungen in der Computergrafik,” mathematik lehren, vol. 2021, no. 228, pp. 19–22, 2021.","short":"L. Höper, L. Malin, R. Biehler, mathematik lehren 2021 (2021) 19–22."},"type":"journal_article","year":"2021"},{"publisher":"Friedrich Verlag","author":[{"full_name":"Hüsing, Sven","first_name":"Sven","last_name":"Hüsing"},{"full_name":"Weiser, Niklas","first_name":"Niklas","last_name":"Weiser"},{"full_name":"Biehler, Rolf","first_name":"Rolf","id":"16274","last_name":"Biehler"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication":"mathematik lehren","volume":2021,"status":"public","date_created":"2023-01-10T10:29:36Z","title":"Faszination 3D-Film: Entwicklung einer 3D-Konstruktion","user_id":"37888","type":"journal_article","year":"2021","citation":{"short":"S. Hüsing, N. Weiser, R. Biehler, mathematik lehren 2021 (2021) 23–27.","ieee":"S. Hüsing, N. Weiser, and R. Biehler, “Faszination 3D-Film: Entwicklung einer 3D-Konstruktion,” mathematik lehren, vol. 2021, no. 228, pp. 23–27, 2021.","chicago":"Hüsing, Sven, Niklas Weiser, and Rolf Biehler. “Faszination 3D-Film: Entwicklung einer 3D-Konstruktion.” mathematik lehren 2021, no. 228 (2021): 23–27.","apa":"Hüsing, S., Weiser, N., & Biehler, R. (2021). Faszination 3D-Film: Entwicklung einer 3D-Konstruktion. mathematik lehren, 2021(228), 23–27.","ama":"Hüsing S, Weiser N, Biehler R. Faszination 3D-Film: Entwicklung einer 3D-Konstruktion. mathematik lehren. 2021;2021(228):23–27.","mla":"Hüsing, Sven, et al. “Faszination 3D-Film: Entwicklung einer 3D-Konstruktion.” mathematik lehren, vol. 2021, no. 228, Friedrich Verlag, 2021, pp. 23–27.","bibtex":"@article{Hüsing_Weiser_Biehler_2021, title={Faszination 3D-Film: Entwicklung einer 3D-Konstruktion}, volume={2021}, number={228}, journal={mathematik lehren}, publisher={Friedrich Verlag}, author={Hüsing, Sven and Weiser, Niklas and Biehler, Rolf}, year={2021}, pages={23–27} }"},"page":"23–27","language":[{"iso":"ger"}],"_id":"35763","date_updated":"2023-01-11T10:16:19Z","intvolume":" 2021","issue":"228"},{"title":"Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"publication_status":"published","publication_identifier":{"issn":["2198-9745","2198-9753"]},"date_updated":"2023-01-11T10:19:25Z","doi":"10.1007/s40753-021-00139-8","language":[{"iso":"eng"}],"abstract":[{"text":"AbstractThe aim of the special issue is to bring together important current international research on innovative teaching and learning practices in mathematics in engineering education, and to develop deeper understandings of the characteristics of current teaching and learning practices that can inform the design and implementation of future innovative practice. The focus of this review paper is to provide a state-of-the-art overview of this emerging field at the cross-roads between mathematics and engineering education, in addition to introducing the papers of this special issue. To guide this paper, we posed three review questions: (1) How can current (teaching/learning/study) practices of mathematics in engineering education be characterized with a view towards innovation?; (2) What are the ‘resources’ (cognitive, material, digital, social) used, and what are those that appear also well suited for innovative courses?; (3) What are promising innovative practices in mathematics in engineering education, and what are the implications for curriculum reform? Looking back across the studies we summarized in the review, we conclude that they are lagging behind the more fundamental changes that are happening in engineering education, whilst addressing selected aspects of innovative changes within the current system of engineering education. At the same time, the nine papers of this special issue contribute new perspectives for innovative practices in mathematics in engineering education, for a better understanding of current practices and for future research.","lang":"eng"}],"user_id":"37888","publication":"International Journal of Research in Undergraduate Mathematics Education","keyword":["Education","Mathematics (miscellaneous)"],"author":[{"last_name":"Pepin","full_name":"Pepin, Birgit","first_name":"Birgit"},{"id":"16274","last_name":"Biehler","full_name":"Biehler, Rolf","first_name":"Rolf"},{"last_name":"Gueudet","first_name":"Ghislaine","full_name":"Gueudet, Ghislaine"}],"publisher":"Springer Science and Business Media LLC","date_created":"2023-01-10T10:43:08Z","status":"public","volume":7,"intvolume":" 7","_id":"35778","issue":"2","page":"163-188","type":"journal_article","year":"2021","citation":{"bibtex":"@article{Pepin_Biehler_Gueudet_2021, title={Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices}, volume={7}, DOI={10.1007/s40753-021-00139-8}, number={2}, journal={International Journal of Research in Undergraduate Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Pepin, Birgit and Biehler, Rolf and Gueudet, Ghislaine}, year={2021}, pages={163–188} }","mla":"Pepin, Birgit, et al. “Mathematics in Engineering Education: A Review of the Recent Literature with a View towards Innovative Practices.” International Journal of Research in Undergraduate Mathematics Education, vol. 7, no. 2, Springer Science and Business Media LLC, 2021, pp. 163–88, doi:10.1007/s40753-021-00139-8.","chicago":"Pepin, Birgit, Rolf Biehler, and Ghislaine Gueudet. “Mathematics in Engineering Education: A Review of the Recent Literature with a View towards Innovative Practices.” International Journal of Research in Undergraduate Mathematics Education 7, no. 2 (2021): 163–88. https://doi.org/10.1007/s40753-021-00139-8.","apa":"Pepin, B., Biehler, R., & Gueudet, G. (2021). Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices. International Journal of Research in Undergraduate Mathematics Education, 7(2), 163–188. https://doi.org/10.1007/s40753-021-00139-8","ama":"Pepin B, Biehler R, Gueudet G. Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices. International Journal of Research in Undergraduate Mathematics Education. 2021;7(2):163-188. doi:10.1007/s40753-021-00139-8","ieee":"B. Pepin, R. Biehler, and G. Gueudet, “Mathematics in Engineering Education: a Review of the Recent Literature with a View towards Innovative Practices,” International Journal of Research in Undergraduate Mathematics Education, vol. 7, no. 2, pp. 163–188, 2021, doi: 10.1007/s40753-021-00139-8.","short":"B. Pepin, R. Biehler, G. Gueudet, International Journal of Research in Undergraduate Mathematics Education 7 (2021) 163–188."}},{"user_id":"37888","volume":24,"date_created":"2023-01-10T10:44:50Z","status":"public","keyword":["Developmental and Educational Psychology","Education","General Mathematics"],"publication":"Mathematical Thinking and Learning","author":[{"full_name":"Podworny, Susanne","first_name":"Susanne","last_name":"Podworny"},{"last_name":"Biehler","id":"16274","first_name":"Rolf","full_name":"Biehler, Rolf"}],"publisher":"Informa UK Limited","issue":"4","_id":"35781","intvolume":" 24","page":"291-311","type":"journal_article","year":"2021","citation":{"ieee":"S. Podworny and R. Biehler, “The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study,” Mathematical Thinking and Learning, vol. 24, no. 4, pp. 291–311, 2021, doi: 10.1080/10986065.2021.1922837.","short":"S. Podworny, R. Biehler, Mathematical Thinking and Learning 24 (2021) 291–311.","bibtex":"@article{Podworny_Biehler_2021, title={The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study}, volume={24}, DOI={10.1080/10986065.2021.1922837}, number={4}, journal={Mathematical Thinking and Learning}, publisher={Informa UK Limited}, author={Podworny, Susanne and Biehler, Rolf}, year={2021}, pages={291–311} }","mla":"Podworny, Susanne, and Rolf Biehler. “The Process of Actively Building a Model for a Randomization Test – Insights into Learners’ Modeling Activities Based on a Case Study.” Mathematical Thinking and Learning, vol. 24, no. 4, Informa UK Limited, 2021, pp. 291–311, doi:10.1080/10986065.2021.1922837.","ama":"Podworny S, Biehler R. The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study. Mathematical Thinking and Learning. 2021;24(4):291-311. doi:10.1080/10986065.2021.1922837","apa":"Podworny, S., & Biehler, R. (2021). The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study. Mathematical Thinking and Learning, 24(4), 291–311. https://doi.org/10.1080/10986065.2021.1922837","chicago":"Podworny, Susanne, and Rolf Biehler. “The Process of Actively Building a Model for a Randomization Test – Insights into Learners’ Modeling Activities Based on a Case Study.” Mathematical Thinking and Learning 24, no. 4 (2021): 291–311. https://doi.org/10.1080/10986065.2021.1922837."},"title":"The process of actively building a model for a randomization test – insights into learners’ modeling activities based on a case study","publication_identifier":{"issn":["1098-6065","1532-7833"]},"publication_status":"published","department":[{"_id":"34"},{"_id":"10"},{"_id":"97"},{"_id":"363"}],"doi":"10.1080/10986065.2021.1922837","date_updated":"2023-01-11T10:20:20Z","language":[{"iso":"eng"}]},{"doi":"10.4324/9780429346859-6","date_updated":"2023-01-11T10:22:23Z","_id":"35704","language":[{"iso":"eng"}],"citation":{"short":"C. Winsløw, R. Biehler, B. Jaworski, F. Rønning, M. Wawro, in: V. Durand-Guerrier, R. Hochmuth, E. Nardi, C. Winsløw (Eds.), Research and Development in University Mathematics Education, Routledge, 2021, pp. 59–79.","ieee":"C. Winsløw, R. Biehler, B. Jaworski, F. Rønning, and M. Wawro, “Education and professional development of university mathematics teachers,” in Research and Development in University Mathematics Education, V. Durand-Guerrier, R. Hochmuth, E. Nardi, and C. Winsløw, Eds. Routledge, 2021, pp. 59–79.","ama":"Winsløw C, Biehler R, Jaworski B, Rønning F, Wawro M. Education and professional development of university mathematics teachers. In: Durand-Guerrier V, Hochmuth R, Nardi E, Winsløw C, eds. Research and Development in University Mathematics Education. Routledge; 2021:59-79. doi:10.4324/9780429346859-6","apa":"Winsløw, C., Biehler, R., Jaworski, B., Rønning, F., & Wawro, M. (2021). Education and professional development of university mathematics teachers. In V. Durand-Guerrier, R. Hochmuth, E. Nardi, & C. Winsløw (Eds.), Research and Development in University Mathematics Education (pp. 59–79). Routledge. https://doi.org/10.4324/9780429346859-6","chicago":"Winsløw, Carl, Rolf Biehler, Barbara Jaworski, Frode Rønning, and Megan Wawro. “Education and Professional Development of University Mathematics Teachers.” In Research and Development in University Mathematics Education, edited by V. Durand-Guerrier, R. Hochmuth, E. Nardi, and C. Winsløw, 59–79. Routledge, 2021. https://doi.org/10.4324/9780429346859-6.","bibtex":"@inbook{Winsløw_Biehler_Jaworski_Rønning_Wawro_2021, title={Education and professional development of university mathematics teachers}, DOI={10.4324/9780429346859-6}, booktitle={Research and Development in University Mathematics Education}, publisher={Routledge}, author={Winsløw, Carl and Biehler, Rolf and Jaworski, Barbara and Rønning, Frode and Wawro, Megan}, editor={Durand-Guerrier, V. and Hochmuth, R. and Nardi, E. and Winsløw, C.}, year={2021}, pages={59–79} }","mla":"Winsløw, Carl, et al. “Education and Professional Development of University Mathematics Teachers.” Research and Development in University Mathematics Education, edited by V. 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Schürmann et al., “Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany,” Sigma newsletter, vol. 22, pp. 5–6, 2021.","short":"M. Schürmann, M. Liebendörfer, L. Gildehaus, N. Schaper, R. Hochmuth, R. Biehler, E. Lankeit, C. Kuklinski, J. Ruge, Sigma Newsletter 22 (2021) 5–6.","bibtex":"@article{Schürmann_Liebendörfer_Gildehaus_Schaper_Hochmuth_Biehler_Lankeit_Kuklinski_Ruge_2021, title={Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany}, volume={22}, journal={Sigma newsletter}, author={Schürmann, Mirko and Liebendörfer, Michael and Gildehaus, Lara and Schaper, Niclas and Hochmuth, Reinhard and Biehler, Rolf and Lankeit, Elisa and Kuklinski, Christiane and Ruge, Johanna}, year={2021}, pages={5–6} }","mla":"Schürmann, Mirko, et al. “Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany.” Sigma Newsletter, vol. 22, 2021, pp. 5–6.","chicago":"Schürmann, Mirko, Michael Liebendörfer, Lara Gildehaus, Niclas Schaper, Reinhard Hochmuth, Rolf Biehler, Elisa Lankeit, Christiane Kuklinski, and Johanna Ruge. “Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany.” Sigma Newsletter 22 (2021): 5–6.","ama":"Schürmann M, Liebendörfer M, Gildehaus L, et al. Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany. Sigma newsletter. 2021;22:5-6.","apa":"Schürmann, M., Liebendörfer, M., Gildehaus, L., Schaper, N., Hochmuth, R., Biehler, R., Lankeit, E., Kuklinski, C., & Ruge, J. (2021). Opportunities and Possibilities of a Network of Mathematical Learning and Support Centres in Germany. Sigma Newsletter, 22, 5–6."},"page":"5-6","_id":"24786","intvolume":" 22","date_updated":"2023-01-17T23:39:04Z"},{"publication_identifier":{"isbn":["978-3-95987-184-6"]},"editor":[{"last_name":"Hein","full_name":"Hein, Kerstin","first_name":"Kerstin"},{"last_name":"Heil","full_name":"Heil, Cathleen","first_name":"Cathleen"},{"first_name":"Silke","full_name":"Ruwisch, Silke","last_name":"Ruwisch"},{"full_name":"Prediger, Susanne","first_name":"Susanne","last_name":"Prediger"}],"date_created":"2023-01-18T22:35:08Z","status":"public","department":[{"_id":"10"}],"publication":"Beiträge zum Mathematikunterricht 2021 vom GDM-Monat 2021 der Gesellschaft für Didaktik der Mathematik (GDM) (1.-25. März 2021)","author":[{"last_name":"Rach","first_name":"Stefanie","full_name":"Rach, Stefanie"},{"last_name":"Liebendörfer","full_name":"Liebendörfer, Michael","first_name":"Michael"}],"publisher":"WTM-Verlag für wissenschaftliche Texte und Medien","title":"Die Bedeutung affektiver Merkmale beim Mathematiklernen","user_id":"30933","place":"Münster","page":"247–248","citation":{"ieee":"S. Rach and M. Liebendörfer, “Die Bedeutung affektiver Merkmale beim Mathematiklernen,” in Beiträge zum Mathematikunterricht 2021 vom GDM-Monat 2021 der Gesellschaft für Didaktik der Mathematik (GDM) (1.-25. März 2021), K. Hein, C. Heil, S. Ruwisch, and S. Prediger, Eds. Münster: WTM-Verlag für wissenschaftliche Texte und Medien, 2021, pp. 247–248.","short":"S. Rach, M. Liebendörfer, in: K. Hein, C. Heil, S. Ruwisch, S. Prediger (Eds.), Beiträge Zum Mathematikunterricht 2021 Vom GDM-Monat 2021 Der Gesellschaft Für Didaktik Der Mathematik (GDM) (1.-25. März 2021), WTM-Verlag für wissenschaftliche Texte und Medien, Münster, 2021, pp. 247–248.","bibtex":"@inbook{Rach_Liebendörfer_2021, place={Münster}, series={Beiträge zum Mathematikunterricht}, title={Die Bedeutung affektiver Merkmale beim Mathematiklernen}, booktitle={Beiträge zum Mathematikunterricht 2021 vom GDM-Monat 2021 der Gesellschaft für Didaktik der Mathematik (GDM) (1.-25. März 2021)}, publisher={WTM-Verlag für wissenschaftliche Texte und Medien}, author={Rach, Stefanie and Liebendörfer, Michael}, editor={Hein, Kerstin and Heil, Cathleen and Ruwisch, Silke and Prediger, Susanne}, year={2021}, pages={247–248}, collection={Beiträge zum Mathematikunterricht} }","mla":"Rach, Stefanie, and Michael Liebendörfer. “Die Bedeutung Affektiver Merkmale Beim Mathematiklernen.” Beiträge Zum Mathematikunterricht 2021 Vom GDM-Monat 2021 Der Gesellschaft Für Didaktik Der Mathematik (GDM) (1.-25. März 2021), edited by Kerstin Hein et al., WTM-Verlag für wissenschaftliche Texte und Medien, 2021, pp. 247–248.","apa":"Rach, S., & Liebendörfer, M. (2021). Die Bedeutung affektiver Merkmale beim Mathematiklernen. In K. Hein, C. Heil, S. Ruwisch, & S. Prediger (Eds.), Beiträge zum Mathematikunterricht 2021 vom GDM-Monat 2021 der Gesellschaft für Didaktik der Mathematik (GDM) (1.-25. März 2021) (pp. 247–248). WTM-Verlag für wissenschaftliche Texte und Medien.","ama":"Rach S, Liebendörfer M. Die Bedeutung affektiver Merkmale beim Mathematiklernen. In: Hein K, Heil C, Ruwisch S, Prediger S, eds. Beiträge Zum Mathematikunterricht 2021 Vom GDM-Monat 2021 Der Gesellschaft Für Didaktik Der Mathematik (GDM) (1.-25. März 2021). Beiträge zum Mathematikunterricht. WTM-Verlag für wissenschaftliche Texte und Medien; 2021:247–248.","chicago":"Rach, Stefanie, and Michael Liebendörfer. “Die Bedeutung Affektiver Merkmale Beim Mathematiklernen.” In Beiträge Zum Mathematikunterricht 2021 Vom GDM-Monat 2021 Der Gesellschaft Für Didaktik Der Mathematik (GDM) (1.-25. März 2021), edited by Kerstin Hein, Cathleen Heil, Silke Ruwisch, and Susanne Prediger, 247–248. Beiträge Zum Mathematikunterricht. Münster: WTM-Verlag für wissenschaftliche Texte und Medien, 2021."},"type":"book_chapter","year":"2021","series_title":"Beiträge zum Mathematikunterricht","_id":"37485","date_updated":"2023-01-18T22:41:32Z"},{"language":[{"iso":"eng"}],"date_updated":"2023-01-18T22:47:00Z","doi":"10.1093/teamat/hrab013","department":[{"_id":"10"}],"publication_status":"published","publication_identifier":{"issn":["0268-3679","1471-6976"]},"title":"Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university","page":"478-496","type":"journal_article","citation":{"apa":"Büchele, S., Liebendörfer, M., & Lankeit, E. (2021). Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university. Teaching Mathematics and Its Applications: An International Journal of the IMA, 40(4), 478–496. https://doi.org/10.1093/teamat/hrab013","ama":"Büchele S, Liebendörfer M, Lankeit E. Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university. Teaching Mathematics and its Applications: An International Journal of the IMA. 2021;40(4):478-496. doi:10.1093/teamat/hrab013","chicago":"Büchele, Stefan, Michael Liebendörfer, and Elisa Lankeit. “Increasing the Effect of a Remedial Mathematics Course by Switching to an Online Format during the COVID-19 Crisis: Evidence from a German University.” Teaching Mathematics and Its Applications: An International Journal of the IMA 40, no. 4 (2021): 478–96. https://doi.org/10.1093/teamat/hrab013.","bibtex":"@article{Büchele_Liebendörfer_Lankeit_2021, title={Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university}, volume={40}, DOI={10.1093/teamat/hrab013}, number={4}, journal={Teaching Mathematics and its Applications: An International Journal of the IMA}, publisher={Oxford University Press (OUP)}, author={Büchele, Stefan and Liebendörfer, Michael and Lankeit, Elisa}, year={2021}, pages={478–496} }","mla":"Büchele, Stefan, et al. “Increasing the Effect of a Remedial Mathematics Course by Switching to an Online Format during the COVID-19 Crisis: Evidence from a German University.” Teaching Mathematics and Its Applications: An International Journal of the IMA, vol. 40, no. 4, Oxford University Press (OUP), 2021, pp. 478–96, doi:10.1093/teamat/hrab013.","short":"S. Büchele, M. Liebendörfer, E. Lankeit, Teaching Mathematics and Its Applications: An International Journal of the IMA 40 (2021) 478–496.","ieee":"S. Büchele, M. Liebendörfer, and E. Lankeit, “Increasing the effect of a remedial mathematics course by switching to an online format during the COVID-19 crisis: evidence from a German university,” Teaching Mathematics and its Applications: An International Journal of the IMA, vol. 40, no. 4, pp. 478–496, 2021, doi: 10.1093/teamat/hrab013."},"year":"2021","_id":"37474","intvolume":" 40","issue":"4","publication":"Teaching Mathematics and its Applications: An International Journal of the IMA","keyword":["Education","General Mathematics"],"publisher":"Oxford University Press (OUP)","author":[{"last_name":"Büchele","first_name":"Stefan","full_name":"Büchele, Stefan"},{"first_name":"Michael","full_name":"Liebendörfer, Michael","last_name":"Liebendörfer"},{"full_name":"Lankeit, Elisa","first_name":"Elisa","last_name":"Lankeit"}],"volume":40,"date_created":"2023-01-18T22:23:50Z","status":"public","abstract":[{"lang":"eng","text":"Abstract\n Due to the COVID-19 crisis, many courses have been offered digitally. Using data from n = 1,173 business students participating in a preparatory mathematics course at a German university that covered the same content as in 2018, 2019 and 2020, we examine how students’ participation and the effect of the preparatory course changed. The data show that the participation rate has fallen slightly, but students’ participation is rather similar to preceding years. Interestingly, students have participated more intensively. There are clear signs of dishonesty in the self-test (use of a calculator) and significant changes in predictors of performance. In particular, the effect of students’ engagement in the course on their performance substantially increased. Further, we found a gender gap in performance affecting women. Finally, the data show that digital courses can be as effective as on-campus courses."}],"user_id":"30933"},{"abstract":[{"lang":"eng","text":"Das gymnasiale Lehramtsstudium der Mathematik ist an deutschen Universitäten unterschiedlich organisiert. Traditionell wurden am Studienbeginn die Fachvorlesungen zur Analysis und Linearen Algebra gemeinsam mit Fachstudierenden gehört. In jüngerer Zeit verbreiten sich alternative Modelle z. B. mit Brückenvorlesungen, die oft spezifisch für das Gymnasiallehramt angeboten werden. Sie können gemeinsame Veranstaltungen mit Fachstudierenden ergänzen oder ersetzen. Dieser Beitrag zeigt auf, welche Modelle wie häufig verbreitet sind, und spricht an, welche hochschuldidaktischen Fragen an der Studiengestaltung hängen."}],"user_id":"30933","title":"Gymnasiales Lehramt Mathematik studieren – eine Übersicht zur Studienorganisation in Deutschland","department":[{"_id":"10"}],"publication":"Mitteilungen der Gesellschaft für Didaktik der Mathematik","author":[{"first_name":"Lara","full_name":"Gildehaus, Lara","last_name":"Gildehaus"},{"last_name":"Göller","first_name":"Robin","full_name":"Göller, Robin"},{"full_name":"Liebendörfer, Michael","first_name":"Michael","last_name":"Liebendörfer"}],"date_created":"2023-01-18T22:31:53Z","status":"public","volume":47,"publication_identifier":{"issn":["2512-9155"]},"intvolume":" 47","_id":"37483","date_updated":"2023-01-18T22:46:49Z","issue":"111","page":"27–32","citation":{"mla":"Gildehaus, Lara, et al. “Gymnasiales Lehramt Mathematik Studieren – Eine Übersicht Zur Studienorganisation in Deutschland.” Mitteilungen Der Gesellschaft Für Didaktik Der Mathematik, vol. 47, no. 111, 2021, pp. 27–32.","bibtex":"@article{Gildehaus_Göller_Liebendörfer_2021, title={Gymnasiales Lehramt Mathematik studieren – eine Übersicht zur Studienorganisation in Deutschland}, volume={47}, number={111}, journal={Mitteilungen der Gesellschaft für Didaktik der Mathematik}, author={Gildehaus, Lara and Göller, Robin and Liebendörfer, Michael}, year={2021}, pages={27–32} }","apa":"Gildehaus, L., Göller, R., & Liebendörfer, M. (2021). Gymnasiales Lehramt Mathematik studieren – eine Übersicht zur Studienorganisation in Deutschland. Mitteilungen Der Gesellschaft Für Didaktik Der Mathematik, 47(111), 27–32.","ama":"Gildehaus L, Göller R, Liebendörfer M. Gymnasiales Lehramt Mathematik studieren – eine Übersicht zur Studienorganisation in Deutschland. Mitteilungen der Gesellschaft für Didaktik der Mathematik. 2021;47(111):27–32.","chicago":"Gildehaus, Lara, Robin Göller, and Michael Liebendörfer. “Gymnasiales Lehramt Mathematik Studieren – Eine Übersicht Zur Studienorganisation in Deutschland.” Mitteilungen Der Gesellschaft Für Didaktik Der Mathematik 47, no. 111 (2021): 27–32.","ieee":"L. Gildehaus, R. Göller, and M. Liebendörfer, “Gymnasiales Lehramt Mathematik studieren – eine Übersicht zur Studienorganisation in Deutschland,” Mitteilungen der Gesellschaft für Didaktik der Mathematik, vol. 47, no. 111, pp. 27–32, 2021.","short":"L. Gildehaus, R. Göller, M. Liebendörfer, Mitteilungen Der Gesellschaft Für Didaktik Der Mathematik 47 (2021) 27–32."},"year":"2021","type":"journal_article"},{"editor":[{"full_name":"Kenner, Steve","first_name":"Steve","last_name":"Kenner"},{"first_name":"T.","full_name":"Oeftering, T.","last_name":"Oeftering"}],"date_created":"2023-01-18T22:31:25Z","status":"public","department":[{"_id":"10"}],"publication":"Schriftenreihe der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft und das vermeintliche Neutralitätsgebot","author":[{"first_name":"Bastian","full_name":"Vajen, Bastian","last_name":"Vajen"},{"last_name":"Gildehaus","first_name":"Lara","full_name":"Gildehaus, Lara"},{"full_name":"Liebendörfer, Michael","first_name":"Michael","last_name":"Liebendörfer"},{"last_name":"Wolf","first_name":"Christoph","full_name":"Wolf, Christoph"}],"publisher":"Wochenschau","title":"Mathematisierung als Herausforderung für die politische Bildung","user_id":"30933","place":"Frankfurt","page":"188–200","year":"2021","type":"conference","citation":{"bibtex":"@inproceedings{Vajen_Gildehaus_Liebendörfer_Wolf_2021, place={Frankfurt}, title={Mathematisierung als Herausforderung für die politische Bildung}, booktitle={Schriftenreihe der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft und das vermeintliche Neutralitätsgebot}, publisher={Wochenschau}, author={Vajen, Bastian and Gildehaus, Lara and Liebendörfer, Michael and Wolf, Christoph}, editor={Kenner, Steve and Oeftering, T.}, year={2021}, pages={188–200} }","mla":"Vajen, Bastian, et al. “Mathematisierung Als Herausforderung Für Die Politische Bildung.” Schriftenreihe Der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft Und Das Vermeintliche Neutralitätsgebot, edited by Steve Kenner and T. Oeftering, Wochenschau, 2021, pp. 188–200.","chicago":"Vajen, Bastian, Lara Gildehaus, Michael Liebendörfer, and Christoph Wolf. “Mathematisierung Als Herausforderung Für Die Politische Bildung.” In Schriftenreihe Der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft Und Das Vermeintliche Neutralitätsgebot, edited by Steve Kenner and T. Oeftering, 188–200. Frankfurt: Wochenschau, 2021.","apa":"Vajen, B., Gildehaus, L., Liebendörfer, M., & Wolf, C. (2021). Mathematisierung als Herausforderung für die politische Bildung. In S. Kenner & T. Oeftering (Eds.), Schriftenreihe der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft und das vermeintliche Neutralitätsgebot (pp. 188–200). Wochenschau.","ama":"Vajen B, Gildehaus L, Liebendörfer M, Wolf C. Mathematisierung als Herausforderung für die politische Bildung. In: Kenner S, Oeftering T, eds. Schriftenreihe Der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft Und Das Vermeintliche Neutralitätsgebot. Wochenschau; 2021:188–200.","ieee":"B. Vajen, L. Gildehaus, M. Liebendörfer, and C. Wolf, “Mathematisierung als Herausforderung für die politische Bildung,” in Schriftenreihe der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft und das vermeintliche Neutralitätsgebot, 2021, pp. 188–200.","short":"B. Vajen, L. Gildehaus, M. Liebendörfer, C. Wolf, in: S. Kenner, T. Oeftering (Eds.), Schriftenreihe Der DVPB. Standortbestimmung Politische Bildung: Gesellschaftspolitische Herausforderungen, Zivilgesellschaft Und Das Vermeintliche Neutralitätsgebot, Wochenschau, Frankfurt, 2021, pp. 188–200."},"_id":"37481","date_updated":"2023-01-18T22:47:23Z"},{"year":"2021","type":"book_chapter","citation":{"short":"R. Göller, L. Gildehaus, M. Liebendörfer, J. Steuding, in: A. Blunck, R. Motzer (Eds.), Mathematik Und Gender: Berichte Und Beiträge Des Arbeitskreise Frauen Und Mathematik, Franzbecker, 2021, pp. 59–76.","ieee":"R. Göller, L. Gildehaus, M. Liebendörfer, and J. Steuding, “Prüfungsformate als Ansatzpunkt gendersensibler universitärer Lehre im Fach Mathematik,” in Mathematik und Gender: Berichte und Beiträge des Arbeitskreise Frauen und Mathematik, vol. 5, A. Blunck and R. Motzer, Eds. Franzbecker, 2021, pp. 59–76.","apa":"Göller, R., Gildehaus, L., Liebendörfer, M., & Steuding, J. (2021). Prüfungsformate als Ansatzpunkt gendersensibler universitärer Lehre im Fach Mathematik. In A. Blunck & R. Motzer (Eds.), Mathematik und Gender: Berichte und Beiträge des Arbeitskreise Frauen und Mathematik (Vol. 5, pp. 59–76). Franzbecker.","ama":"Göller R, Gildehaus L, Liebendörfer M, Steuding J. Prüfungsformate als Ansatzpunkt gendersensibler universitärer Lehre im Fach Mathematik. In: Blunck A, Motzer R, eds. Mathematik Und Gender: Berichte Und Beiträge Des Arbeitskreise Frauen Und Mathematik. Vol 5. Franzbecker; 2021:59–76.","chicago":"Göller, Robin, Lara Gildehaus, Michael Liebendörfer, and Jörn Steuding. “Prüfungsformate Als Ansatzpunkt Gendersensibler Universitärer Lehre Im Fach Mathematik.” In Mathematik Und Gender: Berichte Und Beiträge Des Arbeitskreise Frauen Und Mathematik, edited by Andrea Blunck and Renate Motzer, 5:59–76. Franzbecker, 2021.","bibtex":"@inbook{Göller_Gildehaus_Liebendörfer_Steuding_2021, title={Prüfungsformate als Ansatzpunkt gendersensibler universitärer Lehre im Fach Mathematik}, volume={5}, booktitle={Mathematik und Gender: Berichte und Beiträge des Arbeitskreise Frauen und Mathematik}, publisher={Franzbecker}, author={Göller, Robin and Gildehaus, Lara and Liebendörfer, Michael and Steuding, Jörn}, editor={Blunck, Andrea and Motzer, Renate}, year={2021}, pages={59–76} }","mla":"Göller, Robin, et al. “Prüfungsformate Als Ansatzpunkt Gendersensibler Universitärer Lehre Im Fach Mathematik.” Mathematik Und Gender: Berichte Und Beiträge Des Arbeitskreise Frauen Und Mathematik, edited by Andrea Blunck and Renate Motzer, vol. 5, Franzbecker, 2021, pp. 59–76."},"page":"59–76","date_updated":"2023-01-18T22:47:46Z","_id":"37480","intvolume":" 5","author":[{"last_name":"Göller","full_name":"Göller, Robin","first_name":"Robin"},{"full_name":"Gildehaus, Lara","first_name":"Lara","last_name":"Gildehaus"},{"last_name":"Liebendörfer","first_name":"Michael","full_name":"Liebendörfer, Michael"},{"last_name":"Steuding","first_name":"Jörn","full_name":"Steuding, Jörn"}],"publisher":"Franzbecker","publication":"Mathematik und Gender: Berichte und Beiträge des Arbeitskreise Frauen und Mathematik","department":[{"_id":"10"}],"editor":[{"last_name":"Blunck","first_name":"Andrea","full_name":"Blunck, Andrea"},{"last_name":"Motzer","full_name":"Motzer, Renate","first_name":"Renate"}],"volume":5,"status":"public","date_created":"2023-01-18T22:31:17Z","title":"Prüfungsformate als Ansatzpunkt gendersensibler universitärer Lehre im Fach Mathematik","user_id":"30933"},{"citation":{"chicago":"Haak, Inka, Lara Gildehaus, and Michael Liebendörfer. “Genese Und Funktionen von Lerngruppen in Der Studieneingangsphase.” In Naturwissenschaftlicher Unterricht Und Lehrerbildung Im Umbruch?, 89–92. Universität Duisburg-Essen, 2021.","ama":"Haak I, Gildehaus L, Liebendörfer M. Genese und Funktionen von Lerngruppen in der Studieneingangsphase. In: Naturwissenschaftlicher Unterricht Und Lehrerbildung Im Umbruch?. Universität Duisburg-Essen; 2021:89–92.","apa":"Haak, I., Gildehaus, L., & Liebendörfer, M. (2021). Genese und Funktionen von Lerngruppen in der Studieneingangsphase. Naturwissenschaftlicher Unterricht Und Lehrerbildung Im Umbruch?, 89–92.","bibtex":"@inproceedings{Haak_Gildehaus_Liebendörfer_2021, title={Genese und Funktionen von Lerngruppen in der Studieneingangsphase}, booktitle={Naturwissenschaftlicher Unterricht und Lehrerbildung im Umbruch?}, publisher={Universität Duisburg-Essen}, author={Haak, Inka and Gildehaus, Lara and Liebendörfer, Michael}, year={2021}, pages={89–92} }","mla":"Haak, Inka, et al. “Genese Und Funktionen von Lerngruppen in Der Studieneingangsphase.” Naturwissenschaftlicher Unterricht Und Lehrerbildung Im Umbruch?, Universität Duisburg-Essen, 2021, pp. 89–92.","short":"I. Haak, L. Gildehaus, M. Liebendörfer, in: Naturwissenschaftlicher Unterricht Und Lehrerbildung Im Umbruch?, Universität Duisburg-Essen, 2021, pp. 89–92.","ieee":"I. Haak, L. Gildehaus, and M. Liebendörfer, “Genese und Funktionen von Lerngruppen in der Studieneingangsphase,” in Naturwissenschaftlicher Unterricht und Lehrerbildung im Umbruch?, 2021, pp. 89–92."},"year":"2021","type":"conference","page":"89–92","_id":"37478","date_updated":"2023-01-18T22:44:35Z","status":"public","date_created":"2023-01-18T22:31:03Z","publisher":"Universität Duisburg-Essen","author":[{"last_name":"Haak","first_name":"Inka","full_name":"Haak, Inka"},{"last_name":"Gildehaus","first_name":"Lara","full_name":"Gildehaus, Lara"},{"full_name":"Liebendörfer, Michael","first_name":"Michael","last_name":"Liebendörfer"}],"department":[{"_id":"10"}],"publication":"Naturwissenschaftlicher Unterricht und Lehrerbildung im Umbruch?","user_id":"30933","title":"Genese und Funktionen von Lerngruppen in der Studieneingangsphase"},{"title":"University students’ fully digital study of mathematics: an identification of student-groups via their resources usage and a characterization by personal and affective characteristics","department":[{"_id":"10"}],"publication_identifier":{"issn":["0268-3679","1471-6976"]},"publication_status":"published","date_updated":"2023-01-18T22:49:44Z","doi":"10.1093/teamat/hrab020","language":[{"iso":"eng"}],"abstract":[{"text":"Abstract\n We investigated university students’ study of mathematics in the digital setting context of the COVID-19 pandemic. We gathered data from a survey of 89 students enrolled in a ‘Linear Algebra 1’ course including affective variables, learning strategies, social relatedness and resources considered useful. The results indicate students’ high effort and self-regulation and a high variation in affective characteristics and social relatedness. All the traditional aspects of mathematics teaching (lecture, tutorials and lecture notes) were rated as particularly useful. In addition, the videos from external resources were rated as equally useful as the teaching team’s videos. In contrast, traditional literature such as textbooks was rarely considered useful. The most useful resource rated was communication with peers, underlining the important role of social learning despite fully digital learning environments. Finally, a cluster analysis based on students’ rated usefulness of the resources led to three different user-types. Whereas the ‘digitals’ find the external digital resources very useful (videos, webpages, etc.), the ‘traditionalists’ rate the digitalized traditional resources best (lecture, tutorials, etc.). All resources receive uniformly good ratings from a third group (‘all resource users’). We reflect on our findings in light of the pandemic and describe directions for future research.","lang":"eng"}],"user_id":"30933","keyword":["Education","General Mathematics"],"publication":"Teaching Mathematics and its Applications: An International Journal of the IMA","author":[{"last_name":"Kempen","full_name":"Kempen, Leander","first_name":"Leander"},{"first_name":"Michael","full_name":"Liebendörfer, Michael","last_name":"Liebendörfer"}],"publisher":"Oxford University Press (OUP)","volume":40,"date_created":"2023-01-18T22:23:40Z","status":"public","intvolume":" 40","_id":"37473","issue":"4","page":"436-454","type":"journal_article","year":"2021","citation":{"short":"L. Kempen, M. 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University students’ fully digital study of mathematics: an identification of student-groups via their resources usage and a characterization by personal and affective characteristics. Teaching Mathematics and Its Applications: An International Journal of the IMA, 40(4), 436–454. https://doi.org/10.1093/teamat/hrab020","ama":"Kempen L, Liebendörfer M. University students’ fully digital study of mathematics: an identification of student-groups via their resources usage and a characterization by personal and affective characteristics. 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(2021). Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities. Nonlinear Differential Equatiions and Applicatiions, 28, Article 47.","ama":"Ding M, Winkler M. Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities. Nonlinear Differential Equatiions and Applicatiions. 2021;28.","ieee":"M. Ding and M. Winkler, “Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities.,” Nonlinear Differential Equatiions and Applicatiions, vol. 28, Art. no. 47, 2021.","short":"M. Ding, M. Winkler, Nonlinear Differential Equatiions and Applicatiions 28 (2021)."},"type":"journal_article","year":"2021","user_id":"15645","title":"Small-density solutiions in Keller-Segel systems involving rapidly decaying diffusivities.","author":[{"last_name":"Ding","first_name":"Mengyao","full_name":"Ding, Mengyao"},{"last_name":"Winkler","id":"31496","first_name":"Michael","full_name":"Winkler, Michael"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Nonlinear Differential Equatiions and Applicatiions","status":"public","date_created":"2023-01-09T17:24:06Z","volume":28},{"volume":19,"status":"public","date_created":"2023-01-09T17:32:36Z","author":[{"last_name":"Tao","full_name":"Tao, Youshan","first_name":"Youshan"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler","id":"31496"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Communications in Mathematical Sciences","title":"Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime.","user_id":"15645","year":"2021","type":"journal_article","citation":{"ieee":"Y. Tao and M. Winkler, “Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime.,” Communications in Mathematical Sciences, vol. 19, pp. 829–849, 2021.","short":"Y. Tao, M. Winkler, Communications in Mathematical Sciences 19 (2021) 829–849.","mla":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Two-Dimensional Cross-Diffusion System Modeling Propagation of Urban Crime.” Communications in Mathematical Sciences, vol. 19, 2021, pp. 829–49.","bibtex":"@article{Tao_Winkler_2021, title={Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime.}, volume={19}, journal={Communications in Mathematical Sciences}, author={Tao, Youshan and Winkler, Michael}, year={2021}, pages={829–849} }","apa":"Tao, Y., & Winkler, M. (2021). Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. Communications in Mathematical Sciences, 19, 829–849.","ama":"Tao Y, Winkler M. Global smooth solutions in a two-dimensional cross-diffusion system modeling propagation of urban crime. Communications in Mathematical Sciences. 2021;19:829-849.","chicago":"Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Two-Dimensional Cross-Diffusion System Modeling Propagation of Urban Crime.” Communications in Mathematical Sciences 19 (2021): 829–49."},"page":"829-849","language":[{"iso":"eng"}],"intvolume":" 19","_id":"35605","date_updated":"2023-02-01T10:23:03Z"},{"language":[{"iso":"eng"}],"year":"2021","type":"journal_article","citation":{"bibtex":"@article{Tao_Winkler_2021, title={Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection.}, volume={53}, journal={SIAM Journal on Mathematical Analysis}, author={Tao, Youshan and Winkler, Michael}, year={2021}, pages={1411–1433} }","mla":"Tao, Youshan, and Michael Winkler. “Taxis-Driven Formation of Singular Hotspots in a May-Nowak Type Model for Virus Infection.” SIAM Journal on Mathematical Analysis, vol. 53, 2021, pp. 1411–33.","chicago":"Tao, Youshan, and Michael Winkler. “Taxis-Driven Formation of Singular Hotspots in a May-Nowak Type Model for Virus Infection.” SIAM Journal on Mathematical Analysis 53 (2021): 1411–33.","apa":"Tao, Y., & Winkler, M. (2021). Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection. SIAM Journal on Mathematical Analysis, 53, 1411–1433.","ama":"Tao Y, Winkler M. Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection. SIAM Journal on Mathematical Analysis. 2021;53:1411-1433.","ieee":"Y. Tao and M. Winkler, “Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection.,” SIAM Journal on Mathematical Analysis, vol. 53, pp. 1411–1433, 2021.","short":"Y. Tao, M. Winkler, SIAM Journal on Mathematical Analysis 53 (2021) 1411–1433."},"page":"1411-1433","date_updated":"2023-02-01T10:19:26Z","_id":"35604","intvolume":" 53","author":[{"last_name":"Tao","first_name":"Youshan","full_name":"Tao, Youshan"},{"full_name":"Winkler, Michael","first_name":"Michael","id":"31496","last_name":"Winkler"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"SIAM Journal on Mathematical Analysis","status":"public","date_created":"2023-01-09T17:30:10Z","volume":53,"user_id":"15645","title":"Taxis-driven formation of singular hotspots in a May-Nowak type model for virus infection."},{"language":[{"iso":"eng"}],"page":"1058-1091","citation":{"ieee":"Y. Wang, M. Winkler, and Z. Xiang, “Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.,” Communications in Partial Differential Equations, vol. 46, pp. 1058–1091, 2021.","short":"Y. Wang, M. Winkler, Z. Xiang, Communications in Partial Differential Equations 46 (2021) 1058–1091.","mla":"Wang, Yulan, et al. “Local Energy Estimates and Global Solvability in a Threee-Dimensional Chemotaxis-Fluid System with Prescribed Signal on the Boundary.” Communications in Partial Differential Equations, vol. 46, 2021, pp. 1058–91.","bibtex":"@article{Wang_Winkler_Xiang_2021, title={Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary.}, volume={46}, journal={Communications in Partial Differential Equations}, author={Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}, year={2021}, pages={1058–1091} }","chicago":"Wang, Yulan, Michael Winkler, and Zhaoyin Xiang. “Local Energy Estimates and Global Solvability in a Threee-Dimensional Chemotaxis-Fluid System with Prescribed Signal on the Boundary.” Communications in Partial Differential Equations 46 (2021): 1058–91.","ama":"Wang Y, Winkler M, Xiang Z. Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary. Communications in Partial Differential Equations. 2021;46:1058-1091.","apa":"Wang, Y., Winkler, M., & Xiang, Z. (2021). Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary. Communications in Partial Differential Equations, 46, 1058–1091."},"year":"2021","type":"journal_article","date_updated":"2023-02-01T10:25:34Z","_id":"35610","intvolume":" 46","date_created":"2023-01-09T18:00:41Z","status":"public","volume":46,"publication":"Communications in Partial Differential Equations","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"author":[{"first_name":"Yulan","full_name":"Wang, Yulan","last_name":"Wang"},{"last_name":"Winkler","id":"31496","first_name":"Michael","full_name":"Winkler, Michael"},{"full_name":"Xiang, Zhaoyin","first_name":"Zhaoyin","last_name":"Xiang"}],"user_id":"15645","title":"Local energy estimates and global solvability in a threee-dimensional chemotaxis-fluid system with prescribed signal on the boundary."},{"citation":{"bibtex":"@article{Wang_Winkler_Xiang_2021, title={Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation}, volume={10}, journal={Advances in Nonlinear Analysis}, author={Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}, year={2021}, pages={707–731} }","mla":"Wang, Yulan, et al. “Global Solvability in a Threee-Dimensional Keller-Segel.Stokes System Involving Arbitrary Superlinear Logistic Degradation.” Advances in Nonlinear Analysis, vol. 10, 2021, pp. 707–31.","apa":"Wang, Y., Winkler, M., & Xiang, Z. (2021). Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation. Advances in Nonlinear Analysis, 10, 707–731.","ama":"Wang Y, Winkler M, Xiang Z. Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation. Advances in Nonlinear Analysis. 2021;10:707-731.","chicago":"Wang, Yulan, Michael Winkler, and Zhaoyin Xiang. “Global Solvability in a Threee-Dimensional Keller-Segel.Stokes System Involving Arbitrary Superlinear Logistic Degradation.” Advances in Nonlinear Analysis 10 (2021): 707–31.","ieee":"Y. Wang, M. Winkler, and Z. Xiang, “Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation,” Advances in Nonlinear Analysis, vol. 10, pp. 707–731, 2021.","short":"Y. Wang, M. Winkler, Z. Xiang, Advances in Nonlinear Analysis 10 (2021) 707–731."},"year":"2021","type":"journal_article","page":"707-731","language":[{"iso":"eng"}],"_id":"35611","date_updated":"2023-02-01T10:27:17Z","intvolume":" 10","volume":10,"status":"public","date_created":"2023-01-09T18:03:45Z","author":[{"last_name":"Wang","full_name":"Wang, Yulan","first_name":"Yulan"},{"full_name":"Winkler, Michael","first_name":"Michael","id":"31496","last_name":"Winkler"},{"full_name":"Xiang, Zhaoyin","first_name":"Zhaoyin","last_name":"Xiang"}],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Advances in Nonlinear Analysis","title":"Global solvability in a threee-dimensional Keller-Segel.Stokes system involving arbitrary superlinear logistic degradation","user_id":"15645"},{"language":[{"iso":"eng"}],"type":"journal_article","citation":{"ama":"Tao Y, Winkler M. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete and Continuous Dynamical Systems. 2021;41(A):439-454.","apa":"Tao, Y., & Winkler, M. (2021). Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete and Continuous Dynamical Systems, 41(A), 439–454.","chicago":"Tao, Youshan, and Michael Winkler. “Critical Mass for Infinite-Time Blow-up in a Haptotaxis System with Nonlinear Zero-Order Interaction.” Discrete and Continuous Dynamical Systems 41, no. A (2021): 439–54.","bibtex":"@article{Tao_Winkler_2021, title={Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction}, volume={41}, number={A}, journal={Discrete and Continuous Dynamical Systems}, author={Tao, Youshan and Winkler, Michael}, year={2021}, pages={439–454} }","mla":"Tao, Youshan, and Michael Winkler. “Critical Mass for Infinite-Time Blow-up in a Haptotaxis System with Nonlinear Zero-Order Interaction.” Discrete and Continuous Dynamical Systems, vol. 41, no. A, 2021, pp. 439–54.","short":"Y. Tao, M. Winkler, Discrete and Continuous Dynamical Systems 41 (2021) 439–454.","ieee":"Y. Tao and M. Winkler, “Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction,” Discrete and Continuous Dynamical Systems, vol. 41, no. A, pp. 439–454, 2021."},"year":"2021","page":"439-454","_id":"35608","date_updated":"2023-02-01T10:24:15Z","intvolume":" 41","issue":"--A","author":[{"full_name":"Tao, Youshan","first_name":"Youshan","last_name":"Tao"},{"full_name":"Winkler, Michael","first_name":"Michael","id":"31496","last_name":"Winkler"}],"publication":"Discrete and Continuous Dynamical Systems","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"status":"public","date_created":"2023-01-09T17:56:44Z","volume":41,"user_id":"15645","title":"Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction"},{"publication_identifier":{"issn":["0025-5718","1088-6842"]},"publication_status":"published","department":[{"_id":"102"}],"title":"Imaginary multiquadratic number fields with class group of exponent $3$ and $5$","external_id":{"arxiv":["2004.03308v2"]},"language":[{"iso":"eng"}],"doi":"10.1090/mcom/3609","date_updated":"2023-03-06T08:57:45Z","volume":90,"status":"public","date_created":"2022-12-22T10:48:44Z","publisher":"American Mathematical Society (AMS)","author":[{"last_name":"Klüners","id":"21202","first_name":"Jürgen","full_name":"Klüners, Jürgen"},{"last_name":"Komatsu","first_name":"Toru","full_name":"Komatsu, Toru"}],"keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"publication":"Mathematics of Computation","user_id":"93826","abstract":[{"lang":"eng","text":"In this paper we obtain a complete list of imaginary n-quadratic fields with class groups of exponent 3 and 5 under ERH for every positive integer n where an n-quadratic field is a number field of degree 2ⁿ represented as the composite of n quadratic fields. "}],"citation":{"short":"J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497.","ieee":"J. Klüners and T. Komatsu, “Imaginary multiquadratic number fields with class group of exponent $3$ and $5$,” Mathematics of Computation, vol. 90, no. 329, pp. 1483–1497, 2021, doi: 10.1090/mcom/3609.","apa":"Klüners, J., & Komatsu, T. (2021). Imaginary multiquadratic number fields with class group of exponent $3$ and $5$. Mathematics of Computation, 90(329), 1483–1497. https://doi.org/10.1090/mcom/3609","ama":"Klüners J, Komatsu T. Imaginary multiquadratic number fields with class group of exponent $3$ and $5$. Mathematics of Computation. 2021;90(329):1483-1497. doi:10.1090/mcom/3609","chicago":"Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields with Class Group of Exponent $3$ and $5$.” Mathematics of Computation 90, no. 329 (2021): 1483–97. https://doi.org/10.1090/mcom/3609.","mla":"Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields with Class Group of Exponent $3$ and $5$.” Mathematics of Computation, vol. 90, no. 329, American Mathematical Society (AMS), 2021, pp. 1483–97, doi:10.1090/mcom/3609.","bibtex":"@article{Klüners_Komatsu_2021, title={Imaginary multiquadratic number fields with class group of exponent $3$ and $5$}, volume={90}, DOI={10.1090/mcom/3609}, number={329}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Komatsu, Toru}, year={2021}, pages={1483–1497} }"},"year":"2021","type":"journal_article","page":"1483-1497","issue":"329","_id":"34840","intvolume":" 90"},{"title":"Spanning the isogeny class of a power of an elliptic curve","department":[{"_id":"102"}],"publication_identifier":{"issn":["0025-5718","1088-6842"]},"publication_status":"published","date_updated":"2023-04-04T07:52:43Z","doi":"10.1090/mcom/3672","language":[{"iso":"eng"}],"abstract":[{"text":"Let E be an ordinary elliptic curve over a finite field and g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E⁹ . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our algorithms with examples of curves with many rational points over finite fields. ","lang":"eng"}],"user_id":"93826","publisher":"American Mathematical Society (AMS)","author":[{"last_name":"Kirschmer","id":"82258","first_name":"Markus","full_name":"Kirschmer, Markus"},{"last_name":"Narbonne","first_name":"Fabien","full_name":"Narbonne, Fabien"},{"full_name":"Ritzenthaler, Christophe","first_name":"Christophe","last_name":"Ritzenthaler"},{"last_name":"Robert","first_name":"Damien","full_name":"Robert, Damien"}],"publication":"Mathematics of Computation","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"volume":91,"status":"public","date_created":"2022-12-23T11:02:02Z","_id":"34912","intvolume":" 91","issue":"333","type":"journal_article","year":"2021","citation":{"short":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, D. Robert, Mathematics of Computation 91 (2021) 401–449.","ieee":"M. Kirschmer, F. Narbonne, C. Ritzenthaler, and D. Robert, “Spanning the isogeny class of a power of an elliptic curve,” Mathematics of Computation, vol. 91, no. 333, pp. 401–449, 2021, doi: 10.1090/mcom/3672.","ama":"Kirschmer M, Narbonne F, Ritzenthaler C, Robert D. Spanning the isogeny class of a power of an elliptic curve. Mathematics of Computation. 2021;91(333):401-449. doi:10.1090/mcom/3672","apa":"Kirschmer, M., Narbonne, F., Ritzenthaler, C., & Robert, D. (2021). Spanning the isogeny class of a power of an elliptic curve. Mathematics of Computation, 91(333), 401–449. https://doi.org/10.1090/mcom/3672","chicago":"Kirschmer, Markus, Fabien Narbonne, Christophe Ritzenthaler, and Damien Robert. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” Mathematics of Computation 91, no. 333 (2021): 401–49. https://doi.org/10.1090/mcom/3672.","mla":"Kirschmer, Markus, et al. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” Mathematics of Computation, vol. 91, no. 333, American Mathematical Society (AMS), 2021, pp. 401–49, doi:10.1090/mcom/3672.","bibtex":"@article{Kirschmer_Narbonne_Ritzenthaler_Robert_2021, title={Spanning the isogeny class of a power of an elliptic curve}, volume={91}, DOI={10.1090/mcom/3672}, number={333}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler, Christophe and Robert, Damien}, year={2021}, pages={401–449} }"},"page":"401-449"},{"language":[{"iso":"eng"}],"page":"1051–1109","type":"journal_article","year":"2021","citation":{"short":"I. Burban, R. Abedin, Communications in Mathematical Physics 387 (2021) 1051–1109.","ieee":"I. Burban and R. Abedin, “Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation,” Communications in Mathematical Physics, vol. 387, no. 2, pp. 1051–1109, 2021, doi: 10.1007/s00220-021-04188-7.","chicago":"Burban, Igor, and R. Abedin. “Algebraic Geometry of Lie Bialgebras Defined by Solutions of the Classical Yang-Baxter Equation.” Communications in Mathematical Physics 387, no. 2 (2021): 1051–1109. https://doi.org/10.1007/s00220-021-04188-7.","apa":"Burban, I., & Abedin, R. (2021). Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation. Communications in Mathematical Physics, 387(2), 1051–1109. https://doi.org/10.1007/s00220-021-04188-7","ama":"Burban I, Abedin R. Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation. Communications in Mathematical Physics. 2021;387(2):1051–1109. doi:10.1007/s00220-021-04188-7","bibtex":"@article{Burban_Abedin_2021, title={Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation}, volume={387}, DOI={10.1007/s00220-021-04188-7}, number={2}, journal={Communications in Mathematical Physics}, author={Burban, Igor and Abedin, R.}, year={2021}, pages={1051–1109} }","mla":"Burban, Igor, and R. Abedin. “Algebraic Geometry of Lie Bialgebras Defined by Solutions of the Classical Yang-Baxter Equation.” Communications in Mathematical Physics, vol. 387, no. 2, 2021, pp. 1051–1109, doi:10.1007/s00220-021-04188-7."},"intvolume":" 387","_id":"44329","date_updated":"2023-05-07T01:35:11Z","issue":"2","doi":"10.1007/s00220-021-04188-7","publication":"Communications in Mathematical Physics","department":[{"_id":"602"}],"author":[{"full_name":"Burban, Igor","first_name":"Igor","id":"72064","last_name":"Burban"},{"last_name":"Abedin","full_name":"Abedin, R.","first_name":"R."}],"date_created":"2023-05-02T18:36:54Z","status":"public","publication_status":"published","volume":387,"abstract":[{"text":"This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang–Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples.","lang":"eng"}],"user_id":"49063","title":"Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation"},{"publication_identifier":{"issn":["2049-6613"]},"publication_status":"published","department":[{"_id":"611"},{"_id":"97"}],"isi":"1","title":"Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review","external_id":{"isi":["000614156400001"]},"language":[{"iso":"eng"}],"doi":"10.1002/rev3.3255","date_updated":"2023-06-20T19:04:34Z","volume":9,"status":"public","date_created":"2022-12-22T09:22:46Z","quality_controlled":"1","author":[{"id":"72183","last_name":"Bruns","orcid":"https://orcid.org/0000-0002-6604-5864","full_name":"Bruns, Julia","first_name":"Julia"},{"full_name":"Gasteiger, Hedwig","first_name":"Hedwig","last_name":"Gasteiger"},{"first_name":"Carolin","full_name":"Strahl, Carolin","last_name":"Strahl"}],"publisher":"Wiley","keyword":["content knowledge","domain-specific learning","early childhood education","teacher knowledge"],"publication":"Review of Education","user_id":"49063","article_type":"review","abstract":[{"text":"The role of domain-specific content knowledge is discussed controversially for the early childhood context. Therefore, this review aims at untangling the research on domain-specific content knowledge for early childhood educators by systematically reviewing the conceptual and operational definition of and results on early childhood educators' content knowledge in different domains. Using the scientific databases ERIC, PsycInfo and Web of Sciences, we identified 36 studies on early childhood educators' domain-specific content knowledge. By comparing these studies, we found that conceptualizations of early childhood educators' content knowledge move on a continuum between a scientific related perspective and a practice related perspective. The scientific related perspective defines content knowledge as the knowledge of key concepts, facts and rules of the domain integrating knowledge taught in primary, secondary or upper secondary school. The practice related perspective includes knowledge of key concepts, facts and rules of the domain limited to the knowledge explicitly relevant for teaching in early childhood education as well as selected domain-specific knowledge of children and teaching. Our review shows that the results and implications drawn by the study authors depend on how these authors conceptualize early childhood educators' content knowledge on this continuum. Further research, therefore, needs to consider carefully how early childhood educators' content knowledge is conceptualized. The paper further discusses gaps in this research field, such as validating methods for measuring early childhood educators' content knowledge or implementing more rigorous experimental designs to examine effects of early childhood educators' content knowledge.","lang":"eng"}],"year":"2021","citation":{"ama":"Bruns J, Gasteiger H, Strahl C. Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review. Review of Education. 2021;9(2):500-538. doi:10.1002/rev3.3255","apa":"Bruns, J., Gasteiger, H., & Strahl, C. (2021). Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review. Review of Education, 9(2), 500–538. https://doi.org/10.1002/rev3.3255","chicago":"Bruns, Julia, Hedwig Gasteiger, and Carolin Strahl. “Conceptualising and Measuring Domain-Specific Content Knowledge of Early Childhood Educators: A Systematic Review.” Review of Education 9, no. 2 (2021): 500–538. https://doi.org/10.1002/rev3.3255.","mla":"Bruns, Julia, et al. “Conceptualising and Measuring Domain-Specific Content Knowledge of Early Childhood Educators: A Systematic Review.” Review of Education, vol. 9, no. 2, Wiley, 2021, pp. 500–38, doi:10.1002/rev3.3255.","bibtex":"@article{Bruns_Gasteiger_Strahl_2021, title={Conceptualising and measuring domain-specific content knowledge of early childhood educators: A systematic review}, volume={9}, DOI={10.1002/rev3.3255}, number={2}, journal={Review of Education}, publisher={Wiley}, author={Bruns, Julia and Gasteiger, Hedwig and Strahl, Carolin}, year={2021}, pages={500–538} }","short":"J. Bruns, H. Gasteiger, C. 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