[{"citation":{"bibtex":"@article{Black_Wu_2022, title={Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation}, volume={61}, DOI={<a href=\"https://doi.org/10.1007/s00526-022-02201-y\">10.1007/s00526-022-02201-y</a>}, number={396}, journal={Calculus of Variations and Partial Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Wu, Chunyan}, year={2022} }","ama":"Black T, Wu C. Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation. <i>Calculus of Variations and Partial Differential Equations</i>. 2022;61(3). doi:<a href=\"https://doi.org/10.1007/s00526-022-02201-y\">10.1007/s00526-022-02201-y</a>","mla":"Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary: Eventual Smoothness in a Chemotaxis-Navier–Stokes System with Logistic Proliferation.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 61, no. 3, 96, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s00526-022-02201-y\">10.1007/s00526-022-02201-y</a>.","chicago":"Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary: Eventual Smoothness in a Chemotaxis-Navier–Stokes System with Logistic Proliferation.” <i>Calculus of Variations and Partial Differential Equations</i> 61, no. 3 (2022). <a href=\"https://doi.org/10.1007/s00526-022-02201-y\">https://doi.org/10.1007/s00526-022-02201-y</a>.","short":"T. Black, C. Wu, Calculus of Variations and Partial Differential Equations 61 (2022).","ieee":"T. Black and C. Wu, “Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 61, no. 3, Art. no. 96, 2022, doi: <a href=\"https://doi.org/10.1007/s00526-022-02201-y\">10.1007/s00526-022-02201-y</a>.","apa":"Black, T., &#38; Wu, C. (2022). Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation. <i>Calculus of Variations and Partial Differential Equations</i>, <i>61</i>(3), Article 96. <a href=\"https://doi.org/10.1007/s00526-022-02201-y\">https://doi.org/10.1007/s00526-022-02201-y</a>"},"status":"public","user_id":"23686","volume":61,"publisher":"Springer Science and Business Media LLC","_id":"34677","issue":"3","publication":"Calculus of Variations and Partial Differential Equations","keyword":["Applied Mathematics","Analysis"],"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2022-12-21T09:50:59Z","date_updated":"2023-07-10T11:37:27Z","publication_status":"published","intvolume":"        61","title":"Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation","year":"2022","publication_identifier":{"issn":["0944-2669","1432-0835"]},"author":[{"id":"23686","orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias","full_name":"Black, Tobias"},{"first_name":"Chunyan","last_name":"Wu","full_name":"Wu, Chunyan"}],"doi":"10.1007/s00526-022-02201-y","article_number":"96","language":[{"iso":"eng"}]},{"doi":"10.3934/jgm.2022014","language":[{"iso":"eng"}],"date_updated":"2023-08-10T08:44:55Z","publication_status":"published","intvolume":"        14","article_type":"original","year":"2022","title":"Backward error analysis for variational discretisations of partial  differential equations","author":[{"full_name":"McLachlan, Robert I","first_name":"Robert I","last_name":"McLachlan"},{"id":"85279","full_name":"Offen, Christian","orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"}],"type":"journal_article","department":[{"_id":"636"}],"file":[{"creator":"coffen","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.","date_created":"2022-06-13T09:11:38Z","date_updated":"2022-06-13T09:11:38Z","relation":"main_file","file_size":1507248,"access_level":"open_access","file_name":"2_BlendedBEASymmPDE.pdf","title":"Backward error analysis for variational discretisations of PDEs","content_type":"application/pdf","file_id":"31859"}],"date_created":"2020-10-06T16:33:19Z","abstract":[{"lang":"eng","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."}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/multisymplectic"}]},"issue":"3","publication":"Journal of Geometric Mechanics","ddc":["510"],"user_id":"85279","volume":14,"page":"447 - 471","_id":"19941","publisher":"AIMS","has_accepted_license":"1","status":"public","oa":"1","external_id":{"arxiv":["2006.14172"]},"file_date_updated":"2022-06-13T09:11:38Z","citation":{"short":"R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471.","chicago":"McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i> 14, no. 3 (2022): 447–71. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>.","ieee":"R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations of partial  differential equations,” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, pp. 447–471, 2022, doi: <a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","apa":"McLachlan, R. I., &#38; Offen, C. (2022). Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>, <i>14</i>(3), 447–471. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>","bibtex":"@article{McLachlan_Offen_2022, title={Backward error analysis for variational discretisations of partial  differential equations}, volume={14}, DOI={<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>}, number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan, Robert I and Offen, Christian}, year={2022}, pages={447–471} }","ama":"McLachlan RI, Offen C. Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>. 2022;14(3):447-471. doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>","mla":"McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>."}},{"oa":"1","external_id":{"arxiv":["2108.02492"]},"quality_controlled":"1","file_date_updated":"2021-12-13T14:56:15Z","citation":{"bibtex":"@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned Hamiltonian systems}, volume={32(1)}, DOI={<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i> 32(1) (2022). <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>.","short":"C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022).","ama":"Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. 2022;32(1). doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>","ieee":"C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian systems,” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), 2022, doi: <a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2022). Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, <i>32(1)</i>. <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), AIP, 2022, doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>."},"user_id":"85279","ddc":["510"],"volume":"32(1)","publisher":"AIP","_id":"23382","has_accepted_license":"1","status":"public","type":"journal_article","department":[{"_id":"636"}],"file":[{"creator":"coffen","date_created":"2021-12-13T14:56:15Z","relation":"main_file","date_updated":"2021-12-13T14:56:15Z","file_name":"SymplecticShadowIntegration_AIP.pdf","access_level":"open_access","file_size":2285059,"file_id":"28734","content_type":"application/pdf"}],"date_created":"2021-08-11T08:24:02Z","related_material":{"link":[{"url":"https://github.com/Christian-Offen/symplectic-shadow-integration","relation":"software","description":"GitHub"}]},"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."}],"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","doi":"10.1063/5.0065913","main_file_link":[{"url":"https://aip.scitation.org/doi/abs/10.1063/5.0065913","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-08-10T08:48:14Z","article_type":"original","title":"Symplectic integration of learned Hamiltonian systems","year":"2022","author":[{"id":"85279","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"}]},{"publication":"Beiträge zum Mathematikunterricht","citation":{"chicago":"Dröse, Jennifer. “Verstehensgrundlagen Diagnostizieren - Diagnostisches Denken von Drei Professionalisierungsgruppen.” In <i>Beiträge Zum Mathematikunterricht</i>, 2022.","short":"J. Dröse, in: Beiträge Zum Mathematikunterricht, 2022.","ieee":"J. Dröse, “Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen,” 2022.","apa":"Dröse, J. (2022). Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen. <i>Beiträge Zum Mathematikunterricht</i>.","bibtex":"@inproceedings{Dröse_2022, title={Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen}, booktitle={Beiträge zum Mathematikunterricht}, author={Dröse, Jennifer}, year={2022} }","ama":"Dröse J. Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen. In: <i>Beiträge Zum Mathematikunterricht</i>. ; 2022.","mla":"Dröse, Jennifer. “Verstehensgrundlagen Diagnostizieren - Diagnostisches Denken von Drei Professionalisierungsgruppen.” <i>Beiträge Zum Mathematikunterricht</i>, 2022."},"type":"conference","department":[{"_id":"98"}],"date_created":"2023-01-27T19:00:01Z","date_updated":"2023-08-15T06:04:03Z","status":"public","title":"Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen","year":"2022","author":[{"id":"85820","first_name":"Jennifer","last_name":"Dröse","full_name":"Dröse, Jennifer"}],"user_id":"85820","_id":"40613","language":[{"iso":"eng"}]},{"type":"conference","department":[{"_id":"543"}],"date_created":"2023-09-27T10:01:52Z","publication":"Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","citation":{"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. <i>Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>. ; 2022:773-776.","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} }","mla":"Graf, Lara Marie, et al. “Lernwege von Fachfremd Unterrichtenden Lehrkräften Zur Ablösung Vom Zählenden Rechnen.” <i>Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>, edited by IDMI-Primar Goethe-Universität Frankfurt, 2022, pp. 773–76.","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.","chicago":"Graf, Lara Marie, Uta Häsel-Weide, Marcus Nührenbörger, and Karina Höveler. “Lernwege von Fachfremd Unterrichtenden Lehrkräften Zur Ablösung Vom Zählenden Rechnen.” In <i>Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>, edited by IDMI-Primar Goethe-Universität Frankfurt, 773–76, 2022.","apa":"Graf, L. M., Häsel-Weide, U., Nührenbörger, M., &#38; Höveler, K. (2022). Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), <i>Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i> (pp. 773–776).","ieee":"L. M. Graf, U. Häsel-Weide, M. Nührenbörger, and K. Höveler, “Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen,” in <i>Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, Frankfurt am Main, 2022, pp. 773–776."},"user_id":"44184","page":"773-776","language":[{"iso":"eng"}],"_id":"47520","date_updated":"2023-09-27T10:02:12Z","status":"public","year":"2022","title":"Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen","author":[{"id":"89837","last_name":"Graf","first_name":"Lara Marie","full_name":"Graf, Lara Marie"},{"id":"60267","first_name":"Uta","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta"},{"first_name":"Marcus","last_name":"Nührenbörger","full_name":"Nührenbörger, Marcus"},{"full_name":"Höveler, Karina","last_name":"Höveler","first_name":"Karina"}],"corporate_editor":["IDMI-Primar Goethe-Universität Frankfurt"],"conference":{"end_date":"02.09.2022","name":"56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","start_date":"29.08.2022","location":"Frankfurt am Main"}},{"citation":{"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} }","ama":"Schwerin I. Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis. In: IDMI-Primar Goethe-Universität Frankfurt, ed. <i>Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>. ; 2022:401-404.","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.","chicago":"Schwerin, Imke. “Verdoppeln Und Halbieren Im 2. Schuljahr - Vorgehensweisen Und Verständnis.” In <i>Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>, edited by IDMI-Primar Goethe-Universität Frankfurt, 401–4, 2022.","ieee":"I. Schwerin, “Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis,” in <i>Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, Frankfurt am Main, 2022, pp. 401–404.","apa":"Schwerin, I. (2022). Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), <i>Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i> (pp. 401–404).","mla":"Schwerin, Imke. “Verdoppeln Und Halbieren Im 2. Schuljahr - Vorgehensweisen Und Verständnis.” <i>Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>, edited by IDMI-Primar Goethe-Universität Frankfurt, 2022, pp. 401–04."},"publication":"Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","date_created":"2023-09-27T09:53:36Z","department":[{"_id":"543"}],"type":"conference","conference":{"name":"56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","start_date":"29.08.2022","location":"Frankfurt am Main","end_date":"02.09.2022"},"author":[{"id":"48912","last_name":"Schwerin","first_name":"Imke","full_name":"Schwerin, Imke"}],"corporate_editor":["IDMI-Primar Goethe-Universität Frankfurt"],"status":"public","title":"Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis","year":"2022","date_updated":"2023-09-27T09:54:00Z","language":[{"iso":"eng"}],"_id":"47519","page":"401-404","user_id":"44184"},{"place":"Berlin, Heidelberg","date_created":"2024-09-23T08:51:39Z","type":"book_chapter","department":[{"_id":"363"}],"publication":"Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik","citation":{"apa":"Biehler, R., &#38; Hoffmann, M. (2022). Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium. In <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">https://doi.org/10.1007/978-3-662-63948-1_4</a>","mla":"Biehler, Rolf, and Max Hoffmann. “Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium.” <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>, Springer Berlin Heidelberg, 2022, doi:<a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>.","ieee":"R. Biehler and M. Hoffmann, “Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium,” in <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>, Berlin, Heidelberg: Springer Berlin Heidelberg, 2022.","chicago":"Biehler, Rolf, and Max Hoffmann. “Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium.” In <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. <a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">https://doi.org/10.1007/978-3-662-63948-1_4</a>.","short":"R. Biehler, M. Hoffmann, in: Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, Springer Berlin Heidelberg, Berlin, Heidelberg, 2022.","ama":"Biehler R, Hoffmann M. Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium. In: <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Springer Berlin Heidelberg; 2022. doi:<a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>","bibtex":"@inbook{Biehler_Hoffmann_2022, place={Berlin, Heidelberg}, title={Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>}, booktitle={Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}, publisher={Springer Berlin Heidelberg}, author={Biehler, Rolf and Hoffmann, Max}, year={2022} }"},"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-662-63948-1_4"}],"language":[{"iso":"ger"}],"_id":"56201","publisher":"Springer Berlin Heidelberg","doi":"10.1007/978-3-662-63948-1_4","user_id":"37888","title":"Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium","year":"2022","status":"public","author":[{"id":"16274","last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf"},{"full_name":"Hoffmann, Max","first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","id":"32202"}],"publication_identifier":{"isbn":["9783662639474","9783662639481"],"issn":["2197-8751","2197-876X"]},"date_updated":"2024-09-25T08:26:46Z","publication_status":"published"},{"date_created":"2024-09-23T08:54:03Z","place":"Wiesbaden","type":"book_chapter","department":[{"_id":"363"}],"publication":"Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik","citation":{"ieee":"M. Hoffmann and R. Biehler, “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik – Aufgabenbeispiel und Ergebnisse einer Evaluationsstudie,” in <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>, Wiesbaden: Springer Fachmedien Wiesbaden, 2022.","apa":"Hoffmann, M., &#38; Biehler, R. (2022). Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik – Aufgabenbeispiel und Ergebnisse einer Evaluationsstudie. In <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Springer Fachmedien Wiesbaden. <a href=\"https://doi.org/10.1007/978-3-658-34067-4_20\">https://doi.org/10.1007/978-3-658-34067-4_20</a>","chicago":"Hoffmann, Max, and Rolf Biehler. “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik – Aufgabenbeispiel und Ergebnisse einer Evaluationsstudie.” In <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. <a href=\"https://doi.org/10.1007/978-3-658-34067-4_20\">https://doi.org/10.1007/978-3-658-34067-4_20</a>.","short":"M. Hoffmann, R. Biehler, in: Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, Springer Fachmedien Wiesbaden, Wiesbaden, 2022.","mla":"Hoffmann, Max, and Rolf Biehler. “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik – Aufgabenbeispiel und Ergebnisse einer Evaluationsstudie.” <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>, Springer Fachmedien Wiesbaden, 2022, doi:<a href=\"https://doi.org/10.1007/978-3-658-34067-4_20\">10.1007/978-3-658-34067-4_20</a>.","bibtex":"@inbook{Hoffmann_Biehler_2022, place={Wiesbaden}, title={Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik – Aufgabenbeispiel und Ergebnisse einer Evaluationsstudie}, DOI={<a href=\"https://doi.org/10.1007/978-3-658-34067-4_20\">10.1007/978-3-658-34067-4_20</a>}, booktitle={Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}, publisher={Springer Fachmedien Wiesbaden}, author={Hoffmann, Max and Biehler, Rolf}, year={2022} }","ama":"Hoffmann M, Biehler R. Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik – Aufgabenbeispiel und Ergebnisse einer Evaluationsstudie. In: <i>Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. Springer Fachmedien Wiesbaden; 2022. doi:<a href=\"https://doi.org/10.1007/978-3-658-34067-4_20\">10.1007/978-3-658-34067-4_20</a>"},"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-658-34067-4_20"}],"language":[{"iso":"ger"}],"_id":"56203","publisher":"Springer Fachmedien Wiesbaden","user_id":"37888","doi":"10.1007/978-3-658-34067-4_20","status":"public","year":"2022","title":"Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik – Aufgabenbeispiel und Ergebnisse einer Evaluationsstudie","author":[{"full_name":"Hoffmann, Max","first_name":"Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","id":"32202"},{"id":"16274","full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"}],"publication_identifier":{"issn":["2197-8751","2197-876X"],"isbn":["9783658340667","9783658340674"]},"publication_status":"published","date_updated":"2024-09-25T08:27:00Z"},{"date_updated":"2024-09-25T08:29:42Z","publication_status":"published","status":"public","year":"2022","title":"Civic Statistics for Prospective Teachers: Developing Content and Pedagogical Content Knowledge Through Project Work","author":[{"id":"30619","full_name":"Podworny, Susanne","first_name":"Susanne","orcid":"0000-0002-6313-5987","last_name":"Podworny"},{"full_name":"Frischemeier, Daniel","last_name":"Frischemeier","first_name":"Daniel"},{"full_name":"Biehler, Rolf","last_name":"Biehler","first_name":"Rolf","id":"16274"}],"publication_identifier":{"isbn":["9783031207471","9783031207488"]},"doi":"10.1007/978-3-031-20748-8_15","user_id":"37888","main_file_link":[{"url":"https://doi.org/10.1007/978-3-031-20748-8_15"}],"language":[{"iso":"eng"}],"_id":"43231","publisher":"Springer International Publishing","publication":"Statistics for Empowerment and Social Engagement","citation":{"chicago":"Podworny, Susanne, Daniel Frischemeier, and Rolf Biehler. “Civic Statistics for Prospective Teachers: Developing Content and Pedagogical Content Knowledge Through Project Work.” In <i>Statistics for Empowerment and Social Engagement</i>. 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(2022). Data Visualization Packages for Non-inferential Civic Statistics in High School Classrooms. In <i>Statistics for Empowerment and Social Engagement</i> (pp. 199–236). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-20748-8_9\">https://doi.org/10.1007/978-3-031-20748-8_9</a>","mla":"Frischemeier, Daniel, et al. “Data Visualization Packages for Non-Inferential Civic Statistics in High School Classrooms.” <i>Statistics for Empowerment and Social Engagement</i>, Springer International Publishing, 2022, pp. 199–236, doi:<a href=\"https://doi.org/10.1007/978-3-031-20748-8_9\">10.1007/978-3-031-20748-8_9</a>.","ieee":"D. Frischemeier, S. Podworny, and R. Biehler, “Data Visualization Packages for Non-inferential Civic Statistics in High School Classrooms,” in <i>Statistics for Empowerment and Social Engagement</i>, Cham: Springer International Publishing, 2022, pp. 199–236.","ama":"Frischemeier D, Podworny S, Biehler R. Data Visualization Packages for Non-inferential Civic Statistics in High School Classrooms. In: <i>Statistics for Empowerment and Social Engagement</i>. Springer International Publishing; 2022:199-236. doi:<a href=\"https://doi.org/10.1007/978-3-031-20748-8_9\">10.1007/978-3-031-20748-8_9</a>","short":"D. Frischemeier, S. Podworny, R. Biehler, in: Statistics for Empowerment and Social Engagement, Springer International Publishing, Cham, 2022, pp. 199–236.","chicago":"Frischemeier, Daniel, Susanne Podworny, and Rolf Biehler. “Data Visualization Packages for Non-Inferential Civic Statistics in High School Classrooms.” In <i>Statistics for Empowerment and Social Engagement</i>, 199–236. 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Liebendörfer <i>et al.</i>, “Enriching videos with interactive questions to enhance students’ cognitive activity: concept and implementation,” presented at the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Bozen-Bolzano, Italy, 2022.","apa":"Liebendörfer, M., Profeta, A., Krämer, S., Schlüter, S., Becher, S., Biehler, R., Mai, T., &#38; Schmitz, A. (2022). <i>Enriching videos with interactive questions to enhance students’ cognitive activity: concept and implementation</i>. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Bozen-Bolzano, Italy.","short":"M. Liebendörfer, A. Profeta, S. Krämer, S. Schlüter, S. Becher, R. Biehler, T. Mai, A. 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Enriching videos with interactive questions to enhance students’ cognitive activity: concept and implementation. 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Podworny, F.Y. Fleischer, D. Stroop, R. Biehler, in: 2022.","chicago":"Podworny, Susanne, Franz Yannik Fleischer, Dietlinde Stroop, and Rolf Biehler. “An Example of Rich, Real and Multivariate Survey Data for Use in School,” 2022.","ieee":"S. Podworny, F. Y. Fleischer, D. Stroop, and R. Biehler, “An example of rich, real and multivariate survey data for use in school,” presented at the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Bozen-Bolzano, Italy, 2022.","apa":"Podworny, S., Fleischer, F. Y., Stroop, D., &#38; Biehler, R. (2022). <i>An example of rich, real and multivariate survey data for use in school</i>. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Bozen-Bolzano, Italy.","bibtex":"@inproceedings{Podworny_Fleischer_Stroop_Biehler_2022, title={An example of rich, real and multivariate survey data for use in school}, author={Podworny, Susanne and Fleischer, Franz Yannik and Stroop, Dietlinde and Biehler, Rolf}, year={2022} }","ama":"Podworny S, Fleischer FY, Stroop D, Biehler R. An example of rich, real and multivariate survey data for use in school. In: ; 2022.","mla":"Podworny, Susanne, et al. <i>An Example of Rich, Real and Multivariate Survey Data for Use in School</i>. 2022."},"main_file_link":[{"url":"https://hal.archives-ouvertes.fr/hal-03751842"}],"_id":"39064","language":[{"iso":"eng"}],"user_id":"37888","title":"An example of rich, real and multivariate survey data for use in school","status":"public","year":"2022","author":[{"full_name":"Podworny, Susanne","last_name":"Podworny","first_name":"Susanne","orcid":"0000-0002-6313-5987","id":"30619"},{"id":"42660","full_name":"Fleischer, Franz Yannik","orcid":"https://orcid.org/0000-0003-0318-0329","last_name":"Fleischer","first_name":"Franz Yannik"},{"full_name":"Stroop, Dietlinde","first_name":"Dietlinde","last_name":"Stroop"},{"id":"16274","full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"}],"conference":{"start_date":"2022-02-02","name":"Twelfth Congress of the European Society for Research in Mathematics Education (CERME12)","location":"Bozen-Bolzano, Italy","end_date":"2022-02-06"},"date_updated":"2024-09-25T08:29:28Z"},{"_id":"56251","publisher":"International Association for Statistical Education","user_id":"37888","ddc":["510"],"status":"public","has_accepted_license":"1","file_date_updated":"2024-11-12T10:58:48Z","citation":{"chicago":"Frischemeier, Daniel, and Rolf Biehler. “Design of a Teaching Unit to Develop Primary School Students ́ Reasoning about Uncertainty in Multi-Step Chance Experiments.” In <i>Decision Making Based on Data Proceedings IASE 2019 Satellite Conference</i>. International Association for Statistical Education, 2022. <a href=\"https://doi.org/10.52041/srap.19304\">https://doi.org/10.52041/srap.19304</a>.","short":"D. Frischemeier, R. Biehler, in: Decision Making Based on Data Proceedings IASE 2019 Satellite Conference, International Association for Statistical Education, 2022.","ieee":"D. Frischemeier and R. Biehler, “Design of a teaching unit to develop primary school students ́ reasoning about uncertainty in multi-step chance experiments,” 2022, doi: <a href=\"https://doi.org/10.52041/srap.19304\">10.52041/srap.19304</a>.","apa":"Frischemeier, D., &#38; Biehler, R. (2022). Design of a teaching unit to develop primary school students ́ reasoning about uncertainty in multi-step chance experiments. <i>Decision Making Based on Data Proceedings IASE 2019 Satellite Conference</i>. <a href=\"https://doi.org/10.52041/srap.19304\">https://doi.org/10.52041/srap.19304</a>","bibtex":"@inproceedings{Frischemeier_Biehler_2022, title={Design of a teaching unit to develop primary school students ́ reasoning about uncertainty in multi-step chance experiments}, DOI={<a href=\"https://doi.org/10.52041/srap.19304\">10.52041/srap.19304</a>}, booktitle={Decision Making Based on Data Proceedings IASE 2019 Satellite Conference}, publisher={International Association for Statistical Education}, author={Frischemeier, Daniel and Biehler, Rolf}, year={2022} }","ama":"Frischemeier D, Biehler R. Design of a teaching unit to develop primary school students ́ reasoning about uncertainty in multi-step chance experiments. In: <i>Decision Making Based on Data Proceedings IASE 2019 Satellite Conference</i>. International Association for Statistical Education; 2022. doi:<a href=\"https://doi.org/10.52041/srap.19304\">10.52041/srap.19304</a>","mla":"Frischemeier, Daniel, and Rolf Biehler. “Design of a Teaching Unit to Develop Primary School Students ́ Reasoning about Uncertainty in Multi-Step Chance Experiments.” <i>Decision Making Based on Data Proceedings IASE 2019 Satellite Conference</i>, International Association for Statistical Education, 2022, doi:<a href=\"https://doi.org/10.52041/srap.19304\">10.52041/srap.19304</a>."},"main_file_link":[{"url":"https://www.academia.edu/download/114249671/srap.pdf"}],"language":[{"iso":"eng"}],"doi":"10.52041/srap.19304","year":"2022","title":"Design of a teaching unit to develop primary school students ́ reasoning about uncertainty in multi-step chance experiments","author":[{"full_name":"Frischemeier, Daniel","last_name":"Frischemeier","first_name":"Daniel"},{"full_name":"Biehler, Rolf","last_name":"Biehler","first_name":"Rolf","id":"16274"}],"publication_status":"published","date_updated":"2024-11-12T10:59:05Z","file":[{"file_id":"56996","content_type":"application/pdf","success":1,"file_name":"IASE2019_Satellite_136_FRISCHEM-2.pdf","access_level":"closed","file_size":877055,"relation":"main_file","date_updated":"2024-11-12T10:58:48Z","date_created":"2024-11-12T10:58:48Z","creator":"krueter"}],"date_created":"2024-09-25T08:33:33Z","type":"conference","department":[{"_id":"363"}],"publication":"Decision Making Based on Data Proceedings IASE 2019 Satellite Conference","abstract":[{"text":"<jats:p>Statistical reasoning and the confrontation with first ideas of uncertainty can already be enhanced in primary school. A challenge is how to relate theoretical-combinatorial aspects to empirical frequency aspects, given that fraction concepts are usually not available at primary school. In the frame of a Design Based Research approach we have designed and realized a teaching sequence consisting of seven lessons to develop statistical reasoning about uncertainty of grade 4 students (age 10-11). To supervise their learning processes we collected data on different levels: (a) written pre/post-tests, (b) working notes after each lesson and (c) interviews after the teaching unit. In this paper we will mainly present the design of teaching unit and first results from the analysis of pre- and posttests.</jats:p>","lang":"eng"}]},{"file":[{"success":1,"content_type":"application/pdf","file_id":"64269","date_updated":"2026-02-19T13:17:23Z","relation":"main_file","access_level":"closed","file_size":1510358,"file_name":"HabilitatieThesis.pdf","date_created":"2026-02-19T13:17:23Z","creator":"jobkuit"}],"date_created":"2026-02-19T13:18:11Z","type":"habilitation","department":[{"_id":"10"}],"file_date_updated":"2026-02-19T13:17:23Z","citation":{"ieee":"J. Kuit, <i>Plancherel theory on real spherical spaces</i>. 2022.","apa":"Kuit, J. (2022). <i>Plancherel theory on real spherical spaces</i>.","mla":"Kuit, Job. <i>Plancherel Theory on Real Spherical Spaces</i>. 2022.","bibtex":"@book{Kuit_2022, title={Plancherel theory on real spherical spaces}, author={Kuit, Job}, year={2022} }","short":"J. 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Olbrich, G. Palmirotta, Annals of Global Analysis and Geometry 63 (2022).","chicago":"Olbrich, Martin, and Guendalina Palmirotta. “Delorme’s Intertwining Conditions for Sections of Homogeneous Vector Bundles on Two- and Three-Dimensional Hyperbolic Spaces.” <i>Annals of Global Analysis and Geometry</i> 63, no. 1 (2022). <a href=\"https://doi.org/10.1007/s10455-022-09882-w\">https://doi.org/10.1007/s10455-022-09882-w</a>.","apa":"Olbrich, M., &#38; Palmirotta, G. (2022). Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces. <i>Annals of Global Analysis and Geometry</i>, <i>63</i>(1), Article 9. <a href=\"https://doi.org/10.1007/s10455-022-09882-w\">https://doi.org/10.1007/s10455-022-09882-w</a>","ieee":"M. Olbrich and G. 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Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces. <i>Annals of Global Analysis and Geometry</i>. 2022;63(1). doi:<a href=\"https://doi.org/10.1007/s10455-022-09882-w\">10.1007/s10455-022-09882-w</a>","bibtex":"@article{Olbrich_Palmirotta_2022, title={Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces}, volume={63}, DOI={<a href=\"https://doi.org/10.1007/s10455-022-09882-w\">10.1007/s10455-022-09882-w</a>}, number={19}, journal={Annals of Global Analysis and Geometry}, publisher={Springer Science and Business Media LLC}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2022} }","mla":"Olbrich, Martin, and Guendalina Palmirotta. “Delorme’s Intertwining Conditions for Sections of Homogeneous Vector Bundles on Two- and Three-Dimensional Hyperbolic Spaces.” <i>Annals of Global Analysis and Geometry</i>, vol. 63, no. 1, 9, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10455-022-09882-w\">10.1007/s10455-022-09882-w</a>."}},{"abstract":[{"lang":"eng","text":"We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type $X = G/K$. We prove a characterisation of their range. In fact, from Delorme's Paley-Wiener theorem for compactly supported smooth functions on a real reductive group of Harish-Chandra class, we deduce topological Paley-Wiener and Paley-Wiener-Schwartz theorems for sections."}],"extern":"1","issue":"2","publication":"Journal of Lie theory","department":[{"_id":"10"},{"_id":"548"}],"type":"journal_article","date_created":"2026-02-20T20:04:49Z","intvolume":"        34","date_updated":"2026-02-20T20:07:31Z","publication_status":"published","author":[{"full_name":"Olbrich, Martin","last_name":"Olbrich","first_name":"Martin"},{"id":"109467","last_name":"Palmirotta","first_name":"Guendalina","full_name":"Palmirotta, Guendalina"}],"title":"A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$","year":"2022","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Olbrich_Palmirotta_2022, title={A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$}, volume={34}, number={2}, journal={Journal of Lie theory}, publisher={Heldermann Verlag}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2022}, pages={53--384} }","ama":"Olbrich M, Palmirotta G. 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