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The Dunkl-Laplace transform and Macdonald’s hypergeometric series. <i>Transactions of the American Mathematical Society</i>. 2023;376(4):2419-2447. doi:<a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>","mla":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” <i>Transactions of the American Mathematical Society</i>, vol. 376, no. 4,  American Mathematical Society, 2023, pp. 2419–47, doi:<a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>.","short":"D. Brennecken, M. Rösler, Transactions of the American Mathematical Society 376 (2023) 2419–2447.","chicago":"Brennecken, Dominik, and Margit Rösler. “The Dunkl-Laplace Transform and Macdonald’s Hypergeometric Series.” <i>Transactions of the American Mathematical Society</i> 376, no. 4 (2023): 2419–47. <a href=\"https://doi.org/10.1090/tran/8860\">https://doi.org/10.1090/tran/8860</a>.","ieee":"D. Brennecken and M. Rösler, “The Dunkl-Laplace transform and Macdonald’s hypergeometric series,” <i>Transactions of the American Mathematical Society</i>, vol. 376, no. 4, pp. 2419–2447, 2023, doi: <a href=\"https://doi.org/10.1090/tran/8860\">10.1090/tran/8860</a>.","apa":"Brennecken, D., &#38; Rösler, M. (2023). The Dunkl-Laplace transform and Macdonald’s hypergeometric series. <i>Transactions of the American Mathematical Society</i>, <i>376</i>(4), 2419–2447. <a href=\"https://doi.org/10.1090/tran/8860\">https://doi.org/10.1090/tran/8860</a>"}},{"editor":[{"last_name":"IDMI Primar Goethe-Univeristät Frankfurt","first_name":".","full_name":"IDMI Primar Goethe-Univeristät Frankfurt, ."}],"doi":"https://doi.org/10.37626/GA9783959872089.0","user_id":"85819","_id":"53053","language":[{"iso":"eng"}],"publisher":"WTM","date_updated":"2024-04-26T08:13:52Z","conference":{"name":"56. Jahrestagung der Gesellschaft für Didaktik der Mathematik","location":"Frankfurt am Main"},"author":[{"id":"85819","last_name":"Kolbe","first_name":"Tim","full_name":"Kolbe, Tim"}],"year":"2023","title":"Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung","status":"public","department":[{"_id":"98"}],"type":"conference_abstract","date_created":"2024-03-27T09:29:20Z","citation":{"short":"T. Kolbe, in: . IDMI Primar Goethe-Univeristät Frankfurt (Ed.), Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, WTM, 2023.","chicago":"Kolbe, Tim. “Think-Aloud Beim Hochschulischen Mathematiklernen – Ergebnisse Einer Pilotierung.” In <i>Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>, edited by . IDMI Primar Goethe-Univeristät Frankfurt. WTM, 2023. <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>.","apa":"Kolbe, T. (2023). Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung. In . IDMI Primar Goethe-Univeristät Frankfurt (Ed.), <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>. WTM. <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>","ieee":"T. Kolbe, “Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung,” in <i>Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik</i>, Frankfurt am Main, 2023, doi: <a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>.","ama":"Kolbe T. Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung. In: IDMI Primar Goethe-Univeristät Frankfurt ., ed. <i>Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>. WTM; 2023. doi:<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>","bibtex":"@inproceedings{Kolbe_2023, title={Think-aloud beim hochschulischen Mathematiklernen – Ergebnisse einer Pilotierung}, DOI={<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>}, booktitle={Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, publisher={WTM}, author={Kolbe, Tim}, editor={IDMI Primar Goethe-Univeristät Frankfurt, .}, year={2023} }","mla":"Kolbe, Tim. “Think-Aloud Beim Hochschulischen Mathematiklernen – Ergebnisse Einer Pilotierung.” <i>Beiträge Zum Mathematikunterricht 2022. 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik</i>, edited by . IDMI Primar Goethe-Univeristät Frankfurt, WTM, 2023, doi:<a href=\"https://doi.org/10.37626/GA9783959872089.0\">https://doi.org/10.37626/GA9783959872089.0</a>."},"publication":"Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik"},{"date_updated":"2024-04-30T13:43:22Z","publication_status":"published","status":"public","year":"2023","title":"Characterizing external visualization in mathematics education research: a scoping review","publication_identifier":{"issn":["1863-9690","1863-9704"]},"author":[{"full_name":"Schoenherr, Johanna","first_name":"Johanna","last_name":"Schoenherr"},{"first_name":"Stanislaw","last_name":"Schukajlow","full_name":"Schukajlow, Stanislaw"}],"doi":"10.1007/s11858-023-01494-3","user_id":"99409","_id":"46569","publisher":"Springer Science and Business Media LLC","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to characterize external visualizations in recent mathematics education research in order to develop a common ground and guide future research. A qualitative content analysis of the full texts of 130 studies published between 2018 and 2022 applied a deductive-inductive coding procedure to assess four dimensions: visualization product or process, type of visualization, media, and purpose. The analysis revealed different types of external visualizations including visualizations with physical resemblance ranging from pictorial to abstract visualizations as well as three types of visualizations with structural resemblance: length, area, and relational visualizations. Future research should include measures of visualization products or processes to help explain the demands and affordances that different types of visualizations present to learners and teachers.</jats:p>","lang":"eng"}],"publication":"ZDM – Mathematics Education","citation":{"ama":"Schoenherr J, Schukajlow S. Characterizing external visualization in mathematics education research: a scoping review. <i>ZDM – Mathematics Education</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s11858-023-01494-3\">10.1007/s11858-023-01494-3</a>","bibtex":"@article{Schoenherr_Schukajlow_2023, title={Characterizing external visualization in mathematics education research: a scoping review}, DOI={<a href=\"https://doi.org/10.1007/s11858-023-01494-3\">10.1007/s11858-023-01494-3</a>}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Schoenherr, Johanna and Schukajlow, Stanislaw}, year={2023} }","mla":"Schoenherr, Johanna, and Stanislaw Schukajlow. “Characterizing External Visualization in Mathematics Education Research: A Scoping Review.” <i>ZDM – Mathematics Education</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s11858-023-01494-3\">10.1007/s11858-023-01494-3</a>.","chicago":"Schoenherr, Johanna, and Stanislaw Schukajlow. “Characterizing External Visualization in Mathematics Education Research: A Scoping Review.” <i>ZDM – Mathematics Education</i>, 2023. <a href=\"https://doi.org/10.1007/s11858-023-01494-3\">https://doi.org/10.1007/s11858-023-01494-3</a>.","short":"J. Schoenherr, S. Schukajlow, ZDM – Mathematics Education (2023).","apa":"Schoenherr, J., &#38; Schukajlow, S. (2023). Characterizing external visualization in mathematics education research: a scoping review. <i>ZDM – Mathematics Education</i>. <a href=\"https://doi.org/10.1007/s11858-023-01494-3\">https://doi.org/10.1007/s11858-023-01494-3</a>","ieee":"J. Schoenherr and S. Schukajlow, “Characterizing external visualization in mathematics education research: a scoping review,” <i>ZDM – Mathematics Education</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s11858-023-01494-3\">10.1007/s11858-023-01494-3</a>."},"type":"journal_article","keyword":["General Mathematics","Education"],"department":[{"_id":"913"}],"date_created":"2023-08-17T10:11:45Z"},{"publication":"Mathematical Proceedings of the Cambridge Philosophical Society","issue":"1","department":[{"_id":"100"}],"type":"journal_article","keyword":["General Mathematics"],"date_created":"2024-04-17T12:23:18Z","intvolume":"       175","date_updated":"2024-05-07T08:29:59Z","publication_status":"published","publication_identifier":{"issn":["0305-0041","1469-8064"]},"author":[{"first_name":"Alena","last_name":"Ernst","full_name":"Ernst, Alena","id":"46953"},{"last_name":"Schmidt","first_name":"Kai-Uwe","full_name":"Schmidt, Kai-Uwe"}],"year":"2023","title":"Intersection theorems for finite general linear groups","doi":"10.1017/s0305004123000075","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Ernst_Schmidt_2023, title={Intersection theorems for finite general linear groups}, volume={175}, DOI={<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Ernst, Alena and Schmidt, Kai-Uwe}, year={2023}, pages={129–160} }","ama":"Ernst A, Schmidt K-U. Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2023;175(1):129-160. doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>","mla":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, Cambridge University Press (CUP), 2023, pp. 129–60, doi:<a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","chicago":"Ernst, Alena, and Kai-Uwe Schmidt. “Intersection Theorems for Finite General Linear Groups.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i> 175, no. 1 (2023): 129–60. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>.","short":"A. Ernst, K.-U. Schmidt, Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023) 129–160.","ieee":"A. Ernst and K.-U. Schmidt, “Intersection theorems for finite general linear groups,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 175, no. 1, pp. 129–160, 2023, doi: <a href=\"https://doi.org/10.1017/s0305004123000075\">10.1017/s0305004123000075</a>.","apa":"Ernst, A., &#38; Schmidt, K.-U. (2023). Intersection theorems for finite general linear groups. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, <i>175</i>(1), 129–160. <a href=\"https://doi.org/10.1017/s0305004123000075\">https://doi.org/10.1017/s0305004123000075</a>"},"status":"public","volume":175,"user_id":"46953","_id":"53533","publisher":"Cambridge University Press (CUP)","page":"129-160"},{"date_created":"2023-11-02T11:22:34Z","department":[{"_id":"543"},{"_id":"458"}],"type":"journal_article","citation":{"mla":"Häsel-Weide, Uta, et al. “„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung.” <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i>, vol. 5, no. 1, 2023, pp. 215–29.","bibtex":"@article{Häsel-Weide_Schmidt_Büker_2023, title={„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung}, volume={5}, number={1}, journal={Zeitschrift für Schul- und Professionsentwicklung (PFLB)}, author={Häsel-Weide, Uta and Schmidt, R. and Büker, Petra}, year={2023}, pages={215–229} }","ama":"Häsel-Weide U, Schmidt R, Büker P. „FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung. <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i>. 2023;5(1):215-229.","ieee":"U. Häsel-Weide, R. Schmidt, and P. Büker, “„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung,” <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i>, vol. 5, no. 1, pp. 215–229, 2023.","apa":"Häsel-Weide, U., Schmidt, R., &#38; Büker, P. (2023). „FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung. <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i>, <i>5</i>(1), 215–229.","short":"U. Häsel-Weide, R. Schmidt, P. Büker, Zeitschrift für Schul- und Professionsentwicklung (PFLB) 5 (2023) 215–229.","chicago":"Häsel-Weide, Uta, R. Schmidt, and Petra Büker. “„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung.” <i>Zeitschrift für Schul- und Professionsentwicklung (PFLB)</i> 5, no. 1 (2023): 215–29."},"issue":"1","publication":"Zeitschrift für Schul- und Professionsentwicklung (PFLB)","related_material":{"link":[{"url":"https://doi.org/10.11576/pflb-6763 ","relation":"original"}]},"_id":"48596","language":[{"iso":"ger"}],"page":"215-229","volume":5,"user_id":"26718","author":[{"id":"60267","last_name":"Häsel-Weide","first_name":"Uta","full_name":"Häsel-Weide, Uta"},{"last_name":"Schmidt","first_name":"R.","full_name":"Schmidt, R."},{"first_name":"Petra","last_name":"Büker","full_name":"Büker, Petra","id":"21978"}],"status":"public","title":"„FInDig“: Fach – Inklusion – Digitalisierung vernetzen. Ein Planungs- und Reflexionsmodell für die Lehrkräftebildung","year":"2023","intvolume":"         5","date_updated":"2024-07-23T13:05:48Z"},{"date_created":"2024-07-16T11:09:01Z","type":"journal_article","department":[{"_id":"102"}],"issue":"10","publication":"Int. J. Number Theory","citation":{"ama":"Klahn B, Technau M. Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>. <i>Int J Number Theory</i>. 2023;19(10):2443–2450. doi:<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>","bibtex":"@article{Klahn_Technau_2023, title={Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>}, volume={19}, DOI={<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>}, number={10}, journal={Int. J. Number Theory}, author={Klahn, B. and Technau, Marc}, year={2023}, pages={2443–2450} }","mla":"Klahn, B., and Marc Technau. “Galois Groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.” <i>Int. J. Number Theory</i>, vol. 19, no. 10, 2023, pp. 2443–2450, doi:<a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>.","short":"B. Klahn, M. Technau, Int. J. Number Theory 19 (2023) 2443–2450.","chicago":"Klahn, B., and Marc Technau. “Galois Groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.” <i>Int. J. Number Theory</i> 19, no. 10 (2023): 2443–2450. <a href=\"https://doi.org/10.1142/S1793042123501208\">https://doi.org/10.1142/S1793042123501208</a>.","apa":"Klahn, B., &#38; Technau, M. (2023). Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>. <i>Int. J. Number Theory</i>, <i>19</i>(10), 2443–2450. <a href=\"https://doi.org/10.1142/S1793042123501208\">https://doi.org/10.1142/S1793042123501208</a>","ieee":"B. Klahn and M. Technau, “Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>,” <i>Int. J. Number Theory</i>, vol. 19, no. 10, pp. 2443–2450, 2023, doi: <a href=\"https://doi.org/10.1142/S1793042123501208\">10.1142/S1793042123501208</a>."},"extern":"1","page":"2443–2450","language":[{"iso":"eng"}],"_id":"55277","user_id":"106108","doi":"10.1142/S1793042123501208","volume":19,"status":"public","title":"Galois groups of (ⁿ₀)+(ⁿ₁)X+…+(ⁿ₆)X⁶","year":"2023","author":[{"last_name":"Klahn","first_name":"B.","full_name":"Klahn, B."},{"first_name":"Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","full_name":"Technau, Marc","id":"106108"}],"date_updated":"2024-07-24T07:23:33Z","intvolume":"        19"},{"citation":{"apa":"Minelli, P., Sourmelidis, A., &#38; Technau, M. (2023). Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. <i>Math. Ann.</i>, <i>387</i>, 291–320. <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">https://doi.org/10.1007/s00208-022-02452-2</a>","ieee":"P. Minelli, A. Sourmelidis, and M. Technau, “Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums,” <i>Math. Ann.</i>, vol. 387, pp. 291–320, 2023, doi: <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>.","short":"P. Minelli, A. Sourmelidis, M. Technau, Math. Ann. 387 (2023) 291–320.","chicago":"Minelli, P., A. Sourmelidis, and Marc Technau. “Bias in the Number of Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i> 387 (2023): 291–320. <a href=\"https://doi.org/10.1007/s00208-022-02452-2\">https://doi.org/10.1007/s00208-022-02452-2</a>.","mla":"Minelli, P., et al. “Bias in the Number of Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i>, vol. 387, 2023, pp. 291–320, doi:<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>.","ama":"Minelli P, Sourmelidis A, Technau M. Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums. <i>Math Ann</i>. 2023;387:291–320. doi:<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>","bibtex":"@article{Minelli_Sourmelidis_Technau_2023, title={Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums}, volume={387}, DOI={<a href=\"https://doi.org/10.1007/s00208-022-02452-2\">10.1007/s00208-022-02452-2</a>}, journal={Math. Ann.}, author={Minelli, P. and Sourmelidis, A. and Technau, Marc}, year={2023}, pages={291–320} }"},"publication":"Math. Ann.","extern":"1","date_created":"2024-07-16T11:09:01Z","department":[{"_id":"102"}],"type":"journal_article","author":[{"full_name":"Minelli, P.","last_name":"Minelli","first_name":"P."},{"full_name":"Sourmelidis, A.","first_name":"A.","last_name":"Sourmelidis"},{"id":"106108","first_name":"Marc","last_name":"Technau","orcid":"0000-0001-9650-2459","full_name":"Technau, Marc"}],"year":"2023","title":"Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums","status":"public","intvolume":"       387","date_updated":"2024-07-24T07:26:05Z","language":[{"iso":"eng"}],"_id":"55279","page":"291–320","volume":387,"user_id":"106108","doi":"10.1007/s00208-022-02452-2"},{"user_id":"178","doi":"10.1007/s10543-023-00989-05","volume":63,"article_number":"50","language":[{"iso":"eng"}],"_id":"34803","publisher":"Springer","date_updated":"2024-08-09T08:48:06Z","intvolume":"        63","title":"Deep neural networks on diffeomorphism groups for optimal shape reparametrization","status":"public","year":"2023","author":[{"full_name":"Celledoni, Elena","first_name":"Elena","last_name":"Celledoni"},{"full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge","id":"178"},{"full_name":"Riseth, Jørgen","last_name":"Riseth","first_name":"Jørgen"},{"full_name":"Schmeding, Alexander","first_name":"Alexander","last_name":"Schmeding"}],"type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"external_id":{"arxiv":["2207.11141"]},"date_created":"2022-12-22T07:37:20Z","quality_controlled":"1","publication":"BIT Numerical Mathematics","citation":{"apa":"Celledoni, E., Glöckner, H., Riseth, J., &#38; Schmeding, A. (2023). Deep neural networks on diffeomorphism groups for optimal shape reparametrization. <i>BIT Numerical Mathematics</i>, <i>63</i>, Article 50. <a href=\"https://doi.org/10.1007/s10543-023-00989-05\">https://doi.org/10.1007/s10543-023-00989-05</a>","ieee":"E. Celledoni, H. Glöckner, J. Riseth, and A. Schmeding, “Deep neural networks on diffeomorphism groups for optimal shape reparametrization,” <i>BIT Numerical Mathematics</i>, vol. 63, Art. no. 50, 2023, doi: <a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>.","short":"E. Celledoni, H. Glöckner, J. Riseth, A. 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Deep neural networks on diffeomorphism groups for optimal shape reparametrization. <i>BIT Numerical Mathematics</i>. 2023;63. doi:<a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>","bibtex":"@article{Celledoni_Glöckner_Riseth_Schmeding_2023, title={Deep neural networks on diffeomorphism groups for optimal shape reparametrization}, volume={63}, DOI={<a href=\"https://doi.org/10.1007/s10543-023-00989-05\">10.1007/s10543-023-00989-05</a>}, number={50}, journal={BIT Numerical Mathematics}, publisher={Springer}, author={Celledoni, Elena and Glöckner, Helge and Riseth, Jørgen and Schmeding, Alexander}, year={2023} }"}},{"author":[{"id":"178","last_name":"Glöckner","first_name":"Helge","full_name":"Glöckner, Helge"}],"title":"Diffeomorphism groups of convex polytopes","year":"2023","intvolume":"        30","date_updated":"2024-08-09T08:49:17Z","language":[{"iso":"eng"}],"issue":"1","publication":"Journal of Convex Analysis","abstract":[{"lang":"eng","text":"Let $E$ be a finite-dimensional real vector space and $M\\subseteq E$ be a\r\nconvex polytope with non-empty interior. We turn the group of all\r\n$C^\\infty$-diffeomorphisms of $M$ into a regular Lie group."}],"date_created":"2022-12-22T07:45:13Z","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"journal_article","status":"public","publisher":"Heldermann","_id":"34805","page":"343-358","volume":30,"user_id":"178","citation":{"ama":"Glöckner H. Diffeomorphism groups of convex polytopes. <i>Journal of Convex Analysis</i>. 2023;30(1):343-358.","bibtex":"@article{Glöckner_2023, title={Diffeomorphism groups of convex polytopes}, volume={30}, number={1}, journal={Journal of Convex Analysis}, publisher={Heldermann}, author={Glöckner, Helge}, year={2023}, pages={343–358} }","mla":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal of Convex Analysis</i>, vol. 30, no. 1, Heldermann, 2023, pp. 343–58.","chicago":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal of Convex Analysis</i> 30, no. 1 (2023): 343–58.","short":"H. Glöckner, Journal of Convex Analysis 30 (2023) 343–358.","apa":"Glöckner, H. (2023). Diffeomorphism groups of convex polytopes. <i>Journal of Convex Analysis</i>, <i>30</i>(1), 343–358.","ieee":"H. Glöckner, “Diffeomorphism groups of convex polytopes,” <i>Journal of Convex Analysis</i>, vol. 30, no. 1, pp. 343–358, 2023."},"quality_controlled":"1","external_id":{"arxiv":["2203.09285"]}},{"volume":33,"user_id":"178","language":[{"iso":"eng"}],"_id":"34801","publisher":"Heldermann","page":"271-296","intvolume":"        33","date_updated":"2024-08-09T08:48:51Z","author":[{"first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178"},{"last_name":"Tárrega","first_name":"Luis","full_name":"Tárrega, Luis"}],"title":"Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups ","year":"2023","status":"public","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"journal_article","date_created":"2022-12-22T07:23:57Z","external_id":{"arxiv":["2210.01246"]},"quality_controlled":"1","citation":{"mla":"Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued Function Spaces and Direct Limits of Sobolev-Lie Groups .” <i>Journal of Lie Theory</i>, vol. 33, no. 1, Heldermann, 2023, pp. 271–96.","apa":"Glöckner, H., &#38; Tárrega, L. (2023). Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups . <i>Journal of Lie Theory</i>, <i>33</i>(1), 271–296.","ieee":"H. Glöckner and L. Tárrega, “Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups ,” <i>Journal of Lie Theory</i>, vol. 33, no. 1, pp. 271–296, 2023.","short":"H. Glöckner, L. Tárrega, Journal of Lie Theory 33 (2023) 271–296.","ama":"Glöckner H, Tárrega L. Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups . <i>Journal of Lie Theory</i>. 2023;33(1):271-296.","chicago":"Glöckner, Helge, and Luis Tárrega. “Mapping Groups Associated with Real-Valued Function Spaces and Direct Limits of Sobolev-Lie Groups .” <i>Journal of Lie Theory</i> 33, no. 1 (2023): 271–96.","bibtex":"@article{Glöckner_Tárrega_2023, title={Mapping groups associated with real-valued function spaces and direct limits of Sobolev-Lie groups }, volume={33}, number={1}, journal={Journal of Lie Theory}, publisher={Heldermann}, author={Glöckner, Helge and Tárrega, Luis}, year={2023}, pages={271–296} }"},"publication":"Journal of Lie Theory","issue":"1"},{"user_id":"178","language":[{"iso":"eng"}],"_id":"55575","date_updated":"2024-08-09T09:27:43Z","year":"2023","status":"public","title":"Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen","author":[{"full_name":"Jakob, Johanna","first_name":"Johanna","last_name":"Jakob"}],"type":"preprint","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"external_id":{"arxiv":["2307.03473"]},"date_created":"2024-08-09T09:15:06Z","citation":{"chicago":"Jakob, Johanna. “Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen,” 2023.","short":"J. Jakob, (2023).","ieee":"J. Jakob, “Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen.” 2023.","apa":"Jakob, J. (2023). <i>Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen</i>.","bibtex":"@article{Jakob_2023, title={Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen}, author={Jakob, Johanna}, year={2023} }","ama":"Jakob J. Der Whitneysche Fortsetzungssatz für vektorwertige Funktionen. Published online 2023.","mla":"Jakob, Johanna. <i>Der Whitneysche Fortsetzungssatz Für Vektorwertige Funktionen</i>. 2023."}},{"publisher":"Springer, Cham.","_id":"42163","page":"569-579","volume":14071,"editor":[{"first_name":"F","last_name":"Nielsen","full_name":"Nielsen, F"},{"last_name":"Barbaresco","first_name":"F","full_name":"Barbaresco, F"}],"user_id":"85279","ddc":["510"],"conference":{"location":"Saint-Malo, Palais du Grand Large, France","start_date":"2023-08-30","name":"  GSI'23 6th International Conference on Geometric Science of Information","end_date":"2023-09-01"},"status":"public","has_accepted_license":"1","external_id":{"arxiv":["2302.08232 "]},"oa":"1","citation":{"ieee":"C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in <i>Geometric Science of Information</i>, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen &#38; F. Barbaresco (Eds.), <i>Geometric Science of Information</i> (Vol. 14071, pp. 569–579). Springer, Cham. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>.","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","bibtex":"@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }","ama":"Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. <i>Geometric Science of Information</i>. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>"},"file_date_updated":"2023-08-02T12:04:17Z","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"quality_controlled":"1","series_title":"Lecture Notes in Computer Science (LNCS)","language":[{"iso":"eng"}],"doi":"10.1007/978-3-031-38271-0_57","author":[{"full_name":"Offen, Christian","last_name":"Offen","first_name":"Christian","orcid":"0000-0002-5940-8057","id":"85279"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"}],"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","year":"2023","intvolume":"     14071","publication_status":"published","date_updated":"2024-08-12T13:46:29Z","date_created":"2023-02-16T11:32:48Z","file":[{"creator":"coffen","date_created":"2023-08-02T12:04:17Z","description":"The article shows how to learn models of dynamical systems\nfrom data which are governed by an unknown variational PDE. Rather\nthan employing reduction techniques, we learn a discrete field theory\ngoverned by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is\nnecessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of\nthe discrete Euler–Lagrange equations. Secondly, we develop a method to\nfind solutions to machine learned discrete field theories which constitute\ntravelling waves of the underlying continuous PDE.","file_name":"LDensityLearning.pdf","file_size":1938962,"access_level":"open_access","relation":"main_file","date_updated":"2023-08-02T12:04:17Z","file_id":"46273","content_type":"application/pdf","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves"}],"department":[{"_id":"636"}],"type":"conference","keyword":["System identification","discrete Lagrangians","travelling waves"],"publication":"Geometric Science of Information","abstract":[{"text":"The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.","lang":"eng"}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/LagrangianDensityML","description":"GitHub"}]}},{"citation":{"short":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, eds., Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023.","chicago":"Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, and Carl Winsløw, eds. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Cham: Springer International Publishing, 2023. <a href=\"https://doi.org/10.1007/978-3-031-14175-1\">https://doi.org/10.1007/978-3-031-14175-1</a>.","apa":"Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., &#38; Winsløw, C. (Eds.). (2023). <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-14175-1\">https://doi.org/10.1007/978-3-031-14175-1</a>","ieee":"R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, Eds., <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Cham: Springer International Publishing, 2023.","ama":"Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C, eds. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing; 2023. doi:<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>","bibtex":"@book{Biehler_Liebendörfer_Gueudet_Rasmussen_Winsløw_2023, place={Cham}, title={Practice-Oriented Research in Tertiary Mathematics Education}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>}, publisher={Springer International Publishing}, year={2023} }","mla":"Biehler, Rolf, et al., editors. <i>Practice-Oriented Research in Tertiary Mathematics Education</i>. Springer International Publishing, 2023, doi:<a href=\"https://doi.org/10.1007/978-3-031-14175-1\">10.1007/978-3-031-14175-1</a>."},"department":[{"_id":"10"}],"type":"book_editor","date_created":"2023-01-18T22:17:58Z","place":"Cham","publication_status":"published","date_updated":"2023-01-18T22:47:41Z","publication_identifier":{"issn":["1869-4918","1869-4926"],"isbn":["9783031141744","9783031141751"]},"year":"2023","status":"public","title":"Practice-Oriented Research in Tertiary Mathematics Education","editor":[{"full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"},{"full_name":"Liebendörfer, Michael","last_name":"Liebendörfer","first_name":"Michael"},{"last_name":"Gueudet","first_name":"Ghislaine","full_name":"Gueudet, Ghislaine"},{"first_name":"Chris","last_name":"Rasmussen","full_name":"Rasmussen, Chris"},{"last_name":"Winsløw","first_name":"Carl","full_name":"Winsløw, Carl"}],"user_id":"30933","doi":"10.1007/978-3-031-14175-1","publisher":"Springer International Publishing","_id":"37469"}]