[{"language":[{"iso":"eng"}],"doi":"10.4310/cag.2022.v30.n1.a2","year":"2022","title":"Regularity of Lie groups","author":[{"last_name":"Hanusch","first_name":"Maximilian","full_name":"Hanusch, Maximilian","id":"30905"}],"publication_identifier":{"issn":["1019-8385","1944-9992"]},"date_updated":"2023-01-09T18:07:30Z","publication_status":"published","intvolume":"        30","article_type":"original","date_created":"2022-12-22T09:19:43Z","keyword":["regularity of Lie groups"],"type":"journal_article","department":[{"_id":"93"}],"issue":"1","publication":"Communications in Analysis and Geometry","extern":"1","page":"53-152","publisher":"International Press of Boston","_id":"34817","user_id":"30905","volume":30,"status":"public","citation":{"short":"M. Hanusch, Communications in Analysis and Geometry 30 (2022) 53–152.","chicago":"Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in Analysis and Geometry</i> 30, no. 1 (2022): 53–152. <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>.","apa":"Hanusch, M. (2022). Regularity of Lie groups. <i>Communications in Analysis and Geometry</i>, <i>30</i>(1), 53–152. <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">https://doi.org/10.4310/cag.2022.v30.n1.a2</a>","ieee":"M. Hanusch, “Regularity of Lie groups,” <i>Communications in Analysis and Geometry</i>, vol. 30, no. 1, pp. 53–152, 2022, doi: <a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>.","ama":"Hanusch M. Regularity of Lie groups. <i>Communications in Analysis and Geometry</i>. 2022;30(1):53-152. doi:<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>","bibtex":"@article{Hanusch_2022, title={Regularity of Lie groups}, volume={30}, DOI={<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>}, number={1}, journal={Communications in Analysis and Geometry}, publisher={International Press of Boston}, author={Hanusch, Maximilian}, year={2022}, pages={53–152} }","mla":"Hanusch, Maximilian. “Regularity of Lie Groups.” <i>Communications in Analysis and Geometry</i>, vol. 30, no. 1, International Press of Boston, 2022, pp. 53–152, doi:<a href=\"https://doi.org/10.4310/cag.2022.v30.n1.a2\">10.4310/cag.2022.v30.n1.a2</a>."}},{"type":"working_paper","department":[{"_id":"93"}],"date_created":"2022-12-22T17:06:02Z","citation":{"bibtex":"@book{Hanusch, title={Analysis 1 und 2 Skript/Buch}, publisher={https://maximilianhanusch.wixsite.com/my-site/lehre-teaching}, author={Hanusch, Maximilian} }","ama":"Hanusch M. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching","mla":"Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.","short":"M. Hanusch, Analysis 1 und 2 Skript/Buch, https://maximilianhanusch.wixsite.com/my-site/lehre-teaching, n.d.","chicago":"Hanusch, Maximilian. <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching, n.d.","ieee":"M. Hanusch, <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.","apa":"Hanusch, M. (n.d.). <i>Analysis 1 und 2 Skript/Buch</i>. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching."},"user_id":"30905","page":"385","publisher":"https://maximilianhanusch.wixsite.com/my-site/lehre-teaching","_id":"34856","language":[{"iso":"ger"}],"publication_status":"draft","date_updated":"2023-01-09T18:07:00Z","status":"public","title":"Analysis 1 und 2 Skript/Buch","year":"2022","author":[{"full_name":"Hanusch, Maximilian","first_name":"Maximilian","last_name":"Hanusch","id":"30905"}]},{"intvolume":"        67","date_updated":"2023-01-10T08:13:30Z","publication_status":"published","author":[{"last_name":"Kolb","first_name":"Martin","full_name":"Kolb, Martin","id":"48880"},{"full_name":"Klump, Alexander","last_name":"Klump","first_name":"Alexander","id":"45067"}],"status":"public","year":"2022","title":"Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary","volume":67,"user_id":"85821","_id":"35644","publisher":"Society for Industrial and Applied Mathematics","language":[{"iso":"eng"}],"page":"717-744","citation":{"mla":"Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev Boundary.” <i>Theory of Probability and Its Applications</i>, vol. 67, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 717–44.","apa":"Kolb, M., &#38; Klump, A. (2022). Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary. <i>Theory of Probability and Its Applications</i>, <i>67</i>(4), 717–744.","ieee":"M. Kolb and A. Klump, “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary,” <i>Theory of Probability and its Applications</i>, vol. 67, no. 4, pp. 717–744, 2022.","chicago":"Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev Boundary.” <i>Theory of Probability and Its Applications</i> 67, no. 4 (2022): 717–44.","short":"M. Kolb, A. Klump, Theory of Probability and Its Applications 67 (2022) 717–744.","ama":"Kolb M, Klump A. Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary. <i>Theory of Probability and its Applications</i>. 2022;67(4):717-744.","bibtex":"@article{Kolb_Klump_2022, title={Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev boundary}, volume={67}, number={4}, journal={Theory of Probability and its Applications}, publisher={Society for Industrial and Applied Mathematics}, author={Kolb, Martin and Klump, Alexander}, year={2022}, pages={717–744} }"},"issue":"4","publication":"Theory of Probability and its Applications","department":[{"_id":"96"}],"type":"journal_article","date_created":"2023-01-10T08:13:17Z"},{"date_created":"2023-01-10T08:19:25Z","type":"journal_article","department":[{"_id":"96"}],"issue":"27","publication":"Electronic Journal of Probability","citation":{"short":"M. Kolb, M. Liesenfeld, Electronic Journal of Probability (2022) 1–28.","chicago":"Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no. 27 (2022): 1–28. <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>.","apa":"Kolb, M., &#38; Liesenfeld, M. (2022). On non-extinction in a Fleming-Viot-type particle model with Bessel drift. <i>Electronic Journal of Probability</i>, <i>27</i>, 1–28. <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>","ieee":"M. Kolb and M. Liesenfeld, “On non-extinction in a Fleming-Viot-type particle model with Bessel drift,” <i>Electronic Journal of Probability</i>, no. 27, pp. 1–28, 2022, doi: <a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>.","ama":"Kolb M, Liesenfeld M. On non-extinction in a Fleming-Viot-type particle model with Bessel drift. <i>Electronic Journal of Probability</i>. 2022;(27):1-28. doi:<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>","bibtex":"@article{Kolb_Liesenfeld_2022, title={On non-extinction in a Fleming-Viot-type particle model with Bessel drift}, DOI={<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>}, number={27}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2022}, pages={1–28} }","mla":"Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type Particle Model with Bessel Drift.” <i>Electronic Journal of Probability</i>, no. 27, Institute of Mathematical Statistics, 2022, pp. 1–28, doi:<a href=\"https://doi.org/10.1214/22-EJP866\">https://doi.org/10.1214/22-EJP866</a>."},"abstract":[{"text":"Motivated by the work [6] of Mariusz Bieniek, Krzysztof Burdzy and Soumik Pal we study a Fleming-Viot-type particle system consisting of independently moving particles each driven by generalized Bessel processes on the positive real line. Upon hitting the boundary {0} this particle is killed and an uniformly chosen different one branches into two particles. Using the symmetry of the model and the self similarity property of Bessel processes, we obtain a criterion to decide whether the particles converge to the origin at a finite time. This addresses open problem 1.4 in [6]. Specifically, inspired by [6, Open Problem 1.5], we investigate the case of three moving particles and refine the general result of [6, Theorem 1.1(ii)] extending the regime of drift parameters, where convergence does not occur – even to values, where it does occur when considering the case of only two particles.","lang":"eng"}],"page":"1-28","_id":"35649","publisher":"Institute of Mathematical Statistics","language":[{"iso":"eng"}],"doi":"https://doi.org/10.1214/22-EJP866","user_id":"85821","year":"2022","title":"On non-extinction in a Fleming-Viot-type particle model with Bessel drift","status":"public","author":[{"full_name":"Kolb, Martin","last_name":"Kolb","first_name":"Martin","id":"48880"},{"full_name":"Liesenfeld, Matthias","first_name":"Matthias","last_name":"Liesenfeld"}],"date_updated":"2023-01-10T08:19:38Z","publication_status":"published"},{"publication_status":"published","date_updated":"2023-01-10T08:29:02Z","intvolume":"        27","title":"Persistence of autoregressive sequences with logarithmic tails","year":"2022","status":"public","author":[{"last_name":"Denisov","first_name":"Denis","full_name":"Denisov, Denis"},{"full_name":"Hinrichs, Günter","first_name":"Günter","last_name":"Hinrichs"},{"id":"48880","full_name":"Kolb, Martin","last_name":"Kolb","first_name":"Martin"},{"last_name":"Wachtel","first_name":"Vitali","full_name":"Wachtel, Vitali"}],"user_id":"85821","doi":"https://doi.org/10.48550/arXiv.2203.14772","volume":27,"page":"1-43","publisher":"Institute of Mathematical Statistics","_id":"35650","language":[{"iso":"eng"}],"abstract":[{"text":"We consider autoregressive sequences Xn = aXn−1 + ξn and\r\nMn = max{aMn−1 , ξn} with a constant a ∈ (0, 1) and with positive, in-\r\ndependent and identically distributed innovations {ξk }. It is known that if\r\nP(ξ1 > x) ∼ d\r\nlog x with some d ∈ (0, − log a) then the chains {Xn} and {Mn}\r\nare null recurrent. We investigate the tail behaviour of recurrence times in this\r\ncase of logarithmically decaying tails. More precisely, we show that the tails\r\nof recurrence times are regularly varying of index −1 − d/ log a. We also prove\r\nlimit theorems for {Xn} and {Mn} conditioned to stay over a fixed level x0.\r\nFurthermore, we study tail asymptotics for recurrence times of {Xn} and {Mn}\r\nin the case when these chains are positive recurrent and the tail of log ξ1 is\r\nsubexponential.","lang":"eng"}],"publication":"Electronic Journal of Probability","citation":{"ieee":"D. Denisov, G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of autoregressive sequences with logarithmic tails,” <i>Electronic Journal of Probability</i>, vol. 27, pp. 1–43, 2022, doi: <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>.","apa":"Denisov, D., Hinrichs, G., Kolb, M., &#38; Wachtel, V. (2022). Persistence of autoregressive sequences with logarithmic tails. <i>Electronic Journal of Probability</i>, <i>27</i>, 1–43. <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>","short":"D. Denisov, G. Hinrichs, M. Kolb, V. Wachtel, Electronic Journal of Probability 27 (2022) 1–43.","chicago":"Denisov, Denis, Günter Hinrichs, Martin Kolb, and Vitali Wachtel. “Persistence of Autoregressive Sequences with Logarithmic Tails.” <i>Electronic Journal of Probability</i> 27 (2022): 1–43. <a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>.","mla":"Denisov, Denis, et al. “Persistence of Autoregressive Sequences with Logarithmic Tails.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–43, doi:<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>.","bibtex":"@article{Denisov_Hinrichs_Kolb_Wachtel_2022, title={Persistence of autoregressive sequences with logarithmic tails}, volume={27}, DOI={<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>}, journal={Electronic Journal of Probability}, publisher={Institute of Mathematical Statistics}, author={Denisov, Denis and Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}, year={2022}, pages={1–43} }","ama":"Denisov D, Hinrichs G, Kolb M, Wachtel V. Persistence of autoregressive sequences with logarithmic tails. <i>Electronic Journal of Probability</i>. 2022;27:1-43. doi:<a href=\"https://doi.org/10.48550/arXiv.2203.14772\">https://doi.org/10.48550/arXiv.2203.14772</a>"},"type":"journal_article","department":[{"_id":"96"}],"date_created":"2023-01-10T08:28:12Z"},{"date_updated":"2023-01-11T15:28:21Z","publication_status":"published","title":"Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.","year":"2022","status":"public","author":[{"full_name":"Hoffmann, Max","last_name":"Hoffmann","orcid":"0000-0002-6964-7123","first_name":"Max","id":"32202"},{"id":"16274","first_name":"Rolf","last_name":"Biehler","full_name":"Biehler, Rolf"}],"user_id":"32202","editor":[{"first_name":"Stefan","last_name":"Halverscheid","full_name":"Halverscheid, Stefan"},{"last_name":"Kersten","first_name":"Ina","full_name":"Kersten, Ina"},{"full_name":"Schmidt-Thieme, Barbara","first_name":"Barbara","last_name":"Schmidt-Thieme"}],"page":"351-368","language":[{"iso":"ger"}],"_id":"31367","publisher":"Springer Spektrum","quality_controlled":"1","publication":" Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen ","citation":{"bibtex":"@inproceedings{Hoffmann_Biehler_2022, place={Wiesbaden}, title={Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.}, booktitle={ Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen }, publisher={Springer Spektrum}, author={Hoffmann, Max and Biehler, Rolf}, editor={Halverscheid, Stefan and Kersten, Ina and Schmidt-Thieme, Barbara}, year={2022}, pages={351–368} }","ama":"Hoffmann M, Biehler R. Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie. In: Halverscheid S, Kersten I, Schmidt-Thieme B, eds. <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i>. Springer Spektrum; 2022:351-368.","mla":"Hoffmann, Max, and Rolf Biehler. “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.” <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i>, edited by Stefan Halverscheid et al., Springer Spektrum, 2022, pp. 351–68.","short":"M. Hoffmann, R. Biehler, in: S. Halverscheid, I. Kersten, B. Schmidt-Thieme (Eds.),  Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen , Springer Spektrum, Wiesbaden, 2022, pp. 351–368.","chicago":"Hoffmann, Max, and Rolf Biehler. “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.” In <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i>, edited by Stefan Halverscheid, Ina Kersten, and Barbara Schmidt-Thieme, 351–68. Wiesbaden: Springer Spektrum, 2022.","ieee":"M. Hoffmann and R. Biehler, “Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.,” in <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i>, 2022, pp. 351–368.","apa":"Hoffmann, M., &#38; Biehler, R. (2022). Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie. In S. Halverscheid, I. Kersten, &#38; B. Schmidt-Thieme (Eds.), <i> Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen </i> (pp. 351–368). Springer Spektrum."},"type":"conference","department":[{"_id":"97"}],"place":"Wiesbaden","date_created":"2022-05-22T14:16:52Z"},{"publication":" Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik","date_created":"2022-05-22T14:03:58Z","department":[{"_id":"97"}],"type":"conference","publication_identifier":{"issn":["2197-8751","2197-876X"],"isbn":["9783662639474","9783662639481"]},"author":[{"id":"16274","full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"},{"id":"32202","full_name":"Hoffmann, Max","orcid":"0000-0002-6964-7123","first_name":"Max","last_name":"Hoffmann"}],"title":"Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium","year":"2022","publication_status":"published","date_updated":"2023-01-11T15:29:09Z","language":[{"iso":"ger"}],"main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-662-63948-1_4"}],"doi":"10.1007/978-3-662-63948-1_4","citation":{"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> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i>, edited by Viktor Isaev, Andreas Eichler, and Frank Loose, 49–72. Berlin, Heidelberg: Springer, 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: V. Isaev, A. Eichler, F. Loose (Eds.),  Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik, Springer, Berlin, Heidelberg, 2022, pp. 49–72.","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 V. Isaev, A. Eichler, &#38; F. Loose (Eds.), <i> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i> (pp. 49–72). Springer. <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>","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> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i>, 2022, pp. 49–72, doi: <a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>.","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: Isaev V, Eichler A, Loose F, eds. <i> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i>. Springer; 2022:49–72. doi:<a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>","bibtex":"@inproceedings{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={ Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik}, publisher={Springer}, author={Biehler, Rolf and Hoffmann, Max}, editor={Isaev, Viktor and Eichler, Andreas and Loose, Frank}, year={2022}, pages={49–72} }","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> Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik</i>, edited by Viktor Isaev et al., Springer, 2022, pp. 49–72, doi:<a href=\"https://doi.org/10.1007/978-3-662-63948-1_4\">10.1007/978-3-662-63948-1_4</a>."},"quality_controlled":"1","place":"Berlin, Heidelberg","status":"public","publisher":"Springer","_id":"31365","page":" 49–72","editor":[{"last_name":"Isaev","first_name":"Viktor","full_name":"Isaev, Viktor"},{"last_name":"Eichler","first_name":"Andreas","full_name":"Eichler, Andreas"},{"full_name":"Loose, Frank","first_name":"Frank","last_name":"Loose"}],"user_id":"32202"},{"author":[{"id":"85820","full_name":"Dröse, Jennifer","last_name":"Dröse","first_name":"Jennifer"},{"first_name":"P.","last_name":"Neugebauer","full_name":"Neugebauer, P."},{"full_name":"Delucchi Danhier, R.","first_name":"R.","last_name":"Delucchi Danhier"},{"last_name":"Mertins","first_name":"B.","full_name":"Mertins, B."}],"year":"2022","title":"Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen","status":"public","date_updated":"2023-11-02T08:07:31Z","language":[{"iso":"ger"}],"_id":"45373","page":"209-225","editor":[{"full_name":"Kleine, P.","first_name":"P.","last_name":"Kleine"},{"last_name":"Graulich","first_name":"N.","full_name":"Graulich, N."},{"first_name":"J.","last_name":"Kuhn","full_name":"Kuhn, J."},{"full_name":"Schindler, M.","first_name":"M.","last_name":"Schindler"}],"user_id":"85820","doi":"https://doi.org/10.1007/978-3-662-63214-7","citation":{"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.","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 <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i>, edited by P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, 209–25, 2022. <a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>.","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 <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i>, P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, Eds. 2022, pp. 209–225.","apa":"Dröse, J., Neugebauer, P., Delucchi Danhier, R., &#38; Mertins, B. (2022). Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen. In P. Kleine, N. Graulich, J. Kuhn, &#38; M. Schindler (Eds.), <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i> (pp. 209–225). <a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>","bibtex":"@inbook{Dröse_Neugebauer_Delucchi Danhier_Mertins_2022, title={Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>}, 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} }","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. <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i>. ; 2022:209-225. doi:<a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>","mla":"Dröse, Jennifer, et al. “Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen.” <i>Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis</i>, edited by P. Kleine et al., 2022, pp. 209–25, doi:<a href=\"https://doi.org/10.1007/978-3-662-63214-7\">https://doi.org/10.1007/978-3-662-63214-7</a>."},"publication":"Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis","quality_controlled":"1","date_created":"2023-05-31T06:22:21Z","department":[{"_id":"98"}],"type":"book_chapter"},{"citation":{"ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical control policies using kernel methods,” London, 2022, pp. 1870–1875.","mla":"Vertovec, Nikolaus, et al. <i>Verification of Safety Critical Control Policies Using Kernel Methods</i>. 2022, pp. 1870–75.","apa":"Vertovec, N., Ober-Blöbaum, S., &#38; Margellos, K. (2022). <i>Verification of safety critical control policies using kernel methods</i>. 1870–1875.","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} }","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.","ama":"Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control policies using kernel methods. In: ; 2022:1870-1875.","chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022."},"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."}],"date_created":"2022-03-31T11:14:13Z","department":[{"_id":"636"}],"type":"conference","conference":{"end_date":"2022-07-15","location":"London","start_date":"2022-07-12","name":"2022 European Control Conference (ECC)"},"author":[{"full_name":"Vertovec, Nikolaus","last_name":"Vertovec","first_name":"Nikolaus","id":"93930"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"first_name":"Kostas","last_name":"Margellos","full_name":"Margellos, Kostas"}],"title":"Verification of safety critical control policies using kernel methods","year":"2022","status":"public","has_accepted_license":"1","date_updated":"2023-11-29T10:00:18Z","language":[{"iso":"eng"}],"_id":"30733","page":"1870-1875","ddc":["510"],"user_id":"15694"},{"editor":[{"full_name":"Fernandez, C.","last_name":"Fernandez","first_name":"C."},{"full_name":"Llinares, S.","last_name":"Llinares","first_name":"S."},{"first_name":"A.","last_name":"Gutiérrez","full_name":"Gutiérrez, A."},{"full_name":"Planas, N.","last_name":"Planas","first_name":"N."}],"user_id":"85820","language":[{"iso":"eng"}],"_id":"45378","date_updated":"2023-11-02T08:05:31Z","author":[{"first_name":"Jennifer","last_name":"Dröse","full_name":"Dröse, Jennifer","id":"85820"},{"id":"85190","first_name":"Lena","last_name":"Wessel","full_name":"Wessel, Lena"}],"status":"public","title":"Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task","year":"2022","department":[{"_id":"98"}],"type":"conference","date_created":"2023-05-31T06:54:24Z","quality_controlled":"1","citation":{"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. <i>Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME</i>. ; 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} }","mla":"Dröse, Jennifer, and Lena Wessel. “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task.” <i>Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME</i>, edited by C. Fernandez et al., 2022.","chicago":"Dröse, Jennifer, and Lena Wessel. “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task.” In <i>Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME</i>, edited by C. Fernandez, S. Llinares, A. Gutiérrez, and N. Planas, 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.","apa":"Dröse, J., &#38; Wessel, L. (2022). Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task. In C. Fernandez, S. Llinares, A. Gutiérrez, &#38; N. Planas (Eds.), <i>Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME</i>.","ieee":"J. Dröse and L. Wessel, “Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script Writing Task,” in <i>Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME</i>, 2022."},"publication":"Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME"},{"author":[{"full_name":"Barkhofen, Sonja","first_name":"Sonja","last_name":"Barkhofen","id":"48188"},{"full_name":"Schütte, Philipp","first_name":"Philipp","last_name":"Schütte","id":"50168"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178"}],"title":"Semiclassical formulae For Wigner distributions","year":"2022","intvolume":"        55","article_type":"review","date_updated":"2024-02-06T20:40:45Z","language":[{"iso":"eng"}],"article_number":"244007","doi":"10.1088/1751-8121/ac6d2b","publication":"Journal of Physics A: Mathematical and Theoretical","issue":"24","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"}],"date_created":"2022-05-04T12:23:11Z","department":[{"_id":"623"},{"_id":"548"},{"_id":"10"}],"type":"journal_article","status":"public","publisher":"IOP Publishing Ltd","_id":"31057","volume":55,"user_id":"49178","citation":{"ieee":"S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner distributions,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 24, Art. no. 244007, 2022, doi: <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>.","apa":"Barkhofen, S., Schütte, P., &#38; Weich, T. (2022). Semiclassical formulae For Wigner distributions. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(24), Article 244007. <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">https://doi.org/10.1088/1751-8121/ac6d2b</a>","short":"S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022).","chicago":"Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae For Wigner Distributions.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55, no. 24 (2022). <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">https://doi.org/10.1088/1751-8121/ac6d2b</a>.","mla":"Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 24, 244007, IOP Publishing Ltd, 2022, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>.","bibtex":"@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For Wigner distributions}, volume={55}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>}, 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} }","ama":"Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(24). doi:<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>"},"external_id":{"arxiv":["2201.04892"]}},{"date_created":"2022-05-22T10:56:47Z","type":"dissertation","oa":"1","department":[{"_id":"97"}],"supervisor":[{"full_name":"Biehler, Rolf","first_name":"Rolf","last_name":"Biehler"},{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"}],"citation":{"short":"M. Hoffmann, Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende, 2022.","chicago":"Hoffmann, Max. <i>Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende</i>, 2022. <a href=\"https://doi.org/10.17619/UNIPB/1-1313\">https://doi.org/10.17619/UNIPB/1-1313</a>.","apa":"Hoffmann, M. (2022). <i>Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1313\">https://doi.org/10.17619/UNIPB/1-1313</a>","ieee":"M. Hoffmann, <i>Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende</i>. 2022.","ama":"Hoffmann M. <i>Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende</i>.; 2022. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1313\">10.17619/UNIPB/1-1313</a>","bibtex":"@book{Hoffmann_2022, title={Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1313\">10.17619/UNIPB/1-1313</a>}, author={Hoffmann, Max}, year={2022} }","mla":"Hoffmann, Max. <i>Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie Für Lehramtsstudierende</i>. 2022, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1313\">10.17619/UNIPB/1-1313</a>."},"abstract":[{"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.","lang":"eng"},{"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"}],"page":"410","main_file_link":[{"open_access":"1","url":"https://digital.ub.uni-paderborn.de/hs/content/titleinfo/6503170"}],"_id":"31363","language":[{"iso":"eng"}],"doi":"10.17619/UNIPB/1-1313","user_id":"49063","status":"public","title":"Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende","year":"2022","author":[{"id":"32202","full_name":"Hoffmann, Max","last_name":"Hoffmann","first_name":"Max","orcid":"0000-0002-6964-7123"}],"date_updated":"2024-02-19T06:28:58Z"},{"citation":{"ieee":"K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded degree,” <i>Journal of Spectral Theory</i>, vol. 12, no. 2, pp. 659–681, 2022, doi: <a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>.","apa":"Bux, K.-U., Hilgert, J., &#38; Weich, T. (2022). Poisson transforms for trees of bounded degree. <i>Journal of Spectral Theory</i>, <i>12</i>(2), 659–681. <a href=\"https://doi.org/10.4171/jst/414\">https://doi.org/10.4171/jst/414</a>","short":"K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.","chicago":"Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Poisson Transforms for Trees of Bounded Degree.” <i>Journal of Spectral Theory</i> 12, no. 2 (2022): 659–81. <a href=\"https://doi.org/10.4171/jst/414\">https://doi.org/10.4171/jst/414</a>.","mla":"Bux, Kai-Uwe, et al. “Poisson Transforms for Trees of Bounded Degree.” <i>Journal of Spectral Theory</i>, vol. 12, no. 2, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 659–81, doi:<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>.","bibtex":"@article{Bux_Hilgert_Weich_2022, title={Poisson transforms for trees of bounded degree}, volume={12}, DOI={<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>}, number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}, year={2022}, pages={659–681} }","ama":"Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree. <i>Journal of Spectral Theory</i>. 2022;12(2):659-681. doi:<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>"},"user_id":"49063","volume":12,"page":"659-681","publisher":"European Mathematical Society - EMS - Publishing House GmbH","_id":"35322","status":"public","type":"journal_article","keyword":["Geometry and Topology","Mathematical Physics","Statistical and Nonlinear Physics"],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"date_created":"2023-01-06T08:49:06Z","publication":"Journal of Spectral Theory","issue":"2","doi":"10.4171/jst/414","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2024-02-19T06:28:12Z","intvolume":"        12","year":"2022","title":"Poisson transforms for trees of bounded degree","author":[{"full_name":"Bux, Kai-Uwe","last_name":"Bux","first_name":"Kai-Uwe"},{"full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim","id":"220"},{"full_name":"Weich, Tobias","first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178"}],"publication_identifier":{"issn":["1664-039X"]}},{"citation":{"bibtex":"@article{Hilgert_2022, title={Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021}, volume={69}, DOI={<a href=\"https://doi.org/10.1007/s00591-021-00314-7\">10.1007/s00591-021-00314-7</a>}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2022}, pages={151–153} }","ama":"Hilgert J. Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021. <i>Mathematische Semesterberichte</i>. 2022;69:151–153. doi:<a href=\"https://doi.org/10.1007/s00591-021-00314-7\">10.1007/s00591-021-00314-7</a>","mla":"Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021.” <i>Mathematische Semesterberichte</i>, vol. 69, 2022, pp. 151–153, doi:<a href=\"https://doi.org/10.1007/s00591-021-00314-7\">10.1007/s00591-021-00314-7</a>.","short":"J. Hilgert, Mathematische Semesterberichte 69 (2022) 151–153.","chicago":"Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021.” <i>Mathematische Semesterberichte</i>, 2022. <a href=\"https://doi.org/10.1007/s00591-021-00314-7\">https://doi.org/10.1007/s00591-021-00314-7</a>.","ieee":"J. Hilgert, “Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021,” <i>Mathematische Semesterberichte</i>, vol. 69. pp. 151–153, 2022, doi: <a href=\"https://doi.org/10.1007/s00591-021-00314-7\">10.1007/s00591-021-00314-7</a>.","apa":"Hilgert, J. (2022). Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021. In <i>Mathematische Semesterberichte</i> (Vol. 69, pp. 151–153). <a href=\"https://doi.org/10.1007/s00591-021-00314-7\">https://doi.org/10.1007/s00591-021-00314-7</a>"},"publication":"Mathematische Semesterberichte","department":[{"_id":"91"}],"type":"review","date_created":"2024-02-20T09:49:04Z","intvolume":"        69","publication_status":"published","date_updated":"2024-02-20T09:52:53Z","author":[{"id":"220","first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim"}],"title":"Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition. AMS/MAA Press 2021","year":"2022","status":"public","volume":69,"user_id":"49063","doi":"10.1007/s00591-021-00314-7","language":[{"iso":"eng"}],"_id":"51554","page":"151–153"},{"abstract":[{"lang":"eng","text":"<jats:p> We introduce a new phase field model for tumor growth where viscoelastic effects are taken into account. The model is derived from basic thermodynamical principles and consists of a convected Cahn–Hilliard equation with source terms for the tumor cells and a convected reaction–diffusion equation with boundary supply for the nutrient. Chemotactic terms, which are essential for the invasive behavior of tumors, are taken into account. The model is completed by a viscoelastic system consisting of the Navier–Stokes equation for the hydrodynamic quantities, and a general constitutive equation with stress relaxation for the left Cauchy–Green tensor associated with the elastic part of the total mechanical response of the viscoelastic material. For a specific choice of the elastic energy density and with an additional dissipative term accounting for stress diffusion, we prove existence of global-in-time weak solutions of the viscoelastic model for tumor growth in two space dimensions [Formula: see text] by the passage to the limit in a fully-discrete finite element scheme where a CFL condition, i.e. [Formula: see text], is required. </jats:p><jats:p> Moreover, in arbitrary dimensions [Formula: see text], we show stability and existence of solutions for the fully-discrete finite element scheme, where positive definiteness of the discrete Cauchy–Green tensor is proved with a regularization technique that was first introduced by Barrett and Boyaval [Existence and approximation of a (regularized) Oldroyd-B model, Math. Models Methods Appl. Sci. 21 (2011) 1783–1837]. After that, we improve the regularity results in arbitrary dimensions [Formula: see text] and in two dimensions [Formula: see text], where a CFL condition is required. Then, in two dimensions [Formula: see text], we pass to the limit in the discretization parameters and show that subsequences of discrete solutions converge to a global-in-time weak solution. Finally, we present numerical results in two dimensions [Formula: see text]. </jats:p>"}],"publication":"Mathematical Models and Methods in Applied Sciences","issue":"13","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Modeling and Simulation"],"type":"journal_article","date_created":"2023-07-10T11:47:27Z","intvolume":"        32","publication_status":"published","date_updated":"2024-04-03T09:15:35Z","author":[{"first_name":"Harald","last_name":"Garcke","full_name":"Garcke, Harald"},{"full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","id":"100441"},{"first_name":"Dennis","last_name":"Trautwein","full_name":"Trautwein, Dennis"}],"publication_identifier":{"issn":["0218-2025","1793-6314"]},"title":"Viscoelastic Cahn–Hilliard models for tumor growth","year":"2022","doi":"10.1142/s0218202522500634","language":[{"iso":"eng"}],"citation":{"mla":"Garcke, Harald, et al. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 32, no. 13, World Scientific Pub Co Pte Ltd, 2022, pp. 2673–758, doi:<a href=\"https://doi.org/10.1142/s0218202522500634\">10.1142/s0218202522500634</a>.","ama":"Garcke H, Kovács B, Trautwein D. Viscoelastic Cahn–Hilliard models for tumor growth. <i>Mathematical Models and Methods in Applied Sciences</i>. 2022;32(13):2673-2758. doi:<a href=\"https://doi.org/10.1142/s0218202522500634\">10.1142/s0218202522500634</a>","bibtex":"@article{Garcke_Kovács_Trautwein_2022, title={Viscoelastic Cahn–Hilliard models for tumor growth}, volume={32}, DOI={<a href=\"https://doi.org/10.1142/s0218202522500634\">10.1142/s0218202522500634</a>}, number={13}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Garcke, Harald and Kovács, Balázs and Trautwein, Dennis}, year={2022}, pages={2673–2758} }","apa":"Garcke, H., Kovács, B., &#38; Trautwein, D. (2022). Viscoelastic Cahn–Hilliard models for tumor growth. <i>Mathematical Models and Methods in Applied Sciences</i>, <i>32</i>(13), 2673–2758. <a href=\"https://doi.org/10.1142/s0218202522500634\">https://doi.org/10.1142/s0218202522500634</a>","ieee":"H. Garcke, B. Kovács, and D. Trautwein, “Viscoelastic Cahn–Hilliard models for tumor growth,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 32, no. 13, pp. 2673–2758, 2022, doi: <a href=\"https://doi.org/10.1142/s0218202522500634\">10.1142/s0218202522500634</a>.","chicago":"Garcke, Harald, Balázs Kovács, and Dennis Trautwein. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.” <i>Mathematical Models and Methods in Applied Sciences</i> 32, no. 13 (2022): 2673–2758. <a href=\"https://doi.org/10.1142/s0218202522500634\">https://doi.org/10.1142/s0218202522500634</a>.","short":"H. Garcke, B. Kovács, D. Trautwein, Mathematical Models and Methods in Applied Sciences 32 (2022) 2673–2758."},"status":"public","volume":32,"user_id":"100441","_id":"45970","publisher":"World Scientific Pub Co Pte Ltd","page":"2673-2758"},{"page":"873-925","publisher":"Springer Science and Business Media LLC","_id":"45969","user_id":"100441","volume":151,"status":"public","citation":{"bibtex":"@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces}, volume={151}, DOI={<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs}, year={2022}, pages={873–925} }","ama":"Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. <i>Numerische Mathematik</i>. 2022;151(4):873-925. doi:<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>","mla":"Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.” <i>Numerische Mathematik</i>, vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:<a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>.","chicago":"Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.” <i>Numerische Mathematik</i> 151, no. 4 (2022): 873–925. <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">https://doi.org/10.1007/s00211-022-01301-3</a>.","short":"C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.","ieee":"C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces,” <i>Numerische Mathematik</i>, vol. 151, no. 4, pp. 873–925, 2022, doi: <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">10.1007/s00211-022-01301-3</a>.","apa":"Elliott, C. M., Garcke, H., &#38; Kovács, B. (2022). Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. <i>Numerische Mathematik</i>, <i>151</i>(4), 873–925. <a href=\"https://doi.org/10.1007/s00211-022-01301-3\">https://doi.org/10.1007/s00211-022-01301-3</a>"},"language":[{"iso":"eng"}],"doi":"10.1007/s00211-022-01301-3","year":"2022","title":"Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces","publication_identifier":{"issn":["0029-599X","0945-3245"]},"author":[{"last_name":"Elliott","first_name":"Charles M.","full_name":"Elliott, Charles M."},{"first_name":"Harald","last_name":"Garcke","full_name":"Garcke, Harald"},{"id":"100441","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs","full_name":"Kovács, Balázs"}],"date_updated":"2024-04-03T09:15:44Z","publication_status":"published","intvolume":"       151","date_created":"2023-07-10T11:47:11Z","keyword":["Applied Mathematics","Computational Mathematics"],"type":"journal_article","department":[{"_id":"841"}],"publication":"Numerische Mathematik","issue":"4","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms are proposed, both based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface. One of the numerical methods is proved to be convergent in the<jats:inline-formula><jats:alternatives><jats:tex-math>$$H^1$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>norm with optimal-order for finite elements of degree at least two. We present numerical experiments illustrating the convergence behaviour and demonstrating the qualitative properties of the flow: preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections.</jats:p>","lang":"eng"}]},{"citation":{"mla":"Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.” <i>Numerische Mathematik</i>, vol. 150, no. 4, Springer Science and Business Media LLC, 2022, pp. 1123–64, doi:<a href=\"https://doi.org/10.1007/s00211-022-01277-0\">10.1007/s00211-022-01277-0</a>.","bibtex":"@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic scattering from thin layers}, volume={150}, DOI={<a href=\"https://doi.org/10.1007/s00211-022-01277-0\">10.1007/s00211-022-01277-0</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2022}, pages={1123–1164} }","ama":"Nick J, Kovács B, Lubich C. Time-dependent electromagnetic scattering from thin layers. <i>Numerische Mathematik</i>. 2022;150(4):1123-1164. doi:<a href=\"https://doi.org/10.1007/s00211-022-01277-0\">10.1007/s00211-022-01277-0</a>","ieee":"J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering from thin layers,” <i>Numerische Mathematik</i>, vol. 150, no. 4, pp. 1123–1164, 2022, doi: <a href=\"https://doi.org/10.1007/s00211-022-01277-0\">10.1007/s00211-022-01277-0</a>.","apa":"Nick, J., Kovács, B., &#38; Lubich, C. (2022). Time-dependent electromagnetic scattering from thin layers. <i>Numerische Mathematik</i>, <i>150</i>(4), 1123–1164. <a href=\"https://doi.org/10.1007/s00211-022-01277-0\">https://doi.org/10.1007/s00211-022-01277-0</a>","chicago":"Nick, Jörg, Balázs Kovács, and Christian Lubich. “Time-Dependent Electromagnetic Scattering from Thin Layers.” <i>Numerische Mathematik</i> 150, no. 4 (2022): 1123–64. <a href=\"https://doi.org/10.1007/s00211-022-01277-0\">https://doi.org/10.1007/s00211-022-01277-0</a>.","short":"J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164."},"status":"public","user_id":"100441","volume":150,"page":"1123-1164","publisher":"Springer Science and Business Media LLC","_id":"45963","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this includes a thin coating around a perfect conductor and the skin effect of a highly conducting material. The approach taken in this work is to derive, analyse and discretize a system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. In a familiar second step, the fields are evaluated in the exterior domain by a representation formula, which uses the time-dependent potential operators of Maxwell’s equations. The time-dependent boundary integral equation is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas boundary elements in space. Using the frequency-explicit bounds from the well-posedness analysis given here together with known approximation properties of the numerical methods, the full discretization is proved to be stable and convergent, with explicitly given rates in the case of sufficient regularity. Taking the same Runge–Kutta based convolution quadrature for discretizing the time-dependent representation formulas, the optimal order of convergence is obtained away from the scattering boundary, whereas an order reduction occurs close to the boundary. The theoretical results are illustrated by numerical experiments.</jats:p>"}],"publication":"Numerische Mathematik","issue":"4","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"],"department":[{"_id":"841"}],"date_created":"2023-07-10T11:44:57Z","publication_status":"published","date_updated":"2024-04-03T09:18:23Z","intvolume":"       150","title":"Time-dependent electromagnetic scattering from thin layers","year":"2022","publication_identifier":{"issn":["0029-599X","0945-3245"]},"author":[{"last_name":"Nick","first_name":"Jörg","full_name":"Nick, Jörg"},{"last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441"},{"first_name":"Christian","last_name":"Lubich","full_name":"Lubich, Christian"}],"doi":"10.1007/s00211-022-01277-0","language":[{"iso":"eng"}]},{"citation":{"ieee":"B. Kovács and B. Li, “Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems,” <i>IMA Journal of Numerical Analysis</i>, 2022, doi: <a href=\"https://doi.org/10.1093/imanum/drac033\">10.1093/imanum/drac033</a>.","apa":"Kovács, B., &#38; Li, B. (2022). Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. <i>IMA Journal of Numerical Analysis</i>. <a href=\"https://doi.org/10.1093/imanum/drac033\">https://doi.org/10.1093/imanum/drac033</a>","short":"B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).","chicago":"Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” <i>IMA Journal of Numerical Analysis</i>, 2022. <a href=\"https://doi.org/10.1093/imanum/drac033\">https://doi.org/10.1093/imanum/drac033</a>.","mla":"Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” <i>IMA Journal of Numerical Analysis</i>, Oxford University Press (OUP), 2022, doi:<a href=\"https://doi.org/10.1093/imanum/drac033\">10.1093/imanum/drac033</a>.","bibtex":"@article{Kovács_Li_2022, title={Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems}, DOI={<a href=\"https://doi.org/10.1093/imanum/drac033\">10.1093/imanum/drac033</a>}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }","ama":"Kovács B, Li B. Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. <i>IMA Journal of Numerical Analysis</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1093/imanum/drac033\">10.1093/imanum/drac033</a>"},"publication":"IMA Journal of Numerical Analysis","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations of linear parabolic equations on an evolving surface along characteristic trajectories can preserve maximal $L^p$-regularity in the discrete setting. The result is applied to prove the stability and convergence of time discretizations of nonlinear parabolic equations on an evolving surface, with linearly implicit backward differentiation formulae characteristic trajectories of the surface, for general locally Lipschitz nonlinearities. The discrete maximal $L^p$-regularity is used to prove the boundedness and stability of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is used to bound the nonlinear terms in the stability analysis. Optimal-order error estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm is obtained by combining the stability analysis with the consistency estimates.</jats:p>"}],"date_created":"2023-07-10T11:45:14Z","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","author":[{"id":"100441","first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","full_name":"Kovács, Balázs"},{"full_name":"Li, Buyang","first_name":"Buyang","last_name":"Li"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"status":"public","year":"2022","title":"Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems","date_updated":"2024-04-03T09:17:59Z","publication_status":"published","_id":"45964","publisher":"Oxford University Press (OUP)","language":[{"iso":"eng"}],"doi":"10.1093/imanum/drac033","user_id":"100441"},{"citation":{"chicago":"Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i> 43, no. 2 (2022): 950–75. <a href=\"https://doi.org/10.1093/imanum/drac002\">https://doi.org/10.1093/imanum/drac002</a>.","short":"R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022) 950–975.","ieee":"R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, vol. 43, no. 2, pp. 950–975, 2022, doi: <a href=\"https://doi.org/10.1093/imanum/drac002\">10.1093/imanum/drac002</a>.","apa":"Altmann, R., Kovács, B., &#38; Zimmer, C. (2022). Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>, <i>43</i>(2), 950–975. <a href=\"https://doi.org/10.1093/imanum/drac002\">https://doi.org/10.1093/imanum/drac002</a>","bibtex":"@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={<a href=\"https://doi.org/10.1093/imanum/drac002\">10.1093/imanum/drac002</a>}, number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022}, pages={950–975} }","ama":"Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2022;43(2):950-975. doi:<a href=\"https://doi.org/10.1093/imanum/drac002\">10.1093/imanum/drac002</a>","mla":"Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol. 43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:<a href=\"https://doi.org/10.1093/imanum/drac002\">10.1093/imanum/drac002</a>."},"status":"public","volume":43,"user_id":"100441","publisher":"Oxford University Press (OUP)","_id":"45966","page":"950-975","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>This paper studies bulk–surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential–algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk problem. The splitting approach is combined with bulk–surface finite elements and an implicit Euler discretization of the two subsystems. We prove first-order convergence of the resulting fully discrete scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c h$ for some constant $c&amp;gt;0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen–Cahn type.</jats:p>"}],"publication":"IMA Journal of Numerical Analysis","issue":"2","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","date_created":"2023-07-10T11:45:49Z","intvolume":"        43","date_updated":"2024-04-03T09:16:47Z","publication_status":"published","author":[{"full_name":"Altmann, Robert","first_name":"Robert","last_name":"Altmann"},{"full_name":"Kovács, Balázs","first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","id":"100441"},{"last_name":"Zimmer","first_name":"Christoph","full_name":"Zimmer, Christoph"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"year":"2022","title":"Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions","doi":"10.1093/imanum/drac002","language":[{"iso":"eng"}]},{"publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"last_name":"Csomós","first_name":"Petra","full_name":"Csomós, Petra"},{"last_name":"Farkas","first_name":"Bálint","full_name":"Farkas, Bálint"},{"id":"100441","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs"}],"status":"public","title":"Error estimates for a splitting integrator for abstract semilinear boundary coupled systems","year":"2022","date_updated":"2024-04-03T09:15:52Z","publication_status":"published","_id":"45968","language":[{"iso":"eng"}],"publisher":"Oxford University Press (OUP)","doi":"10.1093/imanum/drac079","user_id":"100441","citation":{"ieee":"P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator for abstract semilinear boundary coupled systems,” <i>IMA Journal of Numerical Analysis</i>, 2022, doi: <a href=\"https://doi.org/10.1093/imanum/drac079\">10.1093/imanum/drac079</a>.","apa":"Csomós, P., Farkas, B., &#38; Kovács, B. (2022). Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. <i>IMA Journal of Numerical Analysis</i>. <a href=\"https://doi.org/10.1093/imanum/drac079\">https://doi.org/10.1093/imanum/drac079</a>","chicago":"Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” <i>IMA Journal of Numerical Analysis</i>, 2022. <a href=\"https://doi.org/10.1093/imanum/drac079\">https://doi.org/10.1093/imanum/drac079</a>.","short":"P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).","mla":"Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” <i>IMA Journal of Numerical Analysis</i>, Oxford University Press (OUP), 2022, doi:<a href=\"https://doi.org/10.1093/imanum/drac079\">10.1093/imanum/drac079</a>.","bibtex":"@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting integrator for abstract semilinear boundary coupled systems}, DOI={<a href=\"https://doi.org/10.1093/imanum/drac079\">10.1093/imanum/drac079</a>}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022} }","ama":"Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. <i>IMA Journal of Numerical Analysis</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1093/imanum/drac079\">10.1093/imanum/drac079</a>"},"publication":"IMA Journal of Numerical Analysis","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.</jats:p>","lang":"eng"}],"date_created":"2023-07-10T11:46:54Z","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article"}]