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Vol 3. ; 2022:347–354.","bibtex":"@inproceedings{Schönherr_Schukajlow_Leopold_2022, title={Drawing instructions, strategic knowledge, strategy-based motivation, and students’ use of drawings}, volume={3}, booktitle={Proceedings of the 45th PME Conference}, author={Schönherr, Johanna and Schukajlow, S. and Leopold, C.}, year={2022}, pages={347–354} }"},"type":"conference","department":[{"_id":"913"}],"date_created":"2023-05-29T17:34:03Z"},{"date_created":"2024-07-16T11:09:01Z","department":[{"_id":"102"}],"type":"journal_article","citation":{"ama":"Elsholtz Ch, Klahn B, Technau M. On polynomials with roots modulo almost all primes. <i>Acta Arith</i>. 2022;205:3(3):251–263. doi:<a href=\"https://doi.org/10.4064/aa220407-9-7\">10.4064/aa220407-9-7</a>","bibtex":"@article{Elsholtz_Klahn_Technau_2022, title={On polynomials with roots modulo almost all primes}, volume={205:3}, DOI={<a href=\"https://doi.org/10.4064/aa220407-9-7\">10.4064/aa220407-9-7</a>}, number={3}, journal={Acta Arith.}, author={Elsholtz, Ch. and Klahn, B. and Technau, Marc}, year={2022}, pages={251–263} }","mla":"Elsholtz, Ch., et al. “On Polynomials with Roots modulo Almost All Primes.” <i>Acta Arith.</i>, vol. 205:3, no. 3, 2022, pp. 251–263, doi:<a href=\"https://doi.org/10.4064/aa220407-9-7\">10.4064/aa220407-9-7</a>.","short":"Ch. Elsholtz, B. Klahn, M. Technau, Acta Arith. 205:3 (2022) 251–263.","chicago":"Elsholtz, Ch., B. Klahn, and Marc Technau. “On Polynomials with Roots modulo Almost All Primes.” <i>Acta Arith.</i> 205:3, no. 3 (2022): 251–263. <a href=\"https://doi.org/10.4064/aa220407-9-7\">https://doi.org/10.4064/aa220407-9-7</a>.","apa":"Elsholtz, Ch., Klahn, B., &#38; Technau, M. (2022). On polynomials with roots modulo almost all primes. <i>Acta Arith.</i>, <i>205:3</i>(3), 251–263. <a href=\"https://doi.org/10.4064/aa220407-9-7\">https://doi.org/10.4064/aa220407-9-7</a>","ieee":"Ch. Elsholtz, B. Klahn, and M. Technau, “On polynomials with roots modulo almost all primes,” <i>Acta Arith.</i>, vol. 205:3, no. 3, pp. 251–263, 2022, doi: <a href=\"https://doi.org/10.4064/aa220407-9-7\">10.4064/aa220407-9-7</a>."},"issue":"3","publication":"Acta Arith.","extern":"1","_id":"55280","language":[{"iso":"eng"}],"page":"251–263","volume":"205:3","user_id":"106108","doi":"10.4064/aa220407-9-7","author":[{"full_name":"Elsholtz, Ch.","last_name":"Elsholtz","first_name":"Ch."},{"first_name":"B.","last_name":"Klahn","full_name":"Klahn, B."},{"id":"106108","first_name":"Marc","last_name":"Technau","orcid":"0000-0001-9650-2459","full_name":"Technau, Marc"}],"year":"2022","title":"On polynomials with roots modulo almost all primes","status":"public","date_updated":"2024-07-24T07:26:22Z"},{"date_created":"2023-01-10T08:50:47Z","department":[{"_id":"363"},{"_id":"67"}],"type":"conference","citation":{"bibtex":"@inproceedings{Fleischer_Hüsing_Biehler_Podworny_Schulte_2022, title={Jupyter Notebooks for Teaching, Learning, and Doing Data Science}, DOI={<a href=\"https://doi.org/10.52041/iase.icots11.t10e3\">10.52041/iase.icots11.t10e3</a>}, booktitle={Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics}, publisher={International Association for Statistical Education}, author={Fleischer, Franz Yannik and Hüsing, Sven and Biehler, Rolf and Podworny, Susanne and Schulte, Carsten}, editor={Peters, S. A. and Zapata-Cardona, L. and Bonafini, F. and Fan, A.}, year={2022} }","ama":"Fleischer FY, Hüsing S, Biehler R, Podworny S, Schulte C. Jupyter Notebooks for Teaching, Learning, and Doing Data Science. In: Peters SA, Zapata-Cardona L, Bonafini F, Fan A, eds. <i>Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics</i>. International Association for Statistical Education; 2022. doi:<a href=\"https://doi.org/10.52041/iase.icots11.t10e3\">10.52041/iase.icots11.t10e3</a>","mla":"Fleischer, Franz Yannik, et al. “Jupyter Notebooks for Teaching, Learning, and Doing Data Science.” <i>Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics</i>, edited by S. A. Peters et al., International Association for Statistical Education, 2022, doi:<a href=\"https://doi.org/10.52041/iase.icots11.t10e3\">10.52041/iase.icots11.t10e3</a>.","short":"F.Y. Fleischer, S. Hüsing, R. Biehler, S. Podworny, C. Schulte, in: S.A. Peters, L. Zapata-Cardona, F. Bonafini, A. Fan (Eds.), Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics, International Association for Statistical Education, 2022.","chicago":"Fleischer, Franz Yannik, Sven Hüsing, Rolf Biehler, Susanne Podworny, and Carsten Schulte. “Jupyter Notebooks for Teaching, Learning, and Doing Data Science.” In <i>Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics</i>, edited by S. A. Peters, L. Zapata-Cardona, F. Bonafini, and A. Fan. International Association for Statistical Education, 2022. <a href=\"https://doi.org/10.52041/iase.icots11.t10e3\">https://doi.org/10.52041/iase.icots11.t10e3</a>.","ieee":"F. Y. Fleischer, S. Hüsing, R. Biehler, S. Podworny, and C. Schulte, “Jupyter Notebooks for Teaching, Learning, and Doing Data Science,” in <i>Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics</i>, 2022, doi: <a href=\"https://doi.org/10.52041/iase.icots11.t10e3\">10.52041/iase.icots11.t10e3</a>.","apa":"Fleischer, F. Y., Hüsing, S., Biehler, R., Podworny, S., &#38; Schulte, C. (2022). Jupyter Notebooks for Teaching, Learning, and Doing Data Science. In S. A. Peters, L. Zapata-Cardona, F. Bonafini, &#38; A. Fan (Eds.), <i>Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics</i>. International Association for Statistical Education. <a href=\"https://doi.org/10.52041/iase.icots11.t10e3\">https://doi.org/10.52041/iase.icots11.t10e3</a>"},"publication":"Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference on Teaching Statistics","abstract":[{"text":"<jats:p>We report on our work with students in our data science courses, focusing on the analysis of students’ results. This study represents an in-depth analysis of students’ creation and documentation of machine learning models. The students were supported by educationally designed Jupyter Notebooks, which are used as worked examples. Using the worked example, students document their results in a so-called computational essay. We examine which aspects of creating computational essays are difficult for students to find out how worked examples should be designed to support students without being too prescriptive. We analyze the computational essays produced by students and draw consequences for redesigning our worked example.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"_id":"35674","publisher":"International Association for Statistical Education","editor":[{"last_name":"Peters","first_name":"S. A.","full_name":"Peters, S. A."},{"last_name":"Zapata-Cardona","first_name":"L.","full_name":"Zapata-Cardona, L."},{"full_name":"Bonafini, F.","first_name":"F.","last_name":"Bonafini"},{"full_name":"Fan, A.","first_name":"A.","last_name":"Fan"}],"doi":"10.52041/iase.icots11.t10e3","user_id":"37888","author":[{"last_name":"Fleischer","first_name":"Franz Yannik","orcid":"https://orcid.org/0000-0003-0318-0329","full_name":"Fleischer, Franz Yannik","id":"42660"},{"id":"58465","full_name":"Hüsing, Sven","last_name":"Hüsing","first_name":"Sven"},{"last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf","id":"16274"},{"id":"30619","first_name":"Susanne","orcid":"0000-0002-6313-5987","last_name":"Podworny","full_name":"Podworny, Susanne"},{"id":"60311","first_name":"Carsten","last_name":"Schulte","full_name":"Schulte, Carsten"}],"year":"2022","status":"public","title":"Jupyter Notebooks for Teaching, Learning, and Doing Data Science","date_updated":"2024-08-21T10:03:47Z","publication_status":"published"},{"article_number":"7","language":[{"iso":"eng"}],"doi":"10.52041/serj.v21i2.61","title":"Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks","year":"2022","publication_identifier":{"issn":["1570-1824"]},"author":[{"id":"42660","full_name":"Fleischer, Franz Yannik","last_name":"Fleischer","orcid":"https://orcid.org/0000-0003-0318-0329","first_name":"Franz Yannik"},{"id":"16274","last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf"},{"id":"60311","first_name":"Carsten","last_name":"Schulte","full_name":"Schulte, Carsten"}],"date_updated":"2024-08-21T10:04:41Z","publication_status":"published","intvolume":"        21","date_created":"2023-01-10T08:48:23Z","keyword":["Education","Statistics and Probability"],"type":"journal_article","department":[{"_id":"363"},{"_id":"67"}],"issue":"2","publication":"Statistics Education Research Journal","abstract":[{"lang":"eng","text":"<jats:p>This study examines modelling with machine learning. In the context of a yearlong data science course, the study explores how upper secondary students apply machine learning with Jupyter Notebooks and document the modelling process as a computational essay incorporating the different steps of the CRISP-DM cycle. The students’ work is based on a teaching module about decision trees in machine learning and a worked example of such a modelling process. The study outlines the students’ performance in carrying out the machine learning technically and reasoning about bias in the data, different data preparation steps, the application context, and the resulting decision model. Furthermore, the context of the study and the theoretical backgrounds are presented.</jats:p>"}],"_id":"35672","publisher":"International Association for Statistical Education","user_id":"37888","volume":21,"status":"public","citation":{"ieee":"F. Y. Fleischer, R. Biehler, and C. Schulte, “Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks,” <i>Statistics Education Research Journal</i>, vol. 21, no. 2, Art. no. 7, 2022, doi: <a href=\"https://doi.org/10.52041/serj.v21i2.61\">10.52041/serj.v21i2.61</a>.","apa":"Fleischer, F. Y., Biehler, R., &#38; Schulte, C. (2022). Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks. <i>Statistics Education Research Journal</i>, <i>21</i>(2), Article 7. <a href=\"https://doi.org/10.52041/serj.v21i2.61\">https://doi.org/10.52041/serj.v21i2.61</a>","short":"F.Y. Fleischer, R. Biehler, C. Schulte, Statistics Education Research Journal 21 (2022).","chicago":"Fleischer, Franz Yannik, Rolf Biehler, and Carsten Schulte. “Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks.” <i>Statistics Education Research Journal</i> 21, no. 2 (2022). <a href=\"https://doi.org/10.52041/serj.v21i2.61\">https://doi.org/10.52041/serj.v21i2.61</a>.","mla":"Fleischer, Franz Yannik, et al. “Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks.” <i>Statistics Education Research Journal</i>, vol. 21, no. 2, 7, International Association for Statistical Education, 2022, doi:<a href=\"https://doi.org/10.52041/serj.v21i2.61\">10.52041/serj.v21i2.61</a>.","bibtex":"@article{Fleischer_Biehler_Schulte_2022, title={Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks}, volume={21}, DOI={<a href=\"https://doi.org/10.52041/serj.v21i2.61\">10.52041/serj.v21i2.61</a>}, number={27}, journal={Statistics Education Research Journal}, publisher={International Association for Statistical Education}, author={Fleischer, Franz Yannik and Biehler, Rolf and Schulte, Carsten}, year={2022} }","ama":"Fleischer FY, Biehler R, Schulte C. Teaching and Learning Data-Driven Machine Learning with Educationally Designed Jupyter Notebooks. <i>Statistics Education Research Journal</i>. 2022;21(2). doi:<a href=\"https://doi.org/10.52041/serj.v21i2.61\">10.52041/serj.v21i2.61</a>"}},{"date_created":"2023-01-18T22:22:25Z","type":"journal_article","keyword":["General Mathematics","Education"],"department":[{"_id":"10"}],"publication":"ZDM – Mathematics Education","citation":{"mla":"Liebendörfer, Michael, et al. “First-Year University Students’ Self-Regulated Learning during the COVID-19 Pandemic: A Qualitative Longitudinal Study.” <i>ZDM – Mathematics Education</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s11858-022-01444-5\">10.1007/s11858-022-01444-5</a>.","bibtex":"@article{Liebendörfer_Kempen_Schukajlow_2022, title={First-year university students’ self-regulated learning during the COVID-19 pandemic: a qualitative longitudinal study}, DOI={<a href=\"https://doi.org/10.1007/s11858-022-01444-5\">10.1007/s11858-022-01444-5</a>}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Liebendörfer, Michael and Kempen, Leander and Schukajlow, Stanislaw}, year={2022} }","ama":"Liebendörfer M, Kempen L, Schukajlow S. First-year university students’ self-regulated learning during the COVID-19 pandemic: a qualitative longitudinal study. <i>ZDM – Mathematics Education</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s11858-022-01444-5\">10.1007/s11858-022-01444-5</a>","ieee":"M. Liebendörfer, L. Kempen, and S. Schukajlow, “First-year university students’ self-regulated learning during the COVID-19 pandemic: a qualitative longitudinal study,” <i>ZDM – Mathematics Education</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s11858-022-01444-5\">10.1007/s11858-022-01444-5</a>.","apa":"Liebendörfer, M., Kempen, L., &#38; Schukajlow, S. (2022). First-year university students’ self-regulated learning during the COVID-19 pandemic: a qualitative longitudinal study. <i>ZDM – Mathematics Education</i>. <a href=\"https://doi.org/10.1007/s11858-022-01444-5\">https://doi.org/10.1007/s11858-022-01444-5</a>","short":"M. Liebendörfer, L. Kempen, S. Schukajlow, ZDM – Mathematics Education (2022).","chicago":"Liebendörfer, Michael, Leander Kempen, and Stanislaw Schukajlow. “First-Year University Students’ Self-Regulated Learning during the COVID-19 Pandemic: A Qualitative Longitudinal Study.” <i>ZDM – Mathematics Education</i>, 2022. <a href=\"https://doi.org/10.1007/s11858-022-01444-5\">https://doi.org/10.1007/s11858-022-01444-5</a>."},"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>When the COVID-19 pandemic began, many universities switched to fully online teaching. This unexpected switching to online teaching was challenging for both teachers and students, and restrictions that were put in place because of pandemic made this challenge even greater. However, new ways of teaching might also open new opportunities for students’ learning. The research question driving our study was as follows: how do students regulate their learning and specifically their choice of resources and peer learning in university mathematics classes that are fully taught online as offered during the COVID-19 pandemic? We report on a longitudinal, qualitative study in which students recorded a brief audio diary twice a week over one whole semester (14 weeks). We focused on three students who completed 70 interviews in total and finished the semester with varying degrees of success. The results show how the students structured their studying (e.g., the roles that deadlines or synchronous teaching events played). They illustrate the strengths and limitations of digital materials provided by the lecturer and the use of complementary media. Further, the pandemic uncovered the double-edged role of simple, often anonymous exchanges (e.g., via Discord servers), with few binding forces for either side, and the significance of stable learning partnerships for students’ success. Our research highlights aspects that should be focal points when comparing traditional instruction and online instruction during the pandemic from a self-regulatory perspective. Practical implications refer to how these aspects can be combined sensibly in fully online courses, but also in blended learning contexts.</jats:p>"}],"_id":"37470","language":[{"iso":"eng"}],"publisher":"Springer Science and Business Media LLC","doi":"10.1007/s11858-022-01444-5","user_id":"30933","status":"public","year":"2022","title":"First-year university students' self-regulated learning during the COVID-19 pandemic: a qualitative longitudinal study","author":[{"full_name":"Liebendörfer, Michael","last_name":"Liebendörfer","first_name":"Michael"},{"first_name":"Leander","last_name":"Kempen","full_name":"Kempen, Leander"},{"full_name":"Schukajlow, Stanislaw","first_name":"Stanislaw","last_name":"Schukajlow"}],"publication_identifier":{"issn":["1863-9690","1863-9704"]},"date_updated":"2023-01-18T22:44:06Z","publication_status":"published"},{"_id":"37472","language":[{"iso":"eng"}],"publisher":"Springer Science and Business Media LLC","user_id":"30933","doi":"10.1007/s40753-022-00188-7","title":"Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students","year":"2022","status":"public","author":[{"first_name":"Christiane","last_name":"Büdenbender-Kuklinski","full_name":"Büdenbender-Kuklinski, Christiane"},{"full_name":"Hochmuth, Reinhard","last_name":"Hochmuth","first_name":"Reinhard"},{"full_name":"Liebendörfer, Michael","first_name":"Michael","last_name":"Liebendörfer"}],"publication_identifier":{"issn":["2198-9745","2198-9753"]},"publication_status":"published","date_updated":"2023-01-18T22:43:43Z","date_created":"2023-01-18T22:22:49Z","type":"journal_article","keyword":["Education","Mathematics (miscellaneous)"],"department":[{"_id":"10"}],"publication":"International Journal of Research in Undergraduate Mathematics Education","citation":{"ieee":"C. Büdenbender-Kuklinski, R. Hochmuth, and M. Liebendörfer, “Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students,” <i>International Journal of Research in Undergraduate Mathematics Education</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s40753-022-00188-7\">10.1007/s40753-022-00188-7</a>.","mla":"Büdenbender-Kuklinski, Christiane, et al. “Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students.” <i>International Journal of Research in Undergraduate Mathematics Education</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s40753-022-00188-7\">10.1007/s40753-022-00188-7</a>.","apa":"Büdenbender-Kuklinski, C., Hochmuth, R., &#38; Liebendörfer, M. (2022). Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students. <i>International Journal of Research in Undergraduate Mathematics Education</i>. <a href=\"https://doi.org/10.1007/s40753-022-00188-7\">https://doi.org/10.1007/s40753-022-00188-7</a>","bibtex":"@article{Büdenbender-Kuklinski_Hochmuth_Liebendörfer_2022, title={Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students}, DOI={<a href=\"https://doi.org/10.1007/s40753-022-00188-7\">10.1007/s40753-022-00188-7</a>}, journal={International Journal of Research in Undergraduate Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Büdenbender-Kuklinski, Christiane and Hochmuth, Reinhard and Liebendörfer, Michael}, year={2022} }","chicago":"Büdenbender-Kuklinski, Christiane, Reinhard Hochmuth, and Michael Liebendörfer. “Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students.” <i>International Journal of Research in Undergraduate Mathematics Education</i>, 2022. <a href=\"https://doi.org/10.1007/s40753-022-00188-7\">https://doi.org/10.1007/s40753-022-00188-7</a>.","ama":"Büdenbender-Kuklinski C, Hochmuth R, Liebendörfer M. Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students. <i>International Journal of Research in Undergraduate Mathematics Education</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s40753-022-00188-7\">10.1007/s40753-022-00188-7</a>","short":"C. Büdenbender-Kuklinski, R. Hochmuth, M. Liebendörfer, International Journal of Research in Undergraduate Mathematics Education (2022)."},"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>As earlier research results suggest that many mathematics teaching students criticize a missing relevance in their studies, we explore explanations and interrelationships of their relevance assessments. We aim at finding out how one could support the students in attributing relevance to their study programs. A two-fold model for relevance assessments in mathematics teacher education is proposed, consisting of relevance content and relevance reasons. We investigate students' relevance perceptions of mathematical topics and of topics’ complexities, as well as their rating of individual and societal/ vocational relevance reasons, all in relation to their perception of the relevance of their overall program of study. Contrary to earlier research findings, our results suggest that mathematics teaching students already do attribute relevance to many content areas and that a preparation for the teaching profession is not the only reason for them to assign relevance. There also seem to be many students who would attribute relevance if they could develop as individuals and pursue their interests. We suggest that giving students opportunities to set individual priorities in their studies could hence support their relevance assessments. As low relevance assessments seem to be connected to students’ motivational problems, students might profit from motivational support, as well.</jats:p>"}]},{"date_updated":"2023-01-20T13:18:15Z","intvolume":"        35","year":"2022","title":"Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary","status":"public","author":[{"first_name":"Johannes","last_name":"Lankeit","full_name":"Lankeit, Johannes"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael","id":"31496"}],"user_id":"15645","volume":35,"page":"719-749","_id":"35528","language":[{"iso":"eng"}],"publication":"Nonlinearity","citation":{"short":"J. Lankeit, M. Winkler, Nonlinearity 35 (2022) 719–749.","chicago":"Lankeit, Johannes, and Michael Winkler. “Radial Solutions to a Chemotaxis-Consumption Model Involving Prescribed Signal Concentrations on the Boundary.” <i>Nonlinearity</i> 35 (2022): 719–49.","ieee":"J. Lankeit and M. Winkler, “Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary,” <i>Nonlinearity</i>, vol. 35, pp. 719–749, 2022.","apa":"Lankeit, J., &#38; Winkler, M. (2022). Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary. <i>Nonlinearity</i>, <i>35</i>, 719–749.","bibtex":"@article{Lankeit_Winkler_2022, title={Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary}, volume={35}, journal={Nonlinearity}, author={Lankeit, Johannes and Winkler, Michael}, year={2022}, pages={719–749} }","ama":"Lankeit J, Winkler M. Radial solutions to a chemotaxis-consumption model involving prescribed signal concentrations on the boundary. <i>Nonlinearity</i>. 2022;35:719-749.","mla":"Lankeit, Johannes, and Michael Winkler. “Radial Solutions to a Chemotaxis-Consumption Model Involving Prescribed Signal Concentrations on the Boundary.” <i>Nonlinearity</i>, vol. 35, 2022, pp. 719–49."},"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2023-01-09T15:33:38Z"},{"intvolume":"       389","date_updated":"2023-01-20T13:17:37Z","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael","id":"31496"}],"status":"public","year":"2022","title":"Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction.","volume":389,"user_id":"15645","language":[{"iso":"eng"}],"_id":"35568","page":"439-489","citation":{"chicago":"Winkler, Michael. “Reaction-Driven Relaxation in Threee-Dimensional Keller-Segel-Navier-Stokes Interaction.” <i>Communications in Mathematical Physics</i> 389 (2022): 439–89.","short":"M. Winkler, Communications in Mathematical Physics 389 (2022) 439–489.","apa":"Winkler, M. (2022). Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction. <i>Communications in Mathematical Physics</i>, <i>389</i>, 439–489.","ieee":"M. Winkler, “Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction.,” <i>Communications in Mathematical Physics</i>, vol. 389, pp. 439–489, 2022.","ama":"Winkler M. Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction. <i>Communications in Mathematical Physics</i>. 2022;389:439-489.","bibtex":"@article{Winkler_2022, title={Reaction-driven relaxation in threee-dimensional Keller-Segel-Navier-Stokes interaction.}, volume={389}, journal={Communications in Mathematical Physics}, author={Winkler, Michael}, year={2022}, pages={439–489} }","mla":"Winkler, Michael. “Reaction-Driven Relaxation in Threee-Dimensional Keller-Segel-Navier-Stokes Interaction.” <i>Communications in Mathematical Physics</i>, vol. 389, 2022, pp. 439–89."},"publication":"Communications in Mathematical Physics","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","date_created":"2023-01-09T16:32:21Z"},{"date_created":"2023-01-09T16:35:09Z","type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Proceedings of the London Mathematical Society","citation":{"apa":"Winkler, M. (2022). A family of mass-critical Keller-Segel systems. <i>Proceedings of the London Mathematical Society</i>, <i>124</i>, 133–181.","ieee":"M. Winkler, “A family of mass-critical Keller-Segel systems.,” <i>Proceedings of the London Mathematical Society</i>, vol. 124, pp. 133–181, 2022.","short":"M. Winkler, Proceedings of the London Mathematical Society 124 (2022) 133–181.","chicago":"Winkler, Michael. “A Family of Mass-Critical Keller-Segel Systems.” <i>Proceedings of the London Mathematical Society</i> 124 (2022): 133–81.","mla":"Winkler, Michael. “A Family of Mass-Critical Keller-Segel Systems.” <i>Proceedings of the London Mathematical Society</i>, vol. 124, 2022, pp. 133–81.","ama":"Winkler M. A family of mass-critical Keller-Segel systems. <i>Proceedings of the London Mathematical Society</i>. 2022;124:133-181.","bibtex":"@article{Winkler_2022, title={A family of mass-critical Keller-Segel systems.}, volume={124}, journal={Proceedings of the London Mathematical Society}, author={Winkler, Michael}, year={2022}, pages={133–181} }"},"page":"133-181","language":[{"iso":"eng"}],"_id":"35574","user_id":"15645","volume":124,"status":"public","title":"A family of mass-critical Keller-Segel systems.","year":"2022","author":[{"id":"31496","last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"date_updated":"2023-01-20T13:17:33Z","intvolume":"       124"},{"date_updated":"2023-01-21T09:30:47Z","intvolume":"        42","title":"Global weak solutions to a chemotaxis-Navier-Stokes system in $R^3$.","status":"public","year":"2022","author":[{"full_name":" Kang, Kyungkeun","last_name":" Kang","first_name":"Kyungkeun"},{"first_name":"Jihoon","last_name":"Lee","full_name":"Lee, Jihoon"},{"full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler","id":"31496"}],"user_id":"15645","volume":42,"page":"5201-5222","_id":"35483","language":[{"iso":"eng"}],"publication":"Discrete and Continuous Dynamical Systems","citation":{"ama":"Kang K, Lee J, Winkler M. Global weak solutions to a chemotaxis-Navier-Stokes system in $R^3$. <i>Discrete and Continuous Dynamical Systems</i>. 2022;42:5201-5222.","bibtex":"@article{ Kang_Lee_Winkler_2022, title={Global weak solutions to a chemotaxis-Navier-Stokes system in $R^3$.}, volume={42}, journal={Discrete and Continuous Dynamical Systems}, author={ Kang, Kyungkeun and Lee, Jihoon and Winkler, Michael}, year={2022}, pages={5201–5222} }","mla":"Kang, Kyungkeun, et al. “Global Weak Solutions to a Chemotaxis-Navier-Stokes System in $R^3$.” <i>Discrete and Continuous Dynamical Systems</i>, vol. 42, 2022, pp. 5201–22.","chicago":"Kang, Kyungkeun, Jihoon Lee, and Michael Winkler. “Global Weak Solutions to a Chemotaxis-Navier-Stokes System in $R^3$.” <i>Discrete and Continuous Dynamical Systems</i> 42 (2022): 5201–22.","short":"K.  Kang, J. Lee, M. Winkler, Discrete and Continuous Dynamical Systems 42 (2022) 5201–5222.","apa":"Kang, K., Lee, J., &#38; Winkler, M. (2022). Global weak solutions to a chemotaxis-Navier-Stokes system in $R^3$. <i>Discrete and Continuous Dynamical Systems</i>, <i>42</i>, 5201–5222.","ieee":"K.  Kang, J. Lee, and M. Winkler, “Global weak solutions to a chemotaxis-Navier-Stokes system in $R^3$.,” <i>Discrete and Continuous Dynamical Systems</i>, vol. 42, pp. 5201–5222, 2022."},"type":"journal_article","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"date_created":"2023-01-09T13:02:46Z"},{"date_created":"2023-01-23T08:31:27Z","type":"journal_article","department":[{"_id":"555"}],"issue":"780","publication":"Contemporary Mathematics","citation":{"ieee":"M. Rösler and M. Voit, “Elementary symmetric polynomials and martingales for Heckman-Opdam processes,” <i>Contemporary Mathematics</i>, no. 780, pp. 243–262, 2022, doi: <a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">10.48550/ARXIV.2108.03228</a>.","apa":"Rösler, M., &#38; Voit, M. (2022). Elementary symmetric polynomials and martingales for Heckman-Opdam processes. <i>Contemporary Mathematics</i>, <i>780</i>, 243–262. <a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">https://doi.org/10.48550/ARXIV.2108.03228</a>","short":"M. Rösler, M. Voit, Contemporary Mathematics (2022) 243–262.","chicago":"Rösler, Margit, and Michael Voit. “Elementary Symmetric Polynomials and Martingales for Heckman-Opdam Processes.” <i>Contemporary Mathematics</i>, no. 780 (2022): 243–62. <a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">https://doi.org/10.48550/ARXIV.2108.03228</a>.","mla":"Rösler, Margit, and Michael Voit. “Elementary Symmetric Polynomials and Martingales for Heckman-Opdam Processes.” <i>Contemporary Mathematics</i>, no. 780, 2022, pp. 243–62, doi:<a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">10.48550/ARXIV.2108.03228</a>.","bibtex":"@article{Rösler_Voit_2022, title={Elementary symmetric polynomials and martingales for Heckman-Opdam processes}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">10.48550/ARXIV.2108.03228</a>}, number={780}, journal={Contemporary Mathematics}, author={Rösler, Margit and Voit, Michael}, year={2022}, pages={243–262} }","ama":"Rösler M, Voit M. Elementary symmetric polynomials and martingales for Heckman-Opdam processes. <i>Contemporary Mathematics</i>. 2022;(780):243-262. doi:<a href=\"https://doi.org/10.48550/ARXIV.2108.03228\">10.48550/ARXIV.2108.03228</a>"},"abstract":[{"lang":"eng","text":"We consider the generators $L_k$ of Heckman-Opdam diffusion processes in the compact and non-compact case in $N$ dimensions for root systems of type $A$ and $B$, with a multiplicity function of the form $k=κk_0$ with some fixed value $k_0$ and a varying constant $κ\\in\\,[0,\\infty[$. Using elementary symmetric functions, we present polynomials which are simultaneous eigenfunctions of the $L_k$ for all $κ\\in\\,]0,\\infty[$. This leads to martingales associated with the Heckman-Opdam diffusions $ (X_{t,1},\\ldots,X_{t,N})_{t\\ge0}$. As our results extend to the freezing case $κ=\\infty$ with a deterministic limit after some renormalization, we find formulas for the expectations $\\mathbb E(\\prod_{j=1}^N(y-X_{t,j})),$ $y\\in\\mathbb C$."}],"page":"243-262","_id":"38039","language":[{"iso":"eng"}],"user_id":"37390","doi":"10.48550/ARXIV.2108.03228","status":"public","title":"Elementary symmetric polynomials and martingales for Heckman-Opdam processes","year":"2022","author":[{"id":"37390","last_name":"Rösler","first_name":"Margit","full_name":"Rösler, Margit"},{"full_name":"Voit, Michael","last_name":"Voit","first_name":"Michael"}],"conference":{"name":"Hypergeometry, integrability and Lie theory"},"publication_status":"published","date_updated":"2023-01-24T22:16:21Z"}]