[{"type":"preprint","department":[{"_id":"101"}],"oa":"1","date_created":"2020-03-13T12:44:12Z","abstract":[{"lang":"eng","text":"Kernel transfer operators, which can be regarded as approximations of\r\ntransfer operators such as the Perron-Frobenius or Koopman operator in\r\nreproducing kernel Hilbert spaces, are defined in terms of covariance and\r\ncross-covariance operators and have been shown to be closely related to the\r\nconditional mean embedding framework developed by the machine learning\r\ncommunity. The goal of this paper is to show how the dominant eigenfunctions of\r\nthese operators in combination with gradient-based optimization techniques can\r\nbe used to detect long-lived coherent patterns in high-dimensional time-series\r\ndata. The results will be illustrated using video data and a fluid flow\r\nexample."}],"project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"publication":"arXiv:1805.10118","citation":{"ama":"Klus S, Peitz S, Schuster I. Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions. <i>arXiv:180510118</i>. 2018.","bibtex":"@article{Klus_Peitz_Schuster_2018, title={Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions}, journal={arXiv:1805.10118}, author={Klus, Stefan and Peitz, Sebastian and Schuster, Ingmar}, year={2018} }","mla":"Klus, Stefan, et al. “Analyzing High-Dimensional Time-Series Data Using Kernel Transfer  Operator Eigenfunctions.” <i>ArXiv:1805.10118</i>, 2018.","short":"S. Klus, S. Peitz, I. Schuster, ArXiv:1805.10118 (2018).","chicago":"Klus, Stefan, Sebastian Peitz, and Ingmar Schuster. “Analyzing High-Dimensional Time-Series Data Using Kernel Transfer  Operator Eigenfunctions.” <i>ArXiv:1805.10118</i>, 2018.","apa":"Klus, S., Peitz, S., &#38; Schuster, I. (2018). Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions. <i>ArXiv:1805.10118</i>.","ieee":"S. Klus, S. Peitz, and I. Schuster, “Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions,” <i>arXiv:1805.10118</i>. 2018."},"user_id":"47427","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/1805.10118.pdf"}],"language":[{"iso":"eng"}],"_id":"16293","date_updated":"2022-01-06T06:52:48Z","year":"2018","status":"public","title":"Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions","author":[{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","id":"47427"},{"first_name":"Ingmar","last_name":"Schuster","full_name":"Schuster, Ingmar"}]},{"department":[{"_id":"542"}],"type":"journal_article","keyword":["Cubic graph","Tait coloring","Snark","Boole coloring","Berge's conjecture","Tutte's 5-flow conjecture"],"date_created":"2019-06-05T09:59:10Z","abstract":[{"lang":"eng","text":"There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs. Since most of them are trivially true for 3-edge-colorable cubic graphs, cubic graphs which are not 3-edge-colorable, often called snarks, play a key role in this context. Here, we survey parameters measuring how far apart a non 3-edge-colorable graph is from being 3-edge-colorable. We study their interrelation and prove some new results. Besides getting new insight into the structure of snarks, we show that such  measures give partial results with respect to these important conjectures. The paper closes with a list of open problems and conjectures."}],"citation":{"bibtex":"@article{Fiol_Mazzuoccolo_Steffen_2018, title={Measures of Edge-Uncolorability of Cubic Graphs}, volume={25}, number={4P4.54}, journal={The Electronic Journal of Combinatorics}, author={Fiol, M. A. and Mazzuoccolo, Guiseppe and Steffen, Eckhard}, year={2018} }","chicago":"Fiol, M. A., Guiseppe Mazzuoccolo, and Eckhard Steffen. “Measures of Edge-Uncolorability of Cubic Graphs.” <i>The Electronic Journal of Combinatorics</i> 25, no. 4 (2018).","short":"M.A. Fiol, G. Mazzuoccolo, E. Steffen, The Electronic Journal of Combinatorics 25 (2018).","ama":"Fiol MA, Mazzuoccolo G, Steffen E. Measures of Edge-Uncolorability of Cubic Graphs. <i>The Electronic Journal of Combinatorics</i>. 2018;25(4).","ieee":"M. A. Fiol, G. Mazzuoccolo, and E. Steffen, “Measures of Edge-Uncolorability of Cubic Graphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 25, no. 4, 2018.","apa":"Fiol, M. A., Mazzuoccolo, G., &#38; Steffen, E. (2018). Measures of Edge-Uncolorability of Cubic Graphs. <i>The Electronic Journal of Combinatorics</i>, <i>25</i>(4).","mla":"Fiol, M. A., et al. “Measures of Edge-Uncolorability of Cubic Graphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 25, no. 4, P4.54, 2018."},"publication":"The Electronic Journal of Combinatorics","issue":"4","volume":25,"user_id":"15540","_id":"10129","language":[{"iso":"eng"}],"article_number":"P4.54","article_type":"original","intvolume":"        25","date_updated":"2022-01-06T06:50:30Z","author":[{"full_name":"Fiol, M. A.","last_name":"Fiol","first_name":"M. A."},{"last_name":"Mazzuoccolo","first_name":"Guiseppe","full_name":"Mazzuoccolo, Guiseppe"},{"last_name":"Steffen","first_name":"Eckhard","full_name":"Steffen, Eckhard","id":"15548"}],"status":"public","title":"Measures of Edge-Uncolorability of Cubic Graphs","year":"2018"},{"citation":{"mla":"Jin, Ligang, et al. “Cores, Joins  and the Fano-Flow Conjectures.” <i>Discussiones Mathematicae Graph Theory</i>, vol. 38, 2018, pp. 165–75, doi:<a href=\"https://doi.org/10.7151/dmgt.1999\">10.7151/dmgt.1999</a>.","bibtex":"@article{Jin_Mazzuoccolo_Steffen_2018, title={Cores, joins  and the Fano-flow conjectures}, volume={38}, DOI={<a href=\"https://doi.org/10.7151/dmgt.1999\">10.7151/dmgt.1999</a>}, journal={Discussiones Mathematicae Graph Theory}, author={Jin, Ligang and Mazzuoccolo, Giuseppe and Steffen, Eckhard}, year={2018}, pages={165–175} }","ama":"Jin L, Mazzuoccolo G, Steffen E. Cores, joins  and the Fano-flow conjectures. <i>Discussiones Mathematicae Graph Theory</i>. 2018;38:165-175. doi:<a href=\"https://doi.org/10.7151/dmgt.1999\">10.7151/dmgt.1999</a>","ieee":"L. Jin, G. Mazzuoccolo, and E. Steffen, “Cores, joins  and the Fano-flow conjectures,” <i>Discussiones Mathematicae Graph Theory</i>, vol. 38, pp. 165–175, 2018.","apa":"Jin, L., Mazzuoccolo, G., &#38; Steffen, E. (2018). Cores, joins  and the Fano-flow conjectures. <i>Discussiones Mathematicae Graph Theory</i>, <i>38</i>, 165–175. <a href=\"https://doi.org/10.7151/dmgt.1999\">https://doi.org/10.7151/dmgt.1999</a>","short":"L. Jin, G. Mazzuoccolo, E. Steffen, Discussiones Mathematicae Graph Theory 38 (2018) 165–175.","chicago":"Jin, Ligang, Giuseppe Mazzuoccolo, and Eckhard Steffen. “Cores, Joins  and the Fano-Flow Conjectures.” <i>Discussiones Mathematicae Graph Theory</i> 38 (2018): 165–75. <a href=\"https://doi.org/10.7151/dmgt.1999\">https://doi.org/10.7151/dmgt.1999</a>."},"publication":"Discussiones Mathematicae Graph Theory","department":[{"_id":"542"}],"type":"journal_article","date_created":"2019-06-05T10:08:41Z","intvolume":"        38","publication_status":"published","date_updated":"2022-01-06T06:50:30Z","author":[{"last_name":"Jin","first_name":"Ligang","full_name":"Jin, Ligang"},{"first_name":"Giuseppe","last_name":"Mazzuoccolo","full_name":"Mazzuoccolo, Giuseppe"},{"id":"15548","last_name":"Steffen","first_name":"Eckhard","full_name":"Steffen, Eckhard"}],"publication_identifier":{"issn":["1234-3099","2083-5892"]},"status":"public","year":"2018","title":"Cores, joins  and the Fano-flow conjectures","volume":38,"user_id":"15540","doi":"10.7151/dmgt.1999","language":[{"iso":"eng"}],"_id":"10132","page":"165-175"},{"title":"Approximating Vizing’s independence number conjecture","status":"public","year":"2018","author":[{"id":"15548","full_name":"Steffen, Eckhard","first_name":"Eckhard","last_name":"Steffen"}],"date_updated":"2022-01-06T06:50:31Z","publication_status":"published","intvolume":"        71","page":"153-160","language":[{"iso":"eng"}],"_id":"10142","user_id":"15540","volume":71,"issue":"1","publication":"Australasian Journal of Combinatorics","citation":{"chicago":"Steffen, Eckhard. “Approximating Vizing’s Independence Number Conjecture.” <i>Australasian Journal of Combinatorics</i> 71, no. 1 (2018): 153–60.","short":"E. Steffen, Australasian Journal of Combinatorics 71 (2018) 153–160.","ieee":"E. Steffen, “Approximating Vizing’s independence number conjecture,” <i>Australasian Journal of Combinatorics</i>, vol. 71, no. 1, pp. 153–160, 2018.","apa":"Steffen, E. (2018). Approximating Vizing’s independence number conjecture. <i>Australasian Journal of Combinatorics</i>, <i>71</i>(1), 153–160.","bibtex":"@article{Steffen_2018, title={Approximating Vizing’s independence number conjecture}, volume={71}, number={1}, journal={Australasian Journal of Combinatorics}, author={Steffen, Eckhard}, year={2018}, pages={153–160} }","ama":"Steffen E. Approximating Vizing’s independence number conjecture. <i>Australasian Journal of Combinatorics</i>. 2018;71(1):153-160.","mla":"Steffen, Eckhard. “Approximating Vizing’s Independence Number Conjecture.” <i>Australasian Journal of Combinatorics</i>, vol. 71, no. 1, 2018, pp. 153–60."},"date_created":"2019-06-07T08:36:36Z","type":"journal_article","department":[{"_id":"542"}]},{"conference":{"name":"52. Jahrestagung der Gesellschaft für Didaktik der Mathematik"},"author":[{"full_name":"Nührenbörger, M.","last_name":"Nührenbörger","first_name":"M."},{"first_name":"D.","last_name":"Bönig","full_name":"Bönig, D."},{"last_name":"Häsel-Weide","first_name":"Uta","full_name":"Häsel-Weide, Uta","id":"60267"},{"full_name":"Korff, N.","last_name":"Korff","first_name":"N."},{"first_name":"P.","last_name":"Scherer","full_name":"Scherer, P."}],"status":"public","year":"2018","title":"Inklusiver Mathematikunterricht - vernetzt zwischen Mathematikdidaktik und Sonderpädagogik","date_updated":"2022-06-20T06:14:33Z","publication_status":"published","language":[{"iso":"ger"}],"_id":"31946","page":"103-104","editor":[{"first_name":"Fachgruppe Didaktik der Mathematik der Universität Paderborn","last_name":"In:","full_name":"In:, Fachgruppe Didaktik der Mathematik der Universität Paderborn"}],"user_id":"85821","citation":{"ama":"Nührenbörger M, Bönig D, Häsel-Weide U, Korff N, Scherer P. Inklusiver Mathematikunterricht - vernetzt zwischen Mathematikdidaktik und Sonderpädagogik. In: In: FD der M der UP, ed. <i>Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV</i>. ; 2018:103-104.","short":"M. Nührenbörger, D. Bönig, U. Häsel-Weide, N. Korff, P. Scherer, in: F.D. der M. der U.P. In: (Ed.), Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV, Münster, 2018, pp. 103–104.","chicago":"Nührenbörger, M., D. Bönig, Uta Häsel-Weide, N. Korff, and P. Scherer. “Inklusiver Mathematikunterricht - vernetzt zwischen Mathematikdidaktik und Sonderpädagogik.” In <i>Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV</i>, edited by Fachgruppe Didaktik der Mathematik der Universität Paderborn In:, 103–4. Münster, 2018.","bibtex":"@inproceedings{Nührenbörger_Bönig_Häsel-Weide_Korff_Scherer_2018, place={Münster}, title={Inklusiver Mathematikunterricht - vernetzt zwischen Mathematikdidaktik und Sonderpädagogik}, booktitle={Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV}, author={Nührenbörger, M. and Bönig, D. and Häsel-Weide, Uta and Korff, N. and Scherer, P.}, editor={In:, Fachgruppe Didaktik der Mathematik der Universität Paderborn}, year={2018}, pages={103–104} }","mla":"Nührenbörger, M., et al. “Inklusiver Mathematikunterricht - vernetzt zwischen Mathematikdidaktik und Sonderpädagogik.” <i>Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV</i>, edited by Fachgruppe Didaktik der Mathematik der Universität Paderborn In:, 2018, pp. 103–04.","apa":"Nührenbörger, M., Bönig, D., Häsel-Weide, U., Korff, N., &#38; Scherer, P. (2018). Inklusiver Mathematikunterricht - vernetzt zwischen Mathematikdidaktik und Sonderpädagogik. In F. D. der M. der U. P. In: (Ed.), <i>Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV</i> (pp. 103–104).","ieee":"M. Nührenbörger, D. Bönig, U. Häsel-Weide, N. Korff, and P. Scherer, “Inklusiver Mathematikunterricht - vernetzt zwischen Mathematikdidaktik und Sonderpädagogik,” in <i>Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV</i>, 2018, pp. 103–104."},"publication":"Beiträge zum Mathematikunterricht 2018. Vorträge zur Mathematikdidaktik und zur Schnittstelle Mathematik/Mathematikdidaktik auf der gemeinsamen Jahrestagung der GDM und DMV","place":"Münster","date_created":"2022-06-20T06:10:38Z","department":[{"_id":"98"},{"_id":"543"}],"type":"conference"},{"page":"19-35","language":[{"iso":"eng"}],"_id":"31953","user_id":"85821","title":"Fostering the Computation Competence of Low Achievers through Cooperative Learning in Inclusive Classrooms: A Longitudinal Study","status":"public","year":"2018","author":[{"full_name":"Moser-Opitz, E.","last_name":"Moser-Opitz","first_name":"E."},{"full_name":"Grob, U.","last_name":"Grob","first_name":"U."},{"first_name":"C.","last_name":"Wittich","full_name":"Wittich, C."},{"full_name":"Häsel-Weide, Uta","last_name":"Häsel-Weide","first_name":"Uta","id":"60267"},{"last_name":"Nührenbörger","first_name":"M.","full_name":"Nührenbörger, M."}],"date_updated":"2022-06-20T06:44:57Z","publication_status":"published","date_created":"2022-06-20T06:44:53Z","type":"journal_article","department":[{"_id":"98"},{"_id":"543"}],"publication":"Learning Disabilities: A Contemporary Journal","issue":"16","citation":{"apa":"Moser-Opitz, E., Grob, U., Wittich, C., Häsel-Weide, U., &#38; Nührenbörger, M. (2018). Fostering the Computation Competence of Low Achievers through Cooperative Learning in Inclusive Classrooms: A Longitudinal Study. <i>Learning Disabilities: A Contemporary Journal</i>, <i>16</i>, 19–35.","ieee":"E. Moser-Opitz, U. Grob, C. Wittich, U. Häsel-Weide, and M. Nührenbörger, “Fostering the Computation Competence of Low Achievers through Cooperative Learning in Inclusive Classrooms: A Longitudinal Study,” <i>Learning Disabilities: A Contemporary Journal</i>, no. 16, pp. 19–35, 2018.","chicago":"Moser-Opitz, E., U. Grob, C. Wittich, Uta Häsel-Weide, and M. Nührenbörger. “Fostering the Computation Competence of Low Achievers through Cooperative Learning in Inclusive Classrooms: A Longitudinal Study.” <i>Learning Disabilities: A Contemporary Journal</i>, no. 16 (2018): 19–35.","short":"E. Moser-Opitz, U. Grob, C. Wittich, U. Häsel-Weide, M. Nührenbörger, Learning Disabilities: A Contemporary Journal (2018) 19–35.","mla":"Moser-Opitz, E., et al. “Fostering the Computation Competence of Low Achievers through Cooperative Learning in Inclusive Classrooms: A Longitudinal Study.” <i>Learning Disabilities: A Contemporary Journal</i>, no. 16, 2018, pp. 19–35.","ama":"Moser-Opitz E, Grob U, Wittich C, Häsel-Weide U, Nührenbörger M. Fostering the Computation Competence of Low Achievers through Cooperative Learning in Inclusive Classrooms: A Longitudinal Study. <i>Learning Disabilities: A Contemporary Journal</i>. 2018;(16):19-35.","bibtex":"@article{Moser-Opitz_Grob_Wittich_Häsel-Weide_Nührenbörger_2018, title={Fostering the Computation Competence of Low Achievers through Cooperative Learning in Inclusive Classrooms: A Longitudinal Study}, number={16}, journal={Learning Disabilities: A Contemporary Journal}, author={Moser-Opitz, E. and Grob, U. and Wittich, C. and Häsel-Weide, Uta and Nührenbörger, M.}, year={2018}, pages={19–35} }"}},{"author":[{"full_name":"Häsel-Weide, Uta","first_name":"Uta","last_name":"Häsel-Weide","id":"60267"},{"full_name":"Nührenbörger, M.","last_name":"Nührenbörger","first_name":"M."},{"last_name":"Reinold","first_name":"M.","full_name":"Reinold, M."}],"publication_identifier":{"isbn":["978-3122009977"]},"status":"public","title":"Förderkommentar Lernen zum Zahlenbuch 3","year":"2018","date_updated":"2022-06-20T06:29:00Z","publication_status":"published","_id":"31952","language":[{"iso":"ger"}],"publisher":"Klett","page":"144","user_id":"85821","citation":{"bibtex":"@book{Häsel-Weide_Nührenbörger_Reinold_2018, place={Leipzig}, title={Förderkommentar Lernen zum Zahlenbuch 3}, publisher={Klett}, author={Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}, year={2018} }","ama":"Häsel-Weide U, Nührenbörger M, Reinold M. <i>Förderkommentar Lernen zum Zahlenbuch 3</i>. Klett; 2018.","mla":"Häsel-Weide, Uta, et al. <i>Förderkommentar Lernen zum Zahlenbuch 3</i>. Klett, 2018.","chicago":"Häsel-Weide, Uta, M. Nührenbörger, and M. Reinold. <i>Förderkommentar Lernen zum Zahlenbuch 3</i>. Leipzig: Klett, 2018.","short":"U. Häsel-Weide, M. Nührenbörger, M. Reinold, Förderkommentar Lernen zum Zahlenbuch 3, Klett, Leipzig, 2018.","ieee":"U. Häsel-Weide, M. Nührenbörger, and M. Reinold, <i>Förderkommentar Lernen zum Zahlenbuch 3</i>. Leipzig: Klett, 2018.","apa":"Häsel-Weide, U., Nührenbörger, M., &#38; Reinold, M. (2018). <i>Förderkommentar Lernen zum Zahlenbuch 3</i>. Klett."},"place":"Leipzig","date_created":"2022-06-20T06:28:50Z","department":[{"_id":"98"},{"_id":"543"}],"type":"misc"},{"place":"Stuttgart","date_created":"2022-06-20T06:25:18Z","department":[{"_id":"98"},{"_id":"543"}],"type":"misc","citation":{"bibtex":"@book{Häsel-Weide_Nührenbörger_Reinold_2018, place={Stuttgart}, title={Das Zahlenbuch 3. Förderheft.}, publisher={Klett}, author={Häsel-Weide, Uta and Nührenbörger, M. and Reinold, M.}, year={2018} }","ama":"Häsel-Weide U, Nührenbörger M, Reinold M. <i>Das Zahlenbuch 3. Förderheft.</i> Klett; 2018.","mla":"Häsel-Weide, Uta, et al. <i>Das Zahlenbuch 3. Förderheft.</i> Klett, 2018.","short":"U. Häsel-Weide, M. Nührenbörger, M. Reinold, Das Zahlenbuch 3. Förderheft., Klett, Stuttgart, 2018.","chicago":"Häsel-Weide, Uta, M. Nührenbörger, and M. Reinold. <i>Das Zahlenbuch 3. Förderheft.</i> Stuttgart: Klett, 2018.","ieee":"U. Häsel-Weide, M. Nührenbörger, and M. Reinold, <i>Das Zahlenbuch 3. Förderheft.</i> Stuttgart: Klett, 2018.","apa":"Häsel-Weide, U., Nührenbörger, M., &#38; Reinold, M. (2018). <i>Das Zahlenbuch 3. Förderheft.</i> Klett."},"language":[{"iso":"ger"}],"_id":"31951","publisher":"Klett","page":"80","user_id":"85821","publication_identifier":{"isbn":["978-3122009939"]},"author":[{"id":"60267","first_name":"Uta","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta"},{"full_name":"Nührenbörger, M.","last_name":"Nührenbörger","first_name":"M."},{"full_name":"Reinold, M.","last_name":"Reinold","first_name":"M."}],"year":"2018","title":"Das Zahlenbuch 3. Förderheft.","status":"public","date_updated":"2022-06-20T06:25:24Z","publication_status":"published"},{"publication_identifier":{"issn":["0036-1410","1095-7154"]},"author":[{"last_name":"Black","orcid":"0000-0001-9963-0800","first_name":"Tobias","full_name":"Black, Tobias","id":"23686"}],"title":"Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion","year":"2018","intvolume":"        50","publication_status":"published","date_updated":"2022-12-21T10:04:57Z","language":[{"iso":"eng"}],"doi":"10.1137/17m1159488","issue":"4","publication":"SIAM Journal on Mathematical Analysis","date_created":"2022-12-21T09:47:01Z","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"type":"journal_article","status":"public","publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"34664","page":"4087-4116","volume":50,"user_id":"23686","citation":{"ama":"Black T. Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion. <i>SIAM Journal on Mathematical Analysis</i>. 2018;50(4):4087-4116. doi:<a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>","bibtex":"@article{Black_2018, title={Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion}, volume={50}, DOI={<a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>}, number={4}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Black, Tobias}, year={2018}, pages={4087–4116} }","mla":"Black, Tobias. “Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 4, Society for Industrial &#38; Applied Mathematics (SIAM), 2018, pp. 4087–116, doi:<a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>.","short":"T. Black, SIAM Journal on Mathematical Analysis 50 (2018) 4087–4116.","chicago":"Black, Tobias. “Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion.” <i>SIAM Journal on Mathematical Analysis</i> 50, no. 4 (2018): 4087–4116. <a href=\"https://doi.org/10.1137/17m1159488\">https://doi.org/10.1137/17m1159488</a>.","apa":"Black, T. (2018). Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion. <i>SIAM Journal on Mathematical Analysis</i>, <i>50</i>(4), 4087–4116. <a href=\"https://doi.org/10.1137/17m1159488\">https://doi.org/10.1137/17m1159488</a>","ieee":"T. Black, “Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 4, pp. 4087–4116, 2018, doi: <a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>."}},{"volume":265,"user_id":"23686","_id":"34666","publisher":"Elsevier BV","page":"2296-2339","status":"public","citation":{"short":"T. Black, Journal of Differential Equations 265 (2018) 2296–2339.","chicago":"Black, Tobias. “Eventual Smoothness of Generalized Solutions to a Singular Chemotaxis-Stokes System in 2D.” <i>Journal of Differential Equations</i> 265, no. 5 (2018): 2296–2339. <a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">https://doi.org/10.1016/j.jde.2018.04.035</a>.","apa":"Black, T. (2018). Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D. <i>Journal of Differential Equations</i>, <i>265</i>(5), 2296–2339. <a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">https://doi.org/10.1016/j.jde.2018.04.035</a>","ieee":"T. Black, “Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D,” <i>Journal of Differential Equations</i>, vol. 265, no. 5, pp. 2296–2339, 2018, doi: <a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>.","ama":"Black T. Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D. <i>Journal of Differential Equations</i>. 2018;265(5):2296-2339. doi:<a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>","bibtex":"@article{Black_2018, title={Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D}, volume={265}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>}, number={5}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Black, Tobias}, year={2018}, pages={2296–2339} }","mla":"Black, Tobias. “Eventual Smoothness of Generalized Solutions to a Singular Chemotaxis-Stokes System in 2D.” <i>Journal of Differential Equations</i>, vol. 265, no. 5, Elsevier BV, 2018, pp. 2296–339, doi:<a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>."},"doi":"10.1016/j.jde.2018.04.035","language":[{"iso":"eng"}],"intvolume":"       265","publication_status":"published","date_updated":"2022-12-21T10:05:11Z","author":[{"id":"23686","full_name":"Black, Tobias","first_name":"Tobias","last_name":"Black","orcid":"0000-0001-9963-0800"}],"publication_identifier":{"issn":["0022-0396"]},"title":"Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D","year":"2018","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"keyword":["Analysis","Applied Mathematics"],"type":"journal_article","date_created":"2022-12-21T09:47:19Z","issue":"5","publication":"Journal of Differential Equations"},{"citation":{"short":"T. Black, Nonlinear Analysis 180 (2018) 129–153.","chicago":"Black, Tobias. “Global Solvability of Chemotaxis–Fluid Systems with Nonlinear Diffusion and Matrix-Valued Sensitivities in Three Dimensions.” <i>Nonlinear Analysis</i> 180 (2018): 129–53. <a href=\"https://doi.org/10.1016/j.na.2018.10.003\">https://doi.org/10.1016/j.na.2018.10.003</a>.","apa":"Black, T. (2018). Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions. <i>Nonlinear Analysis</i>, <i>180</i>, 129–153. <a href=\"https://doi.org/10.1016/j.na.2018.10.003\">https://doi.org/10.1016/j.na.2018.10.003</a>","ieee":"T. Black, “Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions,” <i>Nonlinear Analysis</i>, vol. 180, pp. 129–153, 2018, doi: <a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>.","ama":"Black T. Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions. <i>Nonlinear Analysis</i>. 2018;180:129-153. doi:<a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>","bibtex":"@article{Black_2018, title={Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions}, volume={180}, DOI={<a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Black, Tobias}, year={2018}, pages={129–153} }","mla":"Black, Tobias. “Global Solvability of Chemotaxis–Fluid Systems with Nonlinear Diffusion and Matrix-Valued Sensitivities in Three Dimensions.” <i>Nonlinear Analysis</i>, vol. 180, Elsevier BV, 2018, pp. 129–53, doi:<a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>."},"page":"129-153","publisher":"Elsevier BV","_id":"34667","user_id":"23686","volume":180,"status":"public","date_created":"2022-12-21T09:47:30Z","type":"journal_article","keyword":["Applied Mathematics","Analysis"],"department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"publication":"Nonlinear Analysis","language":[{"iso":"eng"}],"doi":"10.1016/j.na.2018.10.003","year":"2018","title":"Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions","publication_identifier":{"issn":["0362-546X"]},"author":[{"full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","first_name":"Tobias","last_name":"Black","id":"23686"}],"date_updated":"2022-12-21T10:05:04Z","publication_status":"published","intvolume":"       180"},{"issue":"1","publication":"Acta Applicandae Mathematicae","abstract":[{"lang":"eng","text":"In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow."}],"date_created":"2019-03-29T13:30:41Z","department":[{"_id":"101"}],"type":"journal_article","publication_identifier":{"issn":["0167-8019","1572-9036"]},"author":[{"orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"title":"Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling","year":"2018","intvolume":"       161","publication_status":"published","date_updated":"2022-01-21T10:01:41Z","language":[{"iso":"eng"}],"doi":"10.1007/s10440-018-0209-7","citation":{"mla":"Peitz, Sebastian, et al. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” <i>Acta Applicandae Mathematicae</i>, vol. 161, no. 1, 2018, pp. 171–199, doi:<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>.","bibtex":"@article{Peitz_Ober-Blöbaum_Dellnitz_2018, title={Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}, volume={161}, DOI={<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>}, number={1}, journal={Acta Applicandae Mathematicae}, author={Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2018}, pages={171–199} }","ama":"Peitz S, Ober-Blöbaum S, Dellnitz M. Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. <i>Acta Applicandae Mathematicae</i>. 2018;161(1):171–199. doi:<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>","ieee":"S. Peitz, S. Ober-Blöbaum, and M. Dellnitz, “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling,” <i>Acta Applicandae Mathematicae</i>, vol. 161, no. 1, pp. 171–199, 2018, doi: <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>.","apa":"Peitz, S., Ober-Blöbaum, S., &#38; Dellnitz, M. (2018). Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. <i>Acta Applicandae Mathematicae</i>, <i>161</i>(1), 171–199. <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">https://doi.org/10.1007/s10440-018-0209-7</a>","short":"S. Peitz, S. Ober-Blöbaum, M. Dellnitz, Acta Applicandae Mathematicae 161 (2018) 171–199.","chicago":"Peitz, Sebastian, Sina Ober-Blöbaum, and Michael Dellnitz. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” <i>Acta Applicandae Mathematicae</i> 161, no. 1 (2018): 171–199. <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">https://doi.org/10.1007/s10440-018-0209-7</a>."},"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"status":"public","_id":"8753","page":"171–199","volume":161,"user_id":"15694"},{"language":[{"iso":"eng"}],"_id":"29425","user_id":"15694","title":"Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives","status":"public","year":"2018","author":[{"last_name":"Jiménez","first_name":"F.","full_name":"Jiménez, F."},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"}],"conference":{"start_date":"2018-06-11","end_date":"2018-06-15"},"date_updated":"2022-01-21T13:51:41Z","date_created":"2022-01-18T14:49:40Z","type":"conference","department":[{"_id":"636"}],"publication":"6th European Conference on Computational Mechanics","citation":{"ama":"Jiménez F, Ober-Blöbaum S. Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives. In: <i>6th European Conference on Computational Mechanics</i>. ; 2018.","bibtex":"@inproceedings{Jiménez_Ober-Blöbaum_2018, title={Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives}, booktitle={6th European Conference on Computational Mechanics}, author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2018} }","mla":"Jiménez, F., and Sina Ober-Blöbaum. “Necessary Optimality Conditions for Optimally Controlled Dissipative Mechanical Systems Modelled through Fractional Derivatives.” <i>6th European Conference on Computational Mechanics</i>, 2018.","short":"F. Jiménez, S. Ober-Blöbaum, in: 6th European Conference on Computational Mechanics, 2018.","chicago":"Jiménez, F., and Sina Ober-Blöbaum. “Necessary Optimality Conditions for Optimally Controlled Dissipative Mechanical Systems Modelled through Fractional Derivatives.” In <i>6th European Conference on Computational Mechanics</i>, 2018.","apa":"Jiménez, F., &#38; Ober-Blöbaum, S. (2018). Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives. <i>6th European Conference on Computational Mechanics</i>.","ieee":"F. Jiménez and S. Ober-Blöbaum, “Necessary optimality conditions for optimally controlled dissipative mechanical systems modelled through fractional derivatives,” 2018."}},{"corporate_editor":["IFAC-PapersOnLine"],"author":[{"full_name":"Jiménez, F.","last_name":"Jiménez","first_name":"F."},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"year":"2018","status":"public","title":"A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings","date_updated":"2022-01-21T13:53:24Z","language":[{"iso":"eng"}],"_id":"29427","page":"50-55","volume":"51(3)","user_id":"15694","citation":{"bibtex":"@inproceedings{Jiménez_Ober-Blöbaum_2018, title={A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings}, volume={51(3)}, booktitle={6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018}, author={Jiménez, F. and Ober-Blöbaum, Sina}, editor={IFAC-PapersOnLine}, year={2018}, pages={50–55} }","ama":"Jiménez F, Ober-Blöbaum S. A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings. In: IFAC-PapersOnLine, ed. <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018</i>. Vol 51(3). ; 2018:50-55.","mla":"Jiménez, F., and Sina Ober-Blöbaum. “A Fractional Variational Approach for Modelling Dissipative Mechanical Systems Continuous and Discrete Settings.” <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018</i>, edited by IFAC-PapersOnLine, vol. 51(3), 2018, pp. 50–55.","short":"F. Jiménez, S. Ober-Blöbaum, in: IFAC-PapersOnLine (Ed.), 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018, 2018, pp. 50–55.","chicago":"Jiménez, F., and Sina Ober-Blöbaum. “A Fractional Variational Approach for Modelling Dissipative Mechanical Systems Continuous and Discrete Settings.” In <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018</i>, edited by IFAC-PapersOnLine, 51(3):50–55, 2018.","ieee":"F. Jiménez and S. Ober-Blöbaum, “A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings,” in <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018</i>, 2018, vol. 51(3), pp. 50–55.","apa":"Jiménez, F., &#38; Ober-Blöbaum, S. (2018). A fractional variational approach for modelling dissipative mechanical systems continuous and discrete settings. In IFAC-PapersOnLine (Ed.), <i>6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018: Vol. 51(3)</i> (pp. 50–55)."},"publication":"6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018","date_created":"2022-01-18T14:55:51Z","department":[{"_id":"636"}],"type":"conference"},{"publication":"Beiträge zum Mathematikunterricht 2018","department":[{"_id":"97"}],"type":"conference","date_created":"2022-05-22T14:36:18Z","publication_status":"published","date_updated":"2022-05-22T14:38:42Z","corporate_editor":["Fachgruppe Didaktik der Mathematik der Universität Paderborn"],"author":[{"id":"32202","full_name":"Hoffmann, Max","first_name":"Max","last_name":"Hoffmann"}],"year":"2018","title":"Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben","doi":"10.17877/DE290R-19412","language":[{"iso":"ger"}],"main_file_link":[{"open_access":"1","url":"https://eldorado.tu-dortmund.de/handle/2003/37417?locale=de"}],"citation":{"mla":"Hoffmann, Max. “Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben.” <i>Beiträge zum Mathematikunterricht 2018</i>, edited by Fachgruppe Didaktik der Mathematik der Universität Paderborn, WTM-Verlag, 2018, pp. 815–18, doi:<a href=\"https://doi.org/10.17877/DE290R-19412\">10.17877/DE290R-19412</a>.","bibtex":"@inproceedings{Hoffmann_2018, place={Münster}, title={Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben}, DOI={<a href=\"https://doi.org/10.17877/DE290R-19412\">10.17877/DE290R-19412</a>}, booktitle={Beiträge zum Mathematikunterricht 2018}, publisher={WTM-Verlag}, author={Hoffmann, Max}, editor={Fachgruppe Didaktik der Mathematik der Universität Paderborn}, year={2018}, pages={815–818} }","ama":"Hoffmann M. Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben. In: Fachgruppe Didaktik der Mathematik der Universität Paderborn, ed. <i>Beiträge zum Mathematikunterricht 2018</i>. WTM-Verlag; 2018:815-818. doi:<a href=\"https://doi.org/10.17877/DE290R-19412\">10.17877/DE290R-19412</a>","ieee":"M. Hoffmann, “Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben,” in <i>Beiträge zum Mathematikunterricht 2018</i>, 2018, pp. 815–818, doi: <a href=\"https://doi.org/10.17877/DE290R-19412\">10.17877/DE290R-19412</a>.","apa":"Hoffmann, M. (2018). Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben. In Fachgruppe Didaktik der Mathematik der Universität Paderborn (Ed.), <i>Beiträge zum Mathematikunterricht 2018</i> (pp. 815–818). WTM-Verlag. <a href=\"https://doi.org/10.17877/DE290R-19412\">https://doi.org/10.17877/DE290R-19412</a>","short":"M. Hoffmann, in: Fachgruppe Didaktik der Mathematik der Universität Paderborn (Ed.), Beiträge zum Mathematikunterricht 2018, WTM-Verlag, Münster, 2018, pp. 815–818.","chicago":"Hoffmann, Max. “Schnittstellenaufgaben im Praxiseinsatz: Aufgabenbeispiel zur „Bleistiftstetigkeit“ und allgemeine Überlegungen zu möglichen Problemen beim Einsatz solcher Aufgaben.” In <i>Beiträge zum Mathematikunterricht 2018</i>, edited by Fachgruppe Didaktik der Mathematik der Universität Paderborn, 815–18. Münster: WTM-Verlag, 2018. <a href=\"https://doi.org/10.17877/DE290R-19412\">https://doi.org/10.17877/DE290R-19412</a>."},"oa":"1","place":"Münster","status":"public","user_id":"32202","_id":"31371","publisher":"WTM-Verlag","page":"815-818"},{"user_id":"32202","volume":"64 (5)","page":"48–54","language":[{"iso":"ger"}],"_id":"31375","date_updated":"2022-05-22T14:57:14Z","publication_status":"published","status":"public","title":"Anfängervorlesungen","year":"2018","author":[{"last_name":"Grieser","first_name":"Daniel","full_name":"Grieser, Daniel"},{"id":"32202","last_name":"Hoffmann","first_name":"Max","full_name":"Hoffmann, Max"},{"full_name":"Koepf, Wolfram","last_name":"Koepf","first_name":"Wolfram"},{"full_name":"Kramer, Jürg","first_name":"Jürg","last_name":"Kramer"}],"type":"journal_article","department":[{"_id":"97"}],"date_created":"2022-05-22T14:54:04Z","publication":"Der Mathematikunterricht","citation":{"ama":"Grieser D, Hoffmann M, Koepf W, Kramer J. Anfängervorlesungen. <i>Der Mathematikunterricht</i>. 2018;64 (5):48–54.","bibtex":"@article{Grieser_Hoffmann_Koepf_Kramer_2018, title={Anfängervorlesungen}, volume={64 (5)}, journal={Der Mathematikunterricht}, author={Grieser, Daniel and Hoffmann, Max and Koepf, Wolfram and Kramer, Jürg}, year={2018}, pages={48–54} }","mla":"Grieser, Daniel, et al. “Anfängervorlesungen.” <i>Der Mathematikunterricht</i>, vol. 64 (5), 2018, pp. 48–54.","short":"D. Grieser, M. Hoffmann, W. Koepf, J. Kramer, Der Mathematikunterricht 64 (5) (2018) 48–54.","chicago":"Grieser, Daniel, Max Hoffmann, Wolfram Koepf, and Jürg Kramer. “Anfängervorlesungen.” <i>Der Mathematikunterricht</i> 64 (5) (2018): 48–54.","apa":"Grieser, D., Hoffmann, M., Koepf, W., &#38; Kramer, J. (2018). Anfängervorlesungen. <i>Der Mathematikunterricht</i>, <i>64 (5)</i>, 48–54.","ieee":"D. Grieser, M. Hoffmann, W. Koepf, and J. Kramer, “Anfängervorlesungen,” <i>Der Mathematikunterricht</i>, vol. 64 (5), pp. 48–54, 2018."}},{"type":"review","department":[{"_id":"97"}],"date_created":"2022-05-22T15:15:33Z","publication":"Mathematische Semesterberichte","citation":{"bibtex":"@article{Hoffmann_2018, title={Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen}, volume={65}, DOI={<a href=\"https://doi.org/10.1007/s00591-018-0222-y\">10.1007/s00591-018-0222-y</a>}, journal={Mathematische Semesterberichte}, author={Hoffmann, Max}, year={2018}, pages={299–301} }","ama":"Hoffmann M. Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen. <i>Mathematische Semesterberichte</i>. 2018;65:299–301. doi:<a href=\"https://doi.org/10.1007/s00591-018-0222-y\">10.1007/s00591-018-0222-y</a>","mla":"Hoffmann, Max. “Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen.” <i>Mathematische Semesterberichte</i>, vol. 65, 2018, pp. 299–301, doi:<a href=\"https://doi.org/10.1007/s00591-018-0222-y\">10.1007/s00591-018-0222-y</a>.","short":"M. Hoffmann, Mathematische Semesterberichte 65 (2018) 299–301.","chicago":"Hoffmann, Max. “Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen.” <i>Mathematische Semesterberichte</i>, 2018. <a href=\"https://doi.org/10.1007/s00591-018-0222-y\">https://doi.org/10.1007/s00591-018-0222-y</a>.","ieee":"M. Hoffmann, “Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen,” <i>Mathematische Semesterberichte</i>, vol. 65. pp. 299–301, 2018, doi: <a href=\"https://doi.org/10.1007/s00591-018-0222-y\">10.1007/s00591-018-0222-y</a>.","apa":"Hoffmann, M. (2018). Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen. In <i>Mathematische Semesterberichte</i> (Vol. 65, pp. 299–301). <a href=\"https://doi.org/10.1007/s00591-018-0222-y\">https://doi.org/10.1007/s00591-018-0222-y</a>"},"doi":"10.1007/s00591-018-0222-y","user_id":"32202","volume":65,"main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00591-018-0222-y"}],"page":"299–301","language":[{"iso":"ger"}],"_id":"31382","date_updated":"2022-05-22T15:58:46Z","publication_status":"published","intvolume":"        65","status":"public","title":"Rezension: Dörte Haftendorn: Kurven erkunden und verstehen – Mit GeoGebra und anderen Werkzeugen","year":"2018","author":[{"full_name":"Hoffmann, Max","last_name":"Hoffmann","first_name":"Max","id":"32202"}]},{"citation":{"apa":"Greefrath, G., Hoffmann, M., &#38; Koepf, W. (Eds.). (2018). <i>Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?</i>","ieee":"G. Greefrath, M. Hoffmann, and W. Koepf, Eds., <i>Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?</i> 2018.","chicago":"Greefrath, Gilbert, Max Hoffmann, and Wolfram Koepf, eds. <i>Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?</i>, 2018.","short":"G. Greefrath, M. Hoffmann, W. Koepf, eds., Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?, 2018.","mla":"Greefrath, Gilbert, et al., editors. <i>Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?</i> 2018.","ama":"Greefrath G, Hoffmann M, Koepf W, eds. <i>Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?</i>; 2018.","bibtex":"@book{Greefrath_Hoffmann_Koepf_2018, title={Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?}, year={2018} }"},"related_material":{"link":[{"relation":"table_of_contents","url":"https://www.friedrich-verlag.de/shop/mathematik-in-schule-und-hochschule-524203"}]},"date_created":"2022-05-22T15:05:58Z","department":[{"_id":"97"}],"type":"book_editor","title":"Der Mathematikunterricht 64 (5): Mathematik in Schule und Hochschule – wie groß ist die Lücke und wie gehen wir mit ihr um?","year":"2018","status":"public","publication_status":"published","date_updated":"2022-05-22T16:00:16Z","_id":"31380","language":[{"iso":"ger"}],"editor":[{"full_name":"Greefrath, Gilbert","last_name":"Greefrath","first_name":"Gilbert"},{"id":"32202","full_name":"Hoffmann, Max","last_name":"Hoffmann","first_name":"Max"},{"first_name":"Wolfram","last_name":"Koepf","full_name":"Koepf, Wolfram"}],"user_id":"32202"},{"date_created":"2022-09-12T07:50:38Z","type":"journal_article","department":[{"_id":"96"}],"publication":"Journal of Theoretical Probability","citation":{"ama":"Hinrichs G, Kolb M, Wachtel V. Persistence of one-dimensional AR(1)-processes. <i>Journal of Theoretical Probability</i>. 2018;33:65–102. doi:<a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>","bibtex":"@article{Hinrichs_Kolb_Wachtel_2018, title={Persistence of one-dimensional AR(1)-processes}, volume={33}, DOI={<a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>}, journal={Journal of Theoretical Probability}, publisher={Springer Science + Business Media}, author={Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}, year={2018}, pages={65–102} }","mla":"Hinrichs, Günter, et al. “Persistence of One-Dimensional AR(1)-Processes.” <i>Journal of Theoretical Probability</i>, vol. 33, Springer Science + Business Media, 2018, pp. 65–102, doi:<a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.","chicago":"Hinrichs, Günter, Martin Kolb, and Vitali Wachtel. “Persistence of One-Dimensional AR(1)-Processes.” <i>Journal of Theoretical Probability</i> 33 (2018): 65–102. <a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.","short":"G. Hinrichs, M. Kolb, V. Wachtel, Journal of Theoretical Probability 33 (2018) 65–102.","apa":"Hinrichs, G., Kolb, M., &#38; Wachtel, V. (2018). Persistence of one-dimensional AR(1)-processes. <i>Journal of Theoretical Probability</i>, <i>33</i>, 65–102. <a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>","ieee":"G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of one-dimensional AR(1)-processes,” <i>Journal of Theoretical Probability</i>, vol. 33, pp. 65–102, 2018, doi: <a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>."},"abstract":[{"text":"For a class of one-dimensional autoregressive sequences (Xn), we consider the tail behaviour of the stopping time T0=min{n≥1:Xn≤0}. We discuss existing general analytical approaches to this and related problems and propose a new one, which is based on a renewal-type decomposition for the moment generating function of T0 and on the analytical Fredholm alternative. Using this method, we show that Px(T0=n)∼V(x)Rn0 for some 0<R0<1 and a positive R0-harmonic function V. Further, we prove that our conditions on the tail behaviour of the innovations are sharp in the sense that fatter tails produce non-exponential decay factors.","lang":"eng"}],"page":"65–102","language":[{"iso":"eng"}],"_id":"33335","publisher":"Springer Science + Business Media","user_id":"85821","doi":"https://link.springer.com/article/10.1007/s10959-018-0850-0","volume":33,"status":"public","title":"Persistence of one-dimensional AR(1)-processes","year":"2018","author":[{"full_name":"Hinrichs, Günter","last_name":"Hinrichs","first_name":"Günter"},{"id":"48880","full_name":"Kolb, Martin","last_name":"Kolb","first_name":"Martin"},{"full_name":"Wachtel, Vitali","first_name":"Vitali","last_name":"Wachtel"}],"publication_status":"published","date_updated":"2022-09-12T07:52:44Z","intvolume":"        33"},{"publication":"Beiträge zum Mathematikunterricht 2018","citation":{"short":"J. Dröse, in: Fachgruppe Didaktik der Mathematik der Universität Paderborn (Ed.), Beiträge zum Mathematikunterricht 2018, WTM, Münster, 2018, pp. 469–472.","chicago":"Dröse, Jennifer. “Textaufgaben strategisch und sprachlich bewältigen lernen – Pilotstudie zur Wirksamkeit eines Förderkonzepts.” In <i>Beiträge zum Mathematikunterricht 2018</i>, edited by Fachgruppe Didaktik der Mathematik der Universität Paderborn, 469–72. Münster: WTM, 2018.","apa":"Dröse, J. (2018). Textaufgaben strategisch und sprachlich bewältigen lernen – Pilotstudie zur Wirksamkeit eines Förderkonzepts. In Fachgruppe Didaktik der Mathematik der Universität Paderborn (Ed.), <i>Beiträge zum Mathematikunterricht 2018</i> (pp. 469–472). WTM.","ieee":"J. Dröse, “Textaufgaben strategisch und sprachlich bewältigen lernen – Pilotstudie zur Wirksamkeit eines Förderkonzepts,” in <i>Beiträge zum Mathematikunterricht 2018</i>, 2018, pp. 469–472.","ama":"Dröse J. Textaufgaben strategisch und sprachlich bewältigen lernen – Pilotstudie zur Wirksamkeit eines Förderkonzepts. In: Fachgruppe Didaktik der Mathematik der Universität Paderborn, ed. <i>Beiträge zum Mathematikunterricht 2018</i>. WTM; 2018:469-472.","bibtex":"@inproceedings{Dröse_2018, place={Münster}, title={Textaufgaben strategisch und sprachlich bewältigen lernen – Pilotstudie zur Wirksamkeit eines Förderkonzepts}, booktitle={Beiträge zum Mathematikunterricht 2018}, publisher={WTM}, author={Dröse, Jennifer}, editor={Fachgruppe Didaktik der Mathematik der Universität Paderborn}, year={2018}, pages={469–472} }","mla":"Dröse, Jennifer. “Textaufgaben strategisch und sprachlich bewältigen lernen – Pilotstudie zur Wirksamkeit eines Förderkonzepts.” <i>Beiträge zum Mathematikunterricht 2018</i>, edited by Fachgruppe Didaktik der Mathematik der Universität Paderborn, WTM, 2018, pp. 469–72."},"extern":"1","date_created":"2023-05-31T08:15:12Z","place":"Münster","type":"conference","department":[{"_id":"98"}],"status":"public","year":"2018","title":"Textaufgaben strategisch und sprachlich bewältigen lernen – Pilotstudie zur Wirksamkeit eines Förderkonzepts","author":[{"id":"85820","first_name":"Jennifer","last_name":"Dröse","full_name":"Dröse, Jennifer"}],"corporate_editor":["Fachgruppe Didaktik der Mathematik der Universität Paderborn"],"date_updated":"2023-11-02T08:10:36Z","page":"469-472","language":[{"iso":"ger"}],"_id":"45392","publisher":"WTM","user_id":"85820"}]