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Utrecht, 2019.","ama":"Kuklinski C, Liebendörfer M, Hochmuth R, et al. Features of innovative lectures that distinguish them from traditional lectures and their evaluation by attending students. In: <i>Proceedings of {CERME} 11</i>. ; 2019.","short":"C. Kuklinski, M. Liebendörfer, R. Hochmuth, R. Biehler, N. Schaper, E. Lankeit, E. Leis, M. Schürmann, in: Proceedings of {CERME} 11, Utrecht, 2019.","bibtex":"@inbook{Kuklinski_Liebendörfer_Hochmuth_Biehler_Schaper_Lankeit_Leis_Schürmann_2019, place={Utrecht}, title={Features of innovative lectures that distinguish them from traditional lectures and their evaluation by attending students}, booktitle={Proceedings of {CERME} 11}, author={Kuklinski, Christiane and Liebendörfer, Michael and Hochmuth, Reinhard and Biehler, Rolf and Schaper, Niclas and Lankeit, Elisa and Leis, Elena and Schürmann, Mirko}, year={2019} }","apa":"Kuklinski, C., Liebendörfer, M., Hochmuth, R., Biehler, R., Schaper, N., Lankeit, E., Leis, E., &#38; Schürmann, M. (2019). Features of innovative lectures that distinguish them from traditional lectures and their evaluation by attending students. In <i>Proceedings of {CERME} 11</i>.","mla":"Kuklinski, Christiane, et al. “Features of Innovative Lectures That Distinguish Them from Traditional Lectures and Their Evaluation by Attending Students.” <i>Proceedings of {CERME} 11</i>, 2019.","ieee":"C. Kuklinski <i>et al.</i>, “Features of innovative lectures that distinguish them from traditional lectures and their evaluation by attending students,” in <i>Proceedings of {CERME} 11</i>, Utrecht, 2019."},"publication":"Proceedings of {CERME} 11","department":[{"_id":"423"},{"_id":"625"}],"type":"book_chapter","date_created":"2020-05-16T07:32:47Z","place":"Utrecht"},{"type":"journal_article","department":[{"_id":"102"}],"date_created":"2024-07-16T11:09:02Z","extern":"1","issue":"4","publication":"Mathematika","citation":{"mla":"Elsholtz, Ch., et al. “The Maximal Order of Iterated Multiplicative Functions.” <i>Mathematika</i>, vol. 64, no. 4, 2019, pp. 990–1009, doi:<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>.","ama":"Elsholtz Ch, Technau M, Technau N. The maximal order of iterated multiplicative functions. <i>Mathematika</i>. 2019;64(4):990–1009. doi:<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>","bibtex":"@article{Elsholtz_Technau_Technau_2019, title={The maximal order of iterated multiplicative functions}, volume={64}, DOI={<a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>}, number={4}, journal={Mathematika}, author={Elsholtz, Ch. and Technau, Marc and Technau, N.}, year={2019}, pages={990–1009} }","apa":"Elsholtz, Ch., Technau, M., &#38; Technau, N. (2019). The maximal order of iterated multiplicative functions. <i>Mathematika</i>, <i>64</i>(4), 990–1009. <a href=\"https://doi.org/10.1112/S0025579319000214\">https://doi.org/10.1112/S0025579319000214</a>","ieee":"Ch. Elsholtz, M. Technau, and N. Technau, “The maximal order of iterated multiplicative functions,” <i>Mathematika</i>, vol. 64, no. 4, pp. 990–1009, 2019, doi: <a href=\"https://doi.org/10.1112/S0025579319000214\">10.1112/S0025579319000214</a>.","chicago":"Elsholtz, Ch., Marc Technau, and N. Technau. “The Maximal Order of Iterated Multiplicative Functions.” <i>Mathematika</i> 64, no. 4 (2019): 990–1009. <a href=\"https://doi.org/10.1112/S0025579319000214\">https://doi.org/10.1112/S0025579319000214</a>.","short":"Ch. Elsholtz, M. Technau, N. Technau, Mathematika 64 (2019) 990–1009."},"user_id":"106108","doi":"10.1112/S0025579319000214","volume":64,"page":"990–1009","_id":"55284","language":[{"iso":"eng"}],"date_updated":"2024-07-24T07:25:42Z","intvolume":"        64","year":"2019","status":"public","title":"The maximal order of iterated multiplicative functions","author":[{"last_name":"Elsholtz","first_name":"Ch.","full_name":"Elsholtz, Ch."},{"id":"106108","first_name":"Marc","last_name":"Technau","orcid":"0000-0001-9650-2459","full_name":"Technau, Marc"},{"full_name":"Technau, N.","first_name":"N.","last_name":"Technau"}]},{"page":"127–135","_id":"55285","language":[{"iso":"eng"}],"user_id":"106108","doi":"10.7546/nntdm.2019.25.2.127-135","volume":25,"status":"public","title":"Generalised Beatty sets","year":"2019","author":[{"full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","first_name":"Marc","last_name":"Technau","id":"106108"}],"date_updated":"2024-07-24T07:25:59Z","intvolume":"        25","date_created":"2024-07-16T11:09:02Z","type":"journal_article","department":[{"_id":"102"}],"publication":"Notes Number Theory Discrete Math.","issue":"2","citation":{"ieee":"M. Technau, “Generalised Beatty sets,” <i>Notes Number Theory Discrete Math.</i>, vol. 25, no. 2, pp. 127–135, 2019, doi: <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>.","apa":"Technau, M. (2019). Generalised Beatty sets. <i>Notes Number Theory Discrete Math.</i>, <i>25</i>(2), 127–135. <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">https://doi.org/10.7546/nntdm.2019.25.2.127-135</a>","chicago":"Technau, Marc. “Generalised Beatty Sets.” <i>Notes Number Theory Discrete Math.</i> 25, no. 2 (2019): 127–135. <a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">https://doi.org/10.7546/nntdm.2019.25.2.127-135</a>.","short":"M. Technau, Notes Number Theory Discrete Math. 25 (2019) 127–135.","mla":"Technau, Marc. “Generalised Beatty Sets.” <i>Notes Number Theory Discrete Math.</i>, vol. 25, no. 2, 2019, pp. 127–135, doi:<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>.","bibtex":"@article{Technau_2019, title={Generalised Beatty sets}, volume={25}, DOI={<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>}, number={2}, journal={Notes Number Theory Discrete Math.}, author={Technau, Marc}, year={2019}, pages={127–135} }","ama":"Technau M. Generalised Beatty sets. <i>Notes Number Theory Discrete Math</i>. 2019;25(2):127–135. doi:<a href=\"https://doi.org/10.7546/nntdm.2019.25.2.127-135\">10.7546/nntdm.2019.25.2.127-135</a>"},"extern":"1"},{"language":[{"iso":"eng"}],"doi":"10.1007/s00013-019-01348-z","author":[{"id":"82258","first_name":"Markus","last_name":"Kirschmer","full_name":"Kirschmer, Markus"}],"publication_identifier":{"issn":["0003-889X","1420-8938"]},"title":"Determinant groups of Hermitian lattices over local fields","year":"2019","intvolume":"       113","date_updated":"2023-04-04T09:05:04Z","publication_status":"published","date_created":"2022-12-23T11:03:41Z","department":[{"_id":"102"}],"keyword":["General Mathematics"],"type":"journal_article","publication":"Archiv der Mathematik","issue":"4","abstract":[{"lang":"eng","text":"We describe the determinants of the automorphism groups of Hermitian lattices over local fields. Using a result of G. Shimura, this yields an explicit method to compute the special genera in a given genus of Hermitian lattices over a number field."}],"publisher":"Springer Science and Business Media LLC","_id":"34915","page":"337-347","volume":113,"user_id":"93826","status":"public","citation":{"apa":"Kirschmer, M. (2019). Determinant groups of Hermitian lattices over local fields. <i>Archiv Der Mathematik</i>, <i>113</i>(4), 337–347. <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">https://doi.org/10.1007/s00013-019-01348-z</a>","ieee":"M. Kirschmer, “Determinant groups of Hermitian lattices over local fields,” <i>Archiv der Mathematik</i>, vol. 113, no. 4, pp. 337–347, 2019, doi: <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>.","short":"M. Kirschmer, Archiv Der Mathematik 113 (2019) 337–347.","chicago":"Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” <i>Archiv Der Mathematik</i> 113, no. 4 (2019): 337–47. <a href=\"https://doi.org/10.1007/s00013-019-01348-z\">https://doi.org/10.1007/s00013-019-01348-z</a>.","mla":"Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.” <i>Archiv Der Mathematik</i>, vol. 113, no. 4, Springer Science and Business Media LLC, 2019, pp. 337–47, doi:<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>.","ama":"Kirschmer M. Determinant groups of Hermitian lattices over local fields. <i>Archiv der Mathematik</i>. 2019;113(4):337-347. doi:<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>","bibtex":"@article{Kirschmer_2019, title={Determinant groups of Hermitian lattices over local fields}, volume={113}, DOI={<a href=\"https://doi.org/10.1007/s00013-019-01348-z\">10.1007/s00013-019-01348-z</a>}, number={4}, journal={Archiv der Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kirschmer, Markus}, year={2019}, pages={337–347} }"}},{"date_created":"2023-05-31T07:45:22Z","place":"Heidelberg","type":"book","department":[{"_id":"98"}],"citation":{"ieee":"J. Dröse, <i>Textaufgaben lesen und verstehen lernen – Entwicklungsforschungsstudie zur mathematikspezifischen Leseverständnisförderung</i>. Heidelberg: Springer Spektrum, 2019.","apa":"Dröse, J. (2019). <i>Textaufgaben lesen und verstehen lernen – Entwicklungsforschungsstudie zur mathematikspezifischen Leseverständnisförderung</i>. Springer Spektrum.","chicago":"Dröse, Jennifer. <i>Textaufgaben lesen und verstehen lernen – Entwicklungsforschungsstudie zur mathematikspezifischen Leseverständnisförderung</i>. Heidelberg: Springer Spektrum, 2019.","short":"J. Dröse, Textaufgaben lesen und verstehen lernen – Entwicklungsforschungsstudie zur mathematikspezifischen Leseverständnisförderung, Springer Spektrum, Heidelberg, 2019.","mla":"Dröse, Jennifer. <i>Textaufgaben lesen und verstehen lernen – Entwicklungsforschungsstudie zur mathematikspezifischen Leseverständnisförderung</i>. Springer Spektrum, 2019.","bibtex":"@book{Dröse_2019, place={Heidelberg}, title={Textaufgaben lesen und verstehen lernen – Entwicklungsforschungsstudie zur mathematikspezifischen Leseverständnisförderung}, publisher={Springer Spektrum}, author={Dröse, Jennifer}, year={2019} }","ama":"Dröse J. <i>Textaufgaben lesen und verstehen lernen – Entwicklungsforschungsstudie zur mathematikspezifischen Leseverständnisförderung</i>. Springer Spektrum; 2019."},"extern":"1","publisher":"Springer Spektrum","_id":"45387","language":[{"iso":"ger"}],"user_id":"21240","status":"public","year":"2019","title":"Textaufgaben lesen und verstehen lernen – Entwicklungsforschungsstudie zur mathematikspezifischen Leseverständnisförderung","author":[{"last_name":"Dröse","first_name":"Jennifer","full_name":"Dröse, Jennifer","id":"85820"}],"date_updated":"2023-05-31T07:45:36Z"},{"_id":"45390","publisher":"de Gruyter","language":[{"iso":"ger"}],"page":"107-134","editor":[{"first_name":"B.","last_name":"Ahrenholz","full_name":"Ahrenholz, B."},{"last_name":"Jeuk","first_name":"S.","full_name":"Jeuk, S."},{"full_name":"Lütke, B.","last_name":"Lütke","first_name":"B."},{"full_name":"Paetsch, J.","first_name":"J.","last_name":"Paetsch"},{"full_name":"Roll, H.","first_name":"H.","last_name":"Roll"}],"user_id":"21240","author":[{"id":"85820","last_name":"Dröse","first_name":"Jennifer","full_name":"Dröse, Jennifer"},{"full_name":"Prediger, Susanne","last_name":"Prediger","first_name":"Susanne"}],"title":"Scaffolding für fachbezogene textsortenspezifische Lesestrategien – Entwicklungsforschungsstudie zur Förderung des Umgangs mit Textaufgaben","year":"2019","status":"public","date_updated":"2023-05-31T08:03:38Z","place":"Berlin","date_created":"2023-05-31T08:02:17Z","department":[{"_id":"98"}],"type":"book_chapter","citation":{"ama":"Dröse J, Prediger S. Scaffolding für fachbezogene textsortenspezifische Lesestrategien – Entwicklungsforschungsstudie zur Förderung des Umgangs mit Textaufgaben. 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Eichen. “Frühe mathematische Bildung im elementarpädagogischen Alltag.” <i>KiTa aktuell Österreich</i> 7, no. 5 (2019): 85–86."},"publication":"KiTa aktuell Österreich","issue":"5"},{"citation":{"ama":"Bruns J, Gasteiger H. VimaS_num: Measuring situational perception in mathematics of early childhood teachers. In: Graven M, Venkat H, Essien A, Vale P, eds. <i>Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education</i>. 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Gasteiger, “VimaS_num: Measuring situational perception in mathematics of early childhood teachers,” in <i>Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education</i>, Pretoria, South Africa, 2019, vol. 2, pp. 129–136."},"quality_controlled":"1","oa":"1","status":"public","conference":{"location":"Pretoria, South Africa","name":"43rd Conference of the International Group for the Psychology of Mathematics Education"},"page":"129-136","_id":"36529","user_id":"49063","volume":2,"editor":[{"last_name":"Graven","first_name":"Mellony","full_name":"Graven, Mellony"},{"last_name":"Venkat","first_name":"Hamsa","full_name":"Venkat, Hamsa"},{"last_name":"Essien","first_name":"Anthony","full_name":"Essien, Anthony"},{"first_name":"Pamela","last_name":"Vale","full_name":"Vale, Pamela"}],"publication":"Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education","date_created":"2023-01-13T08:51:58Z","type":"conference","department":[{"_id":"611"},{"_id":"97"}],"year":"2019","title":"VimaS_num: Measuring situational perception in mathematics of early childhood teachers","author":[{"first_name":"Julia","last_name":"Bruns","orcid":"https://orcid.org/0000-0002-6604-5864","full_name":"Bruns, Julia","id":"72183"},{"last_name":"Gasteiger","first_name":"Hedwig","full_name":"Gasteiger, Hedwig"}],"publication_status":"published","date_updated":"2023-06-20T19:05:48Z","intvolume":"         2","main_file_link":[{"url":"https://www.igpme.org/publications/current-proceedings/","open_access":"1"}],"language":[{"iso":"eng"}]},{"page":"193-205","language":[{"iso":"eng"}],"_id":"21531","user_id":"49063","doi":"10.1007/s11858-019-01103-2","volume":52,"title":"Mathematical pedagogical content knowledge of early childhood teachers: a standardized situation-related measurement approach","status":"public","year":"2019","publication_identifier":{"issn":["1863-9690","1863-9704"]},"author":[{"full_name":"Gasteiger, Hedwig","first_name":"Hedwig","last_name":"Gasteiger"},{"full_name":"Bruns, Julia","orcid":"https://orcid.org/0000-0002-6604-5864","first_name":"Julia","last_name":"Bruns","id":"72183"},{"full_name":"Benz, Christiane","last_name":"Benz","first_name":"Christiane"},{"last_name":"Brunner","first_name":"Esther","full_name":"Brunner, Esther"},{"first_name":"Priska","last_name":"Sprenger","full_name":"Sprenger, Priska"}],"publication_status":"published","date_updated":"2023-06-20T19:11:34Z","intvolume":"        52","date_created":"2021-03-17T15:19:51Z","type":"journal_article","department":[{"_id":"97"},{"_id":"611"}],"publication":"ZDM","citation":{"chicago":"Gasteiger, Hedwig, Julia Bruns, Christiane Benz, Esther Brunner, and Priska Sprenger. “Mathematical Pedagogical Content Knowledge of Early Childhood Teachers: A Standardized Situation-Related Measurement Approach.” <i>ZDM</i> 52 (2019): 193–205. <a href=\"https://doi.org/10.1007/s11858-019-01103-2\">https://doi.org/10.1007/s11858-019-01103-2</a>.","short":"H. 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Münster: WTM-Verlag, 2019. <a href=\"https://doi.org/10.17877/DE290R-20771\">https://doi.org/10.17877/DE290R-20771</a>.","short":"J. Bruns, H. Gasteiger, in: A. Frank, S. Krauss, K. Binder (Eds.), Beiträge zum Mathematikunterricht 2019, WTM-Verlag,  Münster, 2019, pp. 169–172.","ama":"Bruns J, Gasteiger H. Mathematikdidaktischen Wissen von frühpädagogischen Fachkräften aus kognitiv-situationsbezogener Perspektive – Theoretisches Konstrukt und empirische Erfassung. In: Frank A, Krauss S, Binder K, eds. <i>Beiträge zum Mathematikunterricht 2019</i>. WTM-Verlag; 2019:169-172. doi:<a href=\"https://doi.org/10.17877/DE290R-20771\">10.17877/DE290R-20771</a>","ieee":"J. Bruns and H. 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WTM-Verlag. <a href=\"https://doi.org/10.17877/DE290R-20771\">https://doi.org/10.17877/DE290R-20771</a>","mla":"Bruns, Julia, and Hedwig Gasteiger. “Mathematikdidaktischen Wissen von frühpädagogischen Fachkräften aus kognitiv-situationsbezogener Perspektive – Theoretisches Konstrukt und empirische Erfassung.” <i>Beiträge zum Mathematikunterricht 2019</i>, edited by Andreas Frank et al., WTM-Verlag, 2019, pp. 169–72, doi:<a href=\"https://doi.org/10.17877/DE290R-20771\">10.17877/DE290R-20771</a>."},"main_file_link":[{"url":"https://eldorado.tu-dortmund.de/bitstream/2003/38852/1/BzMU19_BRUNS.pdf","open_access":"1"}],"language":[{"iso":"ger"}],"doi":"10.17877/DE290R-20771","year":"2019","title":"Mathematikdidaktischen Wissen von frühpädagogischen Fachkräften aus kognitiv-situationsbezogener Perspektive – Theoretisches Konstrukt und empirische Erfassung","author":[{"orcid":"https://orcid.org/0000-0002-6604-5864","last_name":"Bruns","first_name":"Julia","full_name":"Bruns, Julia","id":"72183"},{"first_name":"Hedwig","last_name":"Gasteiger","full_name":"Gasteiger, Hedwig"}],"date_updated":"2023-06-20T19:14:14Z","publication_status":"published","date_created":"2023-01-13T09:14:30Z","type":"conference","department":[{"_id":"611"},{"_id":"97"}],"publication":"Beiträge zum Mathematikunterricht 2019"},{"author":[{"id":"99409","first_name":"Johanna","last_name":"Schönherr","full_name":"Schönherr, Johanna"}],"status":"public","year":"2019","title":"Selbst erstellte Skizzen beim mathematischen Modellieren: Ergebnisse einer empirischen Untersuchung [Self-generated drawings for modelling problems: Findings of an empirical study]","publication_status":"published","date_updated":"2023-06-20T19:29:45Z","language":[{"iso":"ger"}],"_id":"45331","publisher":"Springer Spektrum","alternative_title":["(Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik)"],"user_id":"49063","citation":{"bibtex":"@book{Schönherr_2019, place={Wiesbaden}, title={Selbst erstellte Skizzen beim mathematischen Modellieren: Ergebnisse einer empirischen Untersuchung [Self-generated drawings for modelling problems: Findings of an empirical study]}, publisher={Springer Spektrum}, author={Schönherr, Johanna}, year={2019} }","ama":"Schönherr J. <i>Selbst erstellte Skizzen beim mathematischen Modellieren: Ergebnisse einer empirischen Untersuchung [Self-generated drawings for modelling problems: Findings of an empirical study]</i>. 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A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. <i>Communications in Computational Physics</i>, <i>25</i>(2), 564–585. <a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">https://doi.org/10.4208/cicp.OA-2018-0053</a>","bibtex":"@article{Richters_Lass_Walther_Plessl_Kühne_2019, title={A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices}, volume={25}, DOI={<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>}, number={2}, journal={Communications in Computational Physics}, publisher={Global Science Press}, author={Richters, Dorothee and Lass, Michael and Walther, Andrea and Plessl, Christian and Kühne, Thomas}, year={2019}, pages={564–585} }","ama":"Richters D, Lass M, Walther A, Plessl C, Kühne T. A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. <i>Communications in Computational Physics</i>. 2019;25(2):564-585. doi:<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>","mla":"Richters, Dorothee, et al. “A General Algorithm to Calculate the Inverse Principal P-Th Root of Symmetric Positive Definite Matrices.” <i>Communications in Computational Physics</i>, vol. 25, no. 2, Global Science Press, 2019, pp. 564–85, doi:<a href=\"https://doi.org/10.4208/cicp.OA-2018-0053\">10.4208/cicp.OA-2018-0053</a>."},"quality_controlled":"1","project":[{"name":"Performance and Efficiency in HPC with Custom Computing","_id":"32","grant_number":"PL 595/2-1 / 320898746"},{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"external_id":{"arxiv":["1703.02456"]},"title":"A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices","year":"2019","author":[{"last_name":"Richters","first_name":"Dorothee","full_name":"Richters, Dorothee"},{"first_name":"Michael","last_name":"Lass","orcid":"0000-0002-5708-7632","full_name":"Lass, Michael","id":"24135"},{"first_name":"Andrea","last_name":"Walther","full_name":"Walther, Andrea"},{"id":"16153","orcid":"0000-0001-5728-9982","first_name":"Christian","last_name":"Plessl","full_name":"Plessl, Christian"},{"full_name":"Kühne, Thomas","last_name":"Kühne","first_name":"Thomas","id":"49079"}],"date_updated":"2023-09-26T11:45:02Z","intvolume":"        25","language":[{"iso":"eng"}],"doi":"10.4208/cicp.OA-2018-0053","publication":"Communications in Computational Physics","issue":"2","abstract":[{"text":"We address the general mathematical problem of computing the inverse p-th\r\nroot of a given matrix in an efficient way. A new method to construct iteration\r\nfunctions that allow calculating arbitrary p-th roots and their inverses of\r\nsymmetric positive definite matrices is presented. We show that the order of\r\nconvergence is at least quadratic and that adaptively adjusting a parameter q\r\nalways leads to an even faster convergence. In this way, a better performance\r\nthan with previously known iteration schemes is achieved. The efficiency of the\r\niterative functions is demonstrated for various matrices with different\r\ndensities, condition numbers and spectral radii.","lang":"eng"}],"date_created":"2017-07-25T14:48:26Z","type":"journal_article","department":[{"_id":"27"},{"_id":"518"},{"_id":"304"},{"_id":"104"}]},{"user_id":"32655","ddc":["510"],"_id":"16711","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.08824"}],"has_accepted_license":"1","date_updated":"2024-09-24T12:09:27Z","author":[{"id":"32655","full_name":"Gerlach, Raphael","last_name":"Gerlach","first_name":"Raphael"},{"full_name":"Koltai, Péter","last_name":"Koltai","first_name":"Péter"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"title":"Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems","year":"2019","status":"public","department":[{"_id":"101"}],"oa":"1","type":"preprint","date_created":"2020-04-16T14:06:21Z","external_id":{"arxiv":["1902.08824"]},"abstract":[{"text":"Embedding techniques allow the approximations of finite dimensional\r\nattractors and manifolds of infinite dimensional dynamical systems via\r\nsubdivision and continuation methods. These approximations give a topological\r\none-to-one image of the original set. In order to additionally reveal their\r\ngeometry we use diffusion mapst o find intrinsic coordinates. We illustrate our\r\nresults on the unstable manifold of the one-dimensional Kuramoto--Sivashinsky\r\nequation, as well as for the attractor of the Mackey-Glass delay differential\r\nequation.","lang":"eng"}],"citation":{"mla":"Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of  Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 2019.","bibtex":"@article{Gerlach_Koltai_Dellnitz_2019, title={Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems}, journal={arXiv:1902.08824}, author={Gerlach, Raphael and Koltai, Péter and Dellnitz, Michael}, year={2019} }","ama":"Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems. <i>arXiv:190208824</i>. Published online 2019.","ieee":"R. Gerlach, P. Koltai, and M. Dellnitz, “Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems,” <i>arXiv:1902.08824</i>. 2019.","apa":"Gerlach, R., Koltai, P., &#38; Dellnitz, M. (2019). Revealing the intrinsic geometry of finite dimensional invariant sets of  infinite dimensional dynamical systems. In <i>arXiv:1902.08824</i>.","chicago":"Gerlach, Raphael, Péter Koltai, and Michael Dellnitz. “Revealing the Intrinsic Geometry of Finite Dimensional Invariant Sets of  Infinite Dimensional Dynamical Systems.” <i>ArXiv:1902.08824</i>, 2019.","short":"R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019)."},"publication":"arXiv:1902.08824"},{"publication":"AStA Wirtschafts- und Sozialstatistisches Archiv","issue":"1","date_created":"2024-09-25T08:19:16Z","department":[{"_id":"363"}],"type":"journal_article","author":[{"last_name":"Engel","first_name":"Joachim","full_name":"Engel, Joachim"},{"id":"16274","full_name":"Biehler, Rolf","last_name":"Biehler","first_name":"Rolf"},{"full_name":"Frischemeier, Daniel","last_name":"Frischemeier","first_name":"Daniel"},{"orcid":"0000-0002-6313-5987","last_name":"Podworny","first_name":"Susanne","full_name":"Podworny, Susanne","id":"30619"},{"full_name":"Schiller, Achim","last_name":"Schiller","first_name":"Achim"},{"first_name":"Laura","last_name":"Martignon","full_name":"Martignon, Laura"}],"publication_identifier":{"issn":["1863-8155","1863-8163"]},"year":"2019","title":"Erratum to: Zivilstatistik: Konzept einer neuen Perspektive auf Data Literacy und Statistical Literacy","intvolume":"        14","date_updated":"2024-09-25T08:27:59Z","publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://link.springer.com/article/10.1007/s11943-019-00266-4"}],"doi":"10.1007/s11943-019-00266-4","citation":{"bibtex":"@article{Engel_Biehler_Frischemeier_Podworny_Schiller_Martignon_2019, title={Erratum to: Zivilstatistik: Konzept einer neuen Perspektive auf Data Literacy und Statistical Literacy}, volume={14}, DOI={<a href=\"https://doi.org/10.1007/s11943-019-00266-4\">10.1007/s11943-019-00266-4</a>}, number={1}, journal={AStA Wirtschafts- und Sozialstatistisches Archiv}, publisher={Springer Science and Business Media LLC}, author={Engel, Joachim and Biehler, Rolf and Frischemeier, Daniel and Podworny, Susanne and Schiller, Achim and Martignon, Laura}, year={2019}, pages={113–114} }","short":"J. Engel, R. Biehler, D. Frischemeier, S. Podworny, A. Schiller, L. Martignon, AStA Wirtschafts- Und Sozialstatistisches Archiv 14 (2019) 113–114.","ama":"Engel J, Biehler R, Frischemeier D, Podworny S, Schiller A, Martignon L. Erratum to: Zivilstatistik: Konzept einer neuen Perspektive auf Data Literacy und Statistical Literacy. <i>AStA Wirtschafts- und Sozialstatistisches Archiv</i>. 2019;14(1):113-114. doi:<a href=\"https://doi.org/10.1007/s11943-019-00266-4\">10.1007/s11943-019-00266-4</a>","chicago":"Engel, Joachim, Rolf Biehler, Daniel Frischemeier, Susanne Podworny, Achim Schiller, and Laura Martignon. “Erratum to: Zivilstatistik: Konzept Einer Neuen Perspektive Auf Data Literacy Und Statistical Literacy.” <i>AStA Wirtschafts- Und Sozialstatistisches Archiv</i> 14, no. 1 (2019): 113–14. <a href=\"https://doi.org/10.1007/s11943-019-00266-4\">https://doi.org/10.1007/s11943-019-00266-4</a>.","ieee":"J. Engel, R. Biehler, D. Frischemeier, S. Podworny, A. Schiller, and L. Martignon, “Erratum to: Zivilstatistik: Konzept einer neuen Perspektive auf Data Literacy und Statistical Literacy,” <i>AStA Wirtschafts- und Sozialstatistisches Archiv</i>, vol. 14, no. 1, pp. 113–114, 2019, doi: <a href=\"https://doi.org/10.1007/s11943-019-00266-4\">10.1007/s11943-019-00266-4</a>.","mla":"Engel, Joachim, et al. “Erratum to: Zivilstatistik: Konzept Einer Neuen Perspektive Auf Data Literacy Und Statistical Literacy.” <i>AStA Wirtschafts- Und Sozialstatistisches Archiv</i>, vol. 14, no. 1, Springer Science and Business Media LLC, 2019, pp. 113–14, doi:<a href=\"https://doi.org/10.1007/s11943-019-00266-4\">10.1007/s11943-019-00266-4</a>.","apa":"Engel, J., Biehler, R., Frischemeier, D., Podworny, S., Schiller, A., &#38; Martignon, L. (2019). 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