[{"date_updated":"2025-12-16T13:05:36Z","date_created":"2025-12-16T13:05:30Z","author":[{"id":"44239","full_name":"Truong, Ha My","last_name":"Truong","first_name":"Ha My"},{"first_name":"Christoph","full_name":"Vogelsang, Christoph","id":"4245","orcid":"0000-0002-5804-1855","last_name":"Vogelsang"},{"last_name":"Meier","orcid":"https://orcid.org/0000-0002-6756-9440","id":"28542","full_name":"Meier, Jana","first_name":"Jana"}],"title":"Zwischen fortgesetzter Professionalisierung und bewusster Neuorientierung:  Das außerschulische Berufsfeldpraktikum (BFP) aus Sicht von Lehramtsstudierenden ","conference":{"start_date":"2023-06-21","name":"5. IGSP Kongress – «Lernen in zwei Praxen – Praktiken und Qualität(en) Schul- und Berufspraktischer Studien»","location":"Muttenz","end_date":"2023-06-23"},"year":"2023","citation":{"chicago":"Truong, Ha My, Christoph Vogelsang, and Jana Meier. “Zwischen Fortgesetzter Professionalisierung Und Bewusster Neuorientierung:  Das Außerschulische Berufsfeldpraktikum (BFP) Aus Sicht von Lehramtsstudierenden ,” 2023.","ieee":"H. M. Truong, C. Vogelsang, and J. Meier, “Zwischen fortgesetzter Professionalisierung und bewusster Neuorientierung:  Das außerschulische Berufsfeldpraktikum (BFP) aus Sicht von Lehramtsstudierenden ,” presented at the 5. IGSP Kongress – «Lernen in zwei Praxen – Praktiken und Qualität(en) Schul- und Berufspraktischer Studien», Muttenz, 2023.","ama":"Truong HM, Vogelsang C, Meier J. Zwischen fortgesetzter Professionalisierung und bewusster Neuorientierung:  Das außerschulische Berufsfeldpraktikum (BFP) aus Sicht von Lehramtsstudierenden . In: ; 2023.","apa":"Truong, H. M., Vogelsang, C., &#38; Meier, J. (2023). <i>Zwischen fortgesetzter Professionalisierung und bewusster Neuorientierung:  Das außerschulische Berufsfeldpraktikum (BFP) aus Sicht von Lehramtsstudierenden </i>. 5. IGSP Kongress – «Lernen in zwei Praxen – Praktiken und Qualität(en) Schul- und Berufspraktischer Studien», Muttenz.","bibtex":"@inproceedings{Truong_Vogelsang_Meier_2023, title={Zwischen fortgesetzter Professionalisierung und bewusster Neuorientierung:  Das außerschulische Berufsfeldpraktikum (BFP) aus Sicht von Lehramtsstudierenden }, author={Truong, Ha My and Vogelsang, Christoph and Meier, Jana}, year={2023} }","mla":"Truong, Ha My, et al. <i>Zwischen Fortgesetzter Professionalisierung Und Bewusster Neuorientierung:  Das Außerschulische Berufsfeldpraktikum (BFP) Aus Sicht von Lehramtsstudierenden </i>. 2023.","short":"H.M. Truong, C. Vogelsang, J. Meier, in: 2023."},"_id":"63130","user_id":"44239","department":[{"_id":"33"}],"language":[{"iso":"eng"}],"type":"conference","abstract":[{"lang":"eng","text":"Das obligatorische vierwöchige Berufsfeldpraktikum (BFP) für Lehramtsstudierende in\r\nNordrhein-Westfalen verfolgt zwei Ziele. Zum einen sollen die Studierenden berufliche\r\nPerspektiven außerhalb des Schuldienstes kennenlernen (Bauer et al., 2011), zum anderen\r\naber auch „Einblicke in die für den Lehrerberuf relevanten außerschulischen\r\nTätigkeitsfelder“ (LABG, 2002, §12) erhalten. Diese Ziele sind zum Teil gegenläufig und\r\nkönnen abhängig von der konkreten Ausgestaltung (z.B. in welchem Tätigkeitsfeld das BFP\r\nabsolviert wird) nicht gleichzeitig voll erreicht werden. Es stellt sich daher die Frage, welcher\r\nZielschwerpunkt von den Studierenden selbst angestrebt wird. Basierend auf kumulierten\r\nDaten von regelmäßigen Online-Evaluationsbefragungen zum BFP an der Universität\r\nPaderborn (N = 3.156) wird daher exploriert, wie Studierende das BFP ausgestalten und\r\neinschätzen. Es zeigt sich, dass das BFP generell als positiv beurteilt wird. In den gewählten\r\nTätigkeitsfeldern und Rückmeldungen der Studierenden wird aber auch deutlich, dass das\r\nBFP eher als fortgesetzte Professionalisierung für den Lehrberuf und wenig zur Suche nach\r\nberuflichen Alternativen genutzt wird. Es wird also konsistent zur bekannt starken\r\nMotivation von LA-Studierenden für den Zielberuf ausgestaltet (Rothland, 2010). Dabei\r\nbesteht allerdings die Gefahr, dass diese kaum bewusste Erfahrungen in einer Arbeitswelt\r\nmachen, für die sie ihre Schüler*innen vorbereiten müssen (Dreer, 2013)."}],"status":"public"},{"citation":{"chicago":"Truong, Ha My. “Level Up! Gamification in Der Lehrkräfteausbildung (Poster),” 2023.","ieee":"H. M. Truong, “Level Up! Gamification in der Lehrkräfteausbildung (Poster),” presented at the Digitalisierungsbezogene Lehrer*innenbildung an der Universität Paderborn, Paderborn, 2023.","ama":"Truong HM. Level Up! Gamification in der Lehrkräfteausbildung (Poster). In: ; 2023.","mla":"Truong, Ha My. <i>Level Up! Gamification in Der Lehrkräfteausbildung (Poster)</i>. 2023.","bibtex":"@inproceedings{Truong_2023, title={Level Up! Gamification in der Lehrkräfteausbildung (Poster)}, author={Truong, Ha My}, year={2023} }","short":"H.M. Truong, in: 2023.","apa":"Truong, H. M. (2023). <i>Level Up! Gamification in der Lehrkräfteausbildung (Poster)</i>. Digitalisierungsbezogene Lehrer*innenbildung an der Universität Paderborn, Paderborn."},"year":"2023","conference":{"end_date":"2023-04-27","location":"Paderborn","name":"Digitalisierungsbezogene Lehrer*innenbildung an der Universität Paderborn","start_date":"2023-04-27"},"title":"Level Up! Gamification in der Lehrkräfteausbildung (Poster)","author":[{"first_name":"Ha My","id":"44239","full_name":"Truong, Ha My","last_name":"Truong"}],"date_created":"2025-12-16T12:29:05Z","date_updated":"2025-12-16T13:42:05Z","status":"public","abstract":[{"text":"Mit Gamification wird der Einsatz von Spielemechanismen und -designs in nicht-spielerischen Situationen bezeichnet (Werbach, K.; Hunter, D., 2020). Die möglichen Ziele sind dabei, das Verhalten zu verändern und die Motivation zum Lernen sowie die Fähigkeit zur Problemlösung zu erhöhen. (Fischer, S.; Reichmuth, A., 2020)\r\n„Gamification kann als eine Bereicherung in Schule und Unterricht verstanden werden, insofern sie gutgestaltet sowie durchdacht und bedarfsgerecht eingesetzt wird“ (Sailer, M.; Tokls, D.; Mandl, H., 2019).\r\nUm angehende Lehrkräfte dabei zu unterstützen, das volle Potenzial von Gamification (GF) und Game-based Learning (GBL) in ihrem zukünftigen Unterricht auszuschöpfen, wird im Seminar \"Spielend lernen? - Game-based Learning und Gamification im Schulkontext\" eine umfassende Einführung in diese Konzepte geboten. Dabei werden nicht nur theoretische Grundlagen vermittelt, sondern den Studierenden die Möglichkeit gegeben, verschiedene Gamification-Methoden praktisch anzuwenden und zu erleben. Durch den Einsatz der moodle-basierten Plattform PANDA können verschiedene GF-Methoden und Beispiele für GBL nahtlos in das Seminar integriert werden. Dadurch haben die Teilnehmenden die Möglichkeit, die Konzepte von GF und GBL nicht nur theoretisch zu erlernen, sondern sie auch durch eigenes Erleben und praktisches Anwenden zu vertiefen.\r\n","lang":"ger"}],"type":"conference","language":[{"iso":"eng"}],"user_id":"44239","department":[{"_id":"33"}],"_id":"63128"},{"citation":{"apa":"Truong, H. M. (2023). <i>Wie organisiert sind Lehramtsstudierende in ihrer Semester- und Prüfungsphasenplanung? – Entwicklung einer Evaluation zum Selbstorganisationsverhalten</i>. For­schungs­kol­leg Em­pi­ri­sche Bil­dungs­for­schung, online - Paderborn.","bibtex":"@inproceedings{Truong_2023, title={Wie organisiert sind Lehramtsstudierende in ihrer Semester- und Prüfungsphasenplanung? – Entwicklung einer Evaluation zum Selbstorganisationsverhalten}, author={Truong, Ha My}, year={2023} }","short":"H.M. Truong, in: 2023.","mla":"Truong, Ha My. <i>Wie Organisiert Sind Lehramtsstudierende in Ihrer Semester- Und Prüfungsphasenplanung? – Entwicklung Einer Evaluation Zum Selbstorganisationsverhalten</i>. 2023.","ama":"Truong HM. Wie organisiert sind Lehramtsstudierende in ihrer Semester- und Prüfungsphasenplanung? – Entwicklung einer Evaluation zum Selbstorganisationsverhalten. In: ; 2023.","ieee":"H. M. Truong, “Wie organisiert sind Lehramtsstudierende in ihrer Semester- und Prüfungsphasenplanung? – Entwicklung einer Evaluation zum Selbstorganisationsverhalten,” presented at the For­schungs­kol­leg Em­pi­ri­sche Bil­dungs­for­schung, online - Paderborn, 2023.","chicago":"Truong, Ha My. “Wie Organisiert Sind Lehramtsstudierende in Ihrer Semester- Und Prüfungsphasenplanung? – Entwicklung Einer Evaluation Zum Selbstorganisationsverhalten,” 2023."},"status":"public","year":"2023","type":"conference","language":[{"iso":"eng"}],"conference":{"location":"online - Paderborn","end_date":"2023-01-10","start_date":"2023-01-10","name":"For­schungs­kol­leg Em­pi­ri­sche Bil­dungs­for­schung"},"title":"Wie organisiert sind Lehramtsstudierende in ihrer Semester- und Prüfungsphasenplanung? – Entwicklung einer Evaluation zum Selbstorganisationsverhalten","author":[{"full_name":"Truong, Ha My","id":"44239","last_name":"Truong","first_name":"Ha My"}],"user_id":"44239","date_created":"2025-12-16T13:35:10Z","department":[{"_id":"33"}],"date_updated":"2025-12-16T13:43:11Z","_id":"63133"},{"publication_identifier":{"issn":["0003-889X"]},"issue":"2","year":"2023","page":"135-146","intvolume":"       120","citation":{"apa":"Letz, J. C. (2023). Brown representability for triangulated categories with a linear action by a graded ring. <i>Arch. Math. (Basel)</i>, <i>120</i>(2), 135–146. <a href=\"https://doi.org/10.1007/s00013-022-01800-7\">https://doi.org/10.1007/s00013-022-01800-7</a>","mla":"Letz, Janina Carmen. “Brown Representability for Triangulated Categories with a Linear Action by a Graded Ring.” <i>Arch. Math. (Basel)</i>, vol. 120, no. 2, 2023, pp. 135–46, doi:<a href=\"https://doi.org/10.1007/s00013-022-01800-7\">10.1007/s00013-022-01800-7</a>.","short":"J.C. Letz, Arch. Math. (Basel) 120 (2023) 135–146.","bibtex":"@article{Letz_2023, title={Brown representability for triangulated categories with a linear action by a graded ring}, volume={120}, DOI={<a href=\"https://doi.org/10.1007/s00013-022-01800-7\">10.1007/s00013-022-01800-7</a>}, number={2}, journal={Arch. Math. (Basel)}, author={Letz, Janina Carmen}, year={2023}, pages={135–146} }","ama":"Letz JC. Brown representability for triangulated categories with a linear action by a graded ring. <i>Arch Math (Basel)</i>. 2023;120(2):135-146. doi:<a href=\"https://doi.org/10.1007/s00013-022-01800-7\">10.1007/s00013-022-01800-7</a>","ieee":"J. C. Letz, “Brown representability for triangulated categories with a linear action by a graded ring,” <i>Arch. Math. (Basel)</i>, vol. 120, no. 2, pp. 135–146, 2023, doi: <a href=\"https://doi.org/10.1007/s00013-022-01800-7\">10.1007/s00013-022-01800-7</a>.","chicago":"Letz, Janina Carmen. “Brown Representability for Triangulated Categories with a Linear Action by a Graded Ring.” <i>Arch. Math. (Basel)</i> 120, no. 2 (2023): 135–46. <a href=\"https://doi.org/10.1007/s00013-022-01800-7\">https://doi.org/10.1007/s00013-022-01800-7</a>."},"date_updated":"2025-12-16T14:43:49Z","volume":120,"author":[{"orcid":"0000-0002-5497-8296","last_name":"Letz","id":"121953","full_name":"Letz, Janina Carmen","first_name":"Janina Carmen"}],"date_created":"2025-12-16T14:28:22Z","title":"Brown representability for triangulated categories with a linear action by a graded ring","doi":"10.1007/s00013-022-01800-7","publication":"Arch. Math. (Basel)","type":"journal_article","status":"public","_id":"63140","user_id":"121953","extern":"1","language":[{"iso":"eng"}]},{"page":"680-705","intvolume":"        55","citation":{"mla":"Krause, Henning, and Janina Carmen Letz. “The Spectrum of a Well-Generated Tensor-Triangulated Category.” <i>Bull. Lond. Math. Soc.</i>, vol. 55, no. 2, 2023, pp. 680–705, doi:<a href=\"https://doi.org/10.1112/blms.12749\">10.1112/blms.12749</a>.","bibtex":"@article{Krause_Letz_2023, title={The spectrum of a well-generated tensor-triangulated category}, volume={55}, DOI={<a href=\"https://doi.org/10.1112/blms.12749\">10.1112/blms.12749</a>}, number={2}, journal={Bull. Lond. Math. Soc.}, author={Krause, Henning and Letz, Janina Carmen}, year={2023}, pages={680–705} }","short":"H. Krause, J.C. Letz, Bull. Lond. Math. Soc. 55 (2023) 680–705.","apa":"Krause, H., &#38; Letz, J. C. (2023). The spectrum of a well-generated tensor-triangulated category. <i>Bull. Lond. Math. Soc.</i>, <i>55</i>(2), 680–705. <a href=\"https://doi.org/10.1112/blms.12749\">https://doi.org/10.1112/blms.12749</a>","ama":"Krause H, Letz JC. The spectrum of a well-generated tensor-triangulated category. <i>Bull Lond Math Soc</i>. 2023;55(2):680-705. doi:<a href=\"https://doi.org/10.1112/blms.12749\">10.1112/blms.12749</a>","ieee":"H. Krause and J. C. Letz, “The spectrum of a well-generated tensor-triangulated category,” <i>Bull. Lond. Math. Soc.</i>, vol. 55, no. 2, pp. 680–705, 2023, doi: <a href=\"https://doi.org/10.1112/blms.12749\">10.1112/blms.12749</a>.","chicago":"Krause, Henning, and Janina Carmen Letz. “The Spectrum of a Well-Generated Tensor-Triangulated Category.” <i>Bull. Lond. Math. Soc.</i> 55, no. 2 (2023): 680–705. <a href=\"https://doi.org/10.1112/blms.12749\">https://doi.org/10.1112/blms.12749</a>."},"year":"2023","issue":"2","publication_identifier":{"issn":["0024-6093"]},"doi":"10.1112/blms.12749","title":"The spectrum of a well-generated tensor-triangulated category","volume":55,"date_created":"2025-12-16T14:28:26Z","author":[{"first_name":"Henning","full_name":"Krause, Henning","last_name":"Krause"},{"first_name":"Janina Carmen","orcid":"0000-0002-5497-8296","last_name":"Letz","id":"121953","full_name":"Letz, Janina Carmen"}],"date_updated":"2025-12-16T14:45:52Z","status":"public","publication":"Bull. Lond. Math. Soc.","type":"journal_article","extern":"1","language":[{"iso":"eng"}],"user_id":"121953","_id":"63141"},{"date_created":"2023-09-11T13:38:38Z","author":[{"first_name":"Tassja","full_name":"Weber, Tassja","id":"89571","last_name":"Weber"}],"date_updated":"2025-12-16T14:58:36Z","publisher":"Books on Demand GmbH","oa":"1","main_file_link":[{"open_access":"1","url":"https://www.icmbeyond.net/?page_id=2038"}],"conference":{"location":"Chur (Schweiz)","end_date":"2023-02-17","start_date":"2023-02-16","name":"Inverted Classroom and beyond 2023:"},"title":"Nachhaltigkeit in der Bildung fOERdern: Open Educational Resources in der Hochschullehre","publication_status":"published","publication_identifier":{"isbn":["9783752645262"]},"citation":{"ieee":"T. Weber, “Nachhaltigkeit in der Bildung fOERdern: Open Educational Resources in der Hochschullehre,” in <i>Inverted Classroom and beyond 2023: Agile Didaktik für nachhaltige Bildung</i>, Chur (Schweiz), 2023.","chicago":"Weber, Tassja. “Nachhaltigkeit in der Bildung fOERdern: Open Educational Resources in der Hochschullehre.” In <i>Inverted Classroom and beyond 2023: Agile Didaktik für nachhaltige Bildung</i>, edited by Josef Buchner, Christian F. Freisleben-Teutscher, Judtih Hüther, Iris Neiske, Karsten Morisse, Ricarda Reimer, Karin Tengler, and Verein Forum neue Medien in der Lehre Austria Graz. Norderstedt: Books on Demand GmbH, 2023.","ama":"Weber T. Nachhaltigkeit in der Bildung fOERdern: Open Educational Resources in der Hochschullehre. In: Buchner J, Freisleben-Teutscher CF, Hüther J, et al., eds. <i>Inverted Classroom and beyond 2023: Agile Didaktik für nachhaltige Bildung</i>. Books on Demand GmbH; 2023.","apa":"Weber, T. (2023). Nachhaltigkeit in der Bildung fOERdern: Open Educational Resources in der Hochschullehre. In J. Buchner, C. F. Freisleben-Teutscher, J. Hüther, I. Neiske, K. Morisse, R. Reimer, K. Tengler, &#38; Verein Forum neue Medien in der Lehre Austria Graz (Eds.), <i>Inverted Classroom and beyond 2023: Agile Didaktik für nachhaltige Bildung</i>. Books on Demand GmbH.","short":"T. Weber, in: J. Buchner, C.F. Freisleben-Teutscher, J. Hüther, I. Neiske, K. Morisse, R. Reimer, K. Tengler, Verein Forum neue Medien in der Lehre Austria Graz (Eds.), Inverted Classroom and beyond 2023: Agile Didaktik für nachhaltige Bildung, Books on Demand GmbH, Norderstedt, 2023.","bibtex":"@inproceedings{Weber_2023, place={Norderstedt}, title={Nachhaltigkeit in der Bildung fOERdern: Open Educational Resources in der Hochschullehre}, booktitle={Inverted Classroom and beyond 2023: Agile Didaktik für nachhaltige Bildung}, publisher={Books on Demand GmbH}, author={Weber, Tassja}, editor={Buchner, Josef and Freisleben-Teutscher, Christian F. and Hüther, Judtih and Neiske, Iris and Morisse, Karsten and Reimer, Ricarda and Tengler, Karin and Verein Forum neue Medien in der Lehre Austria Graz}, year={2023} }","mla":"Weber, Tassja. “Nachhaltigkeit in der Bildung fOERdern: Open Educational Resources in der Hochschullehre.” <i>Inverted Classroom and beyond 2023: Agile Didaktik für nachhaltige Bildung</i>, edited by Josef Buchner et al., Books on Demand GmbH, 2023."},"corporate_editor":["Verein Forum neue Medien in der Lehre Austria Graz"],"place":"Norderstedt","year":"2023","user_id":"89571","department":[{"_id":"544"}],"_id":"46958","language":[{"iso":"ger"}],"type":"conference","publication":"Inverted Classroom and beyond 2023: Agile Didaktik für nachhaltige Bildung","status":"public","editor":[{"first_name":"Josef","last_name":"Buchner","full_name":"Buchner, Josef"},{"full_name":"Freisleben-Teutscher, Christian F.","last_name":"Freisleben-Teutscher","first_name":"Christian F."},{"full_name":"Hüther, Judtih","last_name":"Hüther","first_name":"Judtih"},{"full_name":"Neiske, Iris","last_name":"Neiske","first_name":"Iris"},{"first_name":"Karsten","last_name":"Morisse","full_name":"Morisse, Karsten"},{"full_name":"Reimer, Ricarda","last_name":"Reimer","first_name":"Ricarda"},{"first_name":"Karin","full_name":"Tengler, Karin","last_name":"Tengler"}]},{"citation":{"apa":"Weber, T., Flinz, C., Mell, R., &#38; Möhrs, C. (2023). Korpora für Deutsch als Fremdsprache – Potenziale und Perspektiven . In M. Beißwenger, E. Gredel, L. Lemnitzer, &#38; R.  Schneider (Eds.), <i> Korpusgestützte Sprachanalyse. Grundlagen, Anwendungen und Analysen</i>. Narr Francke Attempto Verlag.","mla":"Weber, Tassja, et al. “Korpora für Deutsch als Fremdsprache – Potenziale und Perspektiven .” <i> Korpusgestützte Sprachanalyse. Grundlagen, Anwendungen und Analysen</i>, edited by Michael Beißwenger et al., Narr Francke Attempto Verlag, 2023.","bibtex":"@inbook{Weber_Flinz_Mell_Möhrs_2023, place={Tübingen}, series={Studien zur deutschen Sprache}, title={Korpora für Deutsch als Fremdsprache – Potenziale und Perspektiven }, booktitle={ Korpusgestützte Sprachanalyse. Grundlagen, Anwendungen und Analysen}, publisher={Narr Francke Attempto Verlag}, author={Weber, Tassja and Flinz, Carolina and Mell, Ruth and Möhrs, Christine}, editor={Beißwenger, Michael and Gredel, Eva and Lemnitzer, Lothar and  Schneider, Roman}, year={2023}, collection={Studien zur deutschen Sprache} }","short":"T. Weber, C. Flinz, R. Mell, C. Möhrs, in: M. Beißwenger, E. Gredel, L. Lemnitzer, R.  Schneider (Eds.),  Korpusgestützte Sprachanalyse. Grundlagen, Anwendungen und Analysen, Narr Francke Attempto Verlag, Tübingen, 2023.","ama":"Weber T, Flinz C, Mell R, Möhrs C. Korpora für Deutsch als Fremdsprache – Potenziale und Perspektiven . In: Beißwenger M, Gredel E, Lemnitzer L,  Schneider R, eds. <i> Korpusgestützte Sprachanalyse. Grundlagen, Anwendungen und Analysen</i>. Studien zur deutschen Sprache. Narr Francke Attempto Verlag; 2023.","chicago":"Weber, Tassja, Carolina Flinz, Ruth Mell, and Christine Möhrs. “Korpora für Deutsch als Fremdsprache – Potenziale und Perspektiven .” In <i> Korpusgestützte Sprachanalyse. Grundlagen, Anwendungen und Analysen</i>, edited by Michael Beißwenger, Eva Gredel, Lothar Lemnitzer, and Roman  Schneider. Studien zur deutschen Sprache. Tübingen: Narr Francke Attempto Verlag, 2023.","ieee":"T. Weber, C. Flinz, R. Mell, and C. Möhrs, “Korpora für Deutsch als Fremdsprache – Potenziale und Perspektiven ,” in <i> Korpusgestützte Sprachanalyse. Grundlagen, Anwendungen und Analysen</i>, M. Beißwenger, E. Gredel, L. Lemnitzer, and R.  Schneider, Eds. Tübingen: Narr Francke Attempto Verlag, 2023."},"place":"Tübingen","year":"2023","publication_identifier":{"isbn":["978-3-8233-9610-9"]},"publication_status":"published","title":"Korpora für Deutsch als Fremdsprache – Potenziale und Perspektiven ","date_created":"2023-11-01T10:24:10Z","author":[{"last_name":"Weber","id":"89571","full_name":"Weber, Tassja","first_name":"Tassja"},{"first_name":"Carolina","last_name":"Flinz","full_name":"Flinz, Carolina"},{"first_name":"Ruth","last_name":"Mell","full_name":"Mell, Ruth"},{"first_name":"Christine","full_name":"Möhrs, Christine","last_name":"Möhrs"}],"date_updated":"2025-12-16T14:58:47Z","publisher":"Narr Francke Attempto Verlag","status":"public","editor":[{"full_name":"Beißwenger, Michael","last_name":"Beißwenger","first_name":"Michael"},{"first_name":"Eva","last_name":"Gredel","full_name":"Gredel, Eva"},{"first_name":"Lothar","last_name":"Lemnitzer","full_name":"Lemnitzer, Lothar"},{"first_name":"Roman","last_name":" Schneider","full_name":" Schneider, Roman"}],"publication":" Korpusgestützte Sprachanalyse. Grundlagen, Anwendungen und Analysen","type":"book_chapter","language":[{"iso":"ger"}],"series_title":"Studien zur deutschen Sprache","user_id":"89571","_id":"48582"},{"status":"public","type":"journal_article","user_id":"111489","_id":"63172","citation":{"ama":"Jablonski S. Real objects as a reason for mathematical reasoning - A comparison of different task settings. 2023;18(4).","chicago":"Jablonski, S. “Real Objects as a Reason for Mathematical Reasoning - A Comparison of Different Task Settings” 18, no. 4 (2023).","ieee":"S. Jablonski, “Real objects as a reason for mathematical reasoning - A comparison of different task settings,” vol. 18, no. 4, 2023.","short":"S. Jablonski, 18 (2023).","mla":"Jablonski, S. <i>Real Objects as a Reason for Mathematical Reasoning - A Comparison of Different Task Settings</i>. no. 4, 2023.","bibtex":"@article{Jablonski_2023, title={Real objects as a reason for mathematical reasoning - A comparison of different task settings}, volume={18}, number={4}, author={Jablonski, S}, year={2023} }","apa":"Jablonski, S. (2023). <i>Real objects as a reason for mathematical reasoning - A comparison of different task settings</i>. <i>18</i>(4)."},"intvolume":"        18","year":"2023","issue":"4","publication_status":"published","publication_identifier":{"issn":["1306-3030"]},"quality_controlled":"1","title":"Real objects as a reason for mathematical reasoning - A comparison of different task settings","date_created":"2025-12-17T08:53:34Z","author":[{"first_name":"S","full_name":"Jablonski, S","last_name":"Jablonski"}],"volume":18,"date_updated":"2025-12-17T08:56:14Z"},{"language":[{"iso":"eng"}],"_id":"57556","user_id":"111489","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Mathematical modelling emphasizes the connection between mathematics and reality — still, tasks are often exclusively introduced inside the classroom. The paper examines the potential of different task settings for mathematical modelling with real objects: outdoors at the real object itself, with photographs and with a 3D model representation. It is the aim of the study to analyze how far the mathematical modelling steps of students solving the tasks differ in comparison to the settings and representations. In a qualitative study, 19 lower secondary school students worked on tasks of all three settings in a Latin square design. Their working processes in the settings are compared with a special focus on the modelling steps Simplifying and Structuring, as well as Mathematizing. The analysis by means of activity diagrams and a qualitative content analysis shows that both steps are particularly relevant when students work with real objects — independent from the three settings. Still, differences in the actual activities could be observed in the students’ discussion on the appropriateness of a model and in dealing with inaccuracies at the real object. In addition, the process of data collection shows different procedures depending on the setting which presents each of them as an enrichment for the acquisition of modelling skills.</jats:p>","lang":"eng"}],"status":"public","publication":"Educational Studies in Mathematics","type":"journal_article","title":"Is it all about the setting? — A comparison of mathematical modelling with real objects and their representation","doi":"10.1007/s10649-023-10215-2","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-17T08:56:50Z","volume":113,"author":[{"first_name":"Simone","last_name":"Jablonski","full_name":"Jablonski, Simone"}],"date_created":"2024-12-04T10:46:14Z","year":"2023","intvolume":"       113","page":"307-330","citation":{"ieee":"S. Jablonski, “Is it all about the setting? — A comparison of mathematical modelling with real objects and their representation,” <i>Educational Studies in Mathematics</i>, vol. 113, no. 2, pp. 307–330, 2023, doi: <a href=\"https://doi.org/10.1007/s10649-023-10215-2\">10.1007/s10649-023-10215-2</a>.","chicago":"Jablonski, Simone. “Is It All about the Setting? — A Comparison of Mathematical Modelling with Real Objects and Their Representation.” <i>Educational Studies in Mathematics</i> 113, no. 2 (2023): 307–30. <a href=\"https://doi.org/10.1007/s10649-023-10215-2\">https://doi.org/10.1007/s10649-023-10215-2</a>.","ama":"Jablonski S. Is it all about the setting? — A comparison of mathematical modelling with real objects and their representation. <i>Educational Studies in Mathematics</i>. 2023;113(2):307-330. doi:<a href=\"https://doi.org/10.1007/s10649-023-10215-2\">10.1007/s10649-023-10215-2</a>","short":"S. Jablonski, Educational Studies in Mathematics 113 (2023) 307–330.","bibtex":"@article{Jablonski_2023, title={Is it all about the setting? — A comparison of mathematical modelling with real objects and their representation}, volume={113}, DOI={<a href=\"https://doi.org/10.1007/s10649-023-10215-2\">10.1007/s10649-023-10215-2</a>}, number={2}, journal={Educational Studies in Mathematics}, publisher={Springer Science and Business Media LLC}, author={Jablonski, Simone}, year={2023}, pages={307–330} }","mla":"Jablonski, Simone. “Is It All about the Setting? — A Comparison of Mathematical Modelling with Real Objects and Their Representation.” <i>Educational Studies in Mathematics</i>, vol. 113, no. 2, Springer Science and Business Media LLC, 2023, pp. 307–30, doi:<a href=\"https://doi.org/10.1007/s10649-023-10215-2\">10.1007/s10649-023-10215-2</a>.","apa":"Jablonski, S. (2023). Is it all about the setting? — A comparison of mathematical modelling with real objects and their representation. <i>Educational Studies in Mathematics</i>, <i>113</i>(2), 307–330. <a href=\"https://doi.org/10.1007/s10649-023-10215-2\">https://doi.org/10.1007/s10649-023-10215-2</a>"},"publication_identifier":{"issn":["0013-1954","1573-0816"]},"publication_status":"published","issue":"2"},{"publication_status":"published","year":"2023","citation":{"apa":"Höink, D. (2023). Komponierte Ambiguität. Ein anderer Blick auf polyphone Messen des 15. und 16. Jahrhunderts. <i>Kirchenmusikalisches Jahrbuch</i>, <i>107</i>, 21–30.","short":"D. Höink, Kirchenmusikalisches Jahrbuch 107 (2023) 21–30.","bibtex":"@article{Höink_2023, title={Komponierte Ambiguität. Ein anderer Blick auf polyphone Messen des 15. und 16. Jahrhunderts}, volume={107}, journal={Kirchenmusikalisches Jahrbuch}, author={Höink, Dominik}, year={2023}, pages={21–30} }","mla":"Höink, Dominik. “Komponierte Ambiguität. Ein anderer Blick auf polyphone Messen des 15. und 16. Jahrhunderts.” <i>Kirchenmusikalisches Jahrbuch</i>, vol. 107, 2023, pp. 21–30.","ama":"Höink D. Komponierte Ambiguität. Ein anderer Blick auf polyphone Messen des 15. und 16. Jahrhunderts. <i>Kirchenmusikalisches Jahrbuch</i>. 2023;107:21-30.","ieee":"D. Höink, “Komponierte Ambiguität. Ein anderer Blick auf polyphone Messen des 15. und 16. Jahrhunderts,” <i>Kirchenmusikalisches Jahrbuch</i>, vol. 107, pp. 21–30, 2023.","chicago":"Höink, Dominik. “Komponierte Ambiguität. Ein anderer Blick auf polyphone Messen des 15. und 16. Jahrhunderts.” <i>Kirchenmusikalisches Jahrbuch</i> 107 (2023): 21–30."},"intvolume":"       107","page":"21-30","date_updated":"2025-12-17T09:00:59Z","date_created":"2023-11-17T07:28:53Z","author":[{"full_name":"Höink, Dominik","id":"90389","last_name":"Höink","first_name":"Dominik"}],"volume":107,"title":"Komponierte Ambiguität. Ein anderer Blick auf polyphone Messen des 15. und 16. Jahrhunderts","type":"journal_article","publication":"Kirchenmusikalisches Jahrbuch","status":"public","_id":"48994","user_id":"90389","department":[{"_id":"233"},{"_id":"716"}],"language":[{"iso":"ger"}]},{"volume":13,"author":[{"first_name":"S","last_name":"Jablonski","full_name":"Jablonski, S"},{"first_name":"M","last_name":"Ludwig","full_name":"Ludwig, M"}],"date_created":"2025-12-17T08:53:33Z","date_updated":"2025-12-17T08:56:40Z","title":"Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice","issue":"7","publication_identifier":{"issn":["2227-7102"]},"quality_controlled":"1","publication_status":"published","intvolume":"        13","citation":{"apa":"Jablonski, S., &#38; Ludwig, M. (2023). <i>Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice</i>. <i>13</i>(7).","mla":"Jablonski, S., and M. Ludwig. <i>Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice</i>. no. 7, 2023.","bibtex":"@article{Jablonski_Ludwig_2023, title={Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice}, volume={13}, number={7}, author={Jablonski, S and Ludwig, M}, year={2023} }","short":"S. Jablonski, M. Ludwig, 13 (2023).","chicago":"Jablonski, S, and M Ludwig. “Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice” 13, no. 7 (2023).","ieee":"S. Jablonski and M. Ludwig, “Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice,” vol. 13, no. 7, 2023.","ama":"Jablonski S, Ludwig M. Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice. 2023;13(7)."},"year":"2023","user_id":"111489","_id":"63168","type":"journal_article","status":"public"},{"user_id":"111489","_id":"63171","type":"journal_article","status":"public","volume":8,"date_created":"2025-12-17T08:53:33Z","author":[{"full_name":"Jablonski, S","last_name":"Jablonski","first_name":"S"},{"first_name":"S","last_name":"Barlovits","full_name":"Barlovits, S"},{"first_name":"M","last_name":"Ludwig","full_name":"Ludwig, M"}],"date_updated":"2025-12-17T08:56:45Z","title":"How digital tools support the validation of outdoor modelling results","publication_identifier":{"issn":["2504-284X"]},"quality_controlled":"1","publication_status":"published","intvolume":"         8","citation":{"chicago":"Jablonski, S, S Barlovits, and M Ludwig. “How Digital Tools Support the Validation of Outdoor Modelling Results” 8 (2023).","ieee":"S. Jablonski, S. Barlovits, and M. Ludwig, “How digital tools support the validation of outdoor modelling results,” vol. 8, 2023.","ama":"Jablonski S, Barlovits S, Ludwig M. How digital tools support the validation of outdoor modelling results. 2023;8.","bibtex":"@article{Jablonski_Barlovits_Ludwig_2023, title={How digital tools support the validation of outdoor modelling results}, volume={8}, author={Jablonski, S and Barlovits, S and Ludwig, M}, year={2023} }","short":"S. Jablonski, S. Barlovits, M. Ludwig, 8 (2023).","mla":"Jablonski, S., et al. <i>How Digital Tools Support the Validation of Outdoor Modelling Results</i>. 2023.","apa":"Jablonski, S., Barlovits, S., &#38; Ludwig, M. (2023). <i>How digital tools support the validation of outdoor modelling results</i>. <i>8</i>."},"year":"2023"},{"type":"conference","status":"public","_id":"63196","user_id":"31046","department":[{"_id":"33"}],"language":[{"iso":"eng"}],"year":"2023","citation":{"bibtex":"@inproceedings{Decker_Westphal_2023, title={Gendersensible Bildung als ein Thema von vielen im Lehramtsstudium: Das Profil Umgang mit Heterogenität als freiwillige Zusatzqualifikation}, author={Decker, Claudia and Westphal, Petra}, year={2023} }","short":"C. Decker, P. Westphal, in: 2023.","mla":"Decker, Claudia, and Petra Westphal. <i>Gendersensible Bildung Als Ein Thema von Vielen Im Lehramtsstudium: Das Profil Umgang Mit Heterogenität Als Freiwillige Zusatzqualifikation</i>. 2023.","apa":"Decker, C., &#38; Westphal, P. (2023). <i>Gendersensible Bildung als ein Thema von vielen im Lehramtsstudium: Das Profil Umgang mit Heterogenität als freiwillige Zusatzqualifikation</i>. Geschlechtersensible Bildung im Lehramtsstudium in NRW, Soest.","ama":"Decker C, Westphal P. Gendersensible Bildung als ein Thema von vielen im Lehramtsstudium: Das Profil Umgang mit Heterogenität als freiwillige Zusatzqualifikation. In: ; 2023.","chicago":"Decker, Claudia, and Petra Westphal. “Gendersensible Bildung Als Ein Thema von Vielen Im Lehramtsstudium: Das Profil Umgang Mit Heterogenität Als Freiwillige Zusatzqualifikation,” 2023.","ieee":"C. Decker and P. Westphal, “Gendersensible Bildung als ein Thema von vielen im Lehramtsstudium: Das Profil Umgang mit Heterogenität als freiwillige Zusatzqualifikation,” presented at the Geschlechtersensible Bildung im Lehramtsstudium in NRW, Soest, 2023."},"date_updated":"2025-12-18T10:49:44Z","author":[{"first_name":"Claudia","last_name":"Decker","full_name":"Decker, Claudia","id":"31046"},{"first_name":"Petra","full_name":"Westphal, Petra","id":"42377","last_name":"Westphal"}],"date_created":"2025-12-18T10:49:37Z","title":"Gendersensible Bildung als ein Thema von vielen im Lehramtsstudium: Das Profil Umgang mit Heterogenität als freiwillige Zusatzqualifikation","conference":{"start_date":"11.11.2023","name":"Geschlechtersensible Bildung im Lehramtsstudium in NRW","location":"Soest"}},{"type":"journal_article","publication":"PRX Quantum","status":"public","_id":"44081","user_id":"27150","department":[{"_id":"288"},{"_id":"623"},{"_id":"15"}],"article_number":"020306","keyword":["General Physics and Astronomy","Mathematical Physics","Applied Mathematics","Electronic","Optical and Magnetic Materials","Electrical and Electronic Engineering","General Computer Science"],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["2691-3399"]},"issue":"2","year":"2023","citation":{"short":"L. Serino, J. Gil López, M. Stefszky, R. Ricken, C. Eigner, B. Brecht, C. Silberhorn, PRX Quantum 4 (2023).","mla":"Serino, Laura, et al. “Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States.” <i>PRX Quantum</i>, vol. 4, no. 2, 020306, American Physical Society (APS), 2023, doi:<a href=\"https://doi.org/10.1103/prxquantum.4.020306\">10.1103/prxquantum.4.020306</a>.","bibtex":"@article{Serino_Gil López_Stefszky_Ricken_Eigner_Brecht_Silberhorn_2023, title={Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States}, volume={4}, DOI={<a href=\"https://doi.org/10.1103/prxquantum.4.020306\">10.1103/prxquantum.4.020306</a>}, number={2020306}, journal={PRX Quantum}, publisher={American Physical Society (APS)}, author={Serino, Laura and Gil López, Jano and Stefszky, Michael and Ricken, Raimund and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}, year={2023} }","apa":"Serino, L., Gil López, J., Stefszky, M., Ricken, R., Eigner, C., Brecht, B., &#38; Silberhorn, C. (2023). Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States. <i>PRX Quantum</i>, <i>4</i>(2), Article 020306. <a href=\"https://doi.org/10.1103/prxquantum.4.020306\">https://doi.org/10.1103/prxquantum.4.020306</a>","ama":"Serino L, Gil López J, Stefszky M, et al. Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States. <i>PRX Quantum</i>. 2023;4(2). doi:<a href=\"https://doi.org/10.1103/prxquantum.4.020306\">10.1103/prxquantum.4.020306</a>","ieee":"L. Serino <i>et al.</i>, “Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States,” <i>PRX Quantum</i>, vol. 4, no. 2, Art. no. 020306, 2023, doi: <a href=\"https://doi.org/10.1103/prxquantum.4.020306\">10.1103/prxquantum.4.020306</a>.","chicago":"Serino, Laura, Jano Gil López, Michael Stefszky, Raimund Ricken, Christof Eigner, Benjamin Brecht, and Christine Silberhorn. “Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States.” <i>PRX Quantum</i> 4, no. 2 (2023). <a href=\"https://doi.org/10.1103/prxquantum.4.020306\">https://doi.org/10.1103/prxquantum.4.020306</a>."},"intvolume":"         4","publisher":"American Physical Society (APS)","date_updated":"2025-12-18T16:15:18Z","date_created":"2023-04-20T12:38:23Z","author":[{"full_name":"Serino, Laura","id":"88242","last_name":"Serino","first_name":"Laura"},{"first_name":"Jano","last_name":"Gil López","id":"51223","full_name":"Gil López, Jano"},{"first_name":"Michael","last_name":"Stefszky","id":"42777","full_name":"Stefszky, Michael"},{"last_name":"Ricken","full_name":"Ricken, Raimund","first_name":"Raimund"},{"first_name":"Christof","orcid":"https://orcid.org/0000-0002-5693-3083","last_name":"Eigner","full_name":"Eigner, Christof","id":"13244"},{"full_name":"Brecht, Benjamin","id":"27150","last_name":"Brecht","orcid":"0000-0003-4140-0556 ","first_name":"Benjamin"},{"first_name":"Christine","id":"26263","full_name":"Silberhorn, Christine","last_name":"Silberhorn"}],"volume":4,"title":"Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States","doi":"10.1103/prxquantum.4.020306"},{"publication_identifier":{"issn":["0003-2654","1364-5528"]},"publication_status":"published","page":"1887-1897","intvolume":"       148","citation":{"ama":"Rott E, Leppin C, Diederichs T, Garidel P, Johannsmann D. Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration. <i>The Analyst</i>. 2023;148(8):1887-1897. doi:<a href=\"https://doi.org/10.1039/d3an00076a\">10.1039/d3an00076a</a>","chicago":"Rott, Emily, Christian Leppin, Tim Diederichs, Patrick Garidel, and Diethelm Johannsmann. “Protein–Protein Interactions in Solutions of Monoclonal Antibodies Probed by the Dependence of the High-Frequency Viscosity on Temperature and Concentration.” <i>The Analyst</i> 148, no. 8 (2023): 1887–97. <a href=\"https://doi.org/10.1039/d3an00076a\">https://doi.org/10.1039/d3an00076a</a>.","ieee":"E. Rott, C. Leppin, T. Diederichs, P. Garidel, and D. Johannsmann, “Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration,” <i>The Analyst</i>, vol. 148, no. 8, pp. 1887–1897, 2023, doi: <a href=\"https://doi.org/10.1039/d3an00076a\">10.1039/d3an00076a</a>.","apa":"Rott, E., Leppin, C., Diederichs, T., Garidel, P., &#38; Johannsmann, D. (2023). Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration. <i>The Analyst</i>, <i>148</i>(8), 1887–1897. <a href=\"https://doi.org/10.1039/d3an00076a\">https://doi.org/10.1039/d3an00076a</a>","short":"E. Rott, C. Leppin, T. Diederichs, P. Garidel, D. Johannsmann, The Analyst 148 (2023) 1887–1897.","mla":"Rott, Emily, et al. “Protein–Protein Interactions in Solutions of Monoclonal Antibodies Probed by the Dependence of the High-Frequency Viscosity on Temperature and Concentration.” <i>The Analyst</i>, vol. 148, no. 8, Royal Society of Chemistry (RSC), 2023, pp. 1887–97, doi:<a href=\"https://doi.org/10.1039/d3an00076a\">10.1039/d3an00076a</a>.","bibtex":"@article{Rott_Leppin_Diederichs_Garidel_Johannsmann_2023, title={Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration}, volume={148}, DOI={<a href=\"https://doi.org/10.1039/d3an00076a\">10.1039/d3an00076a</a>}, number={8}, journal={The Analyst}, publisher={Royal Society of Chemistry (RSC)}, author={Rott, Emily and Leppin, Christian and Diederichs, Tim and Garidel, Patrick and Johannsmann, Diethelm}, year={2023}, pages={1887–1897} }"},"volume":148,"author":[{"last_name":"Rott","full_name":"Rott, Emily","first_name":"Emily"},{"full_name":"Leppin, Christian","id":"117722","last_name":"Leppin","first_name":"Christian"},{"last_name":"Diederichs","full_name":"Diederichs, Tim","first_name":"Tim"},{"first_name":"Patrick","last_name":"Garidel","full_name":"Garidel, Patrick"},{"first_name":"Diethelm","full_name":"Johannsmann, Diethelm","last_name":"Johannsmann"}],"date_updated":"2025-12-18T17:38:31Z","doi":"10.1039/d3an00076a","type":"journal_article","status":"public","user_id":"117722","_id":"63231","issue":"8","quality_controlled":"1","year":"2023","date_created":"2025-12-18T17:06:08Z","publisher":"Royal Society of Chemistry (RSC)","title":"Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration","publication":"The Analyst","abstract":[{"text":"<jats:p>\r\n            <jats:italic></jats:italic>A QCM-D probes the temperature- and concentration-dependent complex high-frequency viscosity and provides information on protein-protein interactions in solutions of monoclonal antibodies.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}]},{"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>A simulation based on the frequency‐domain lattice Boltzmann method (FreqD‐LBM) is employed to predict the shifts of resonance frequency, Δ<jats:italic>f</jats:italic>, and half bandwidth, ΔΓ, of a quartz crystal microbalance with dissipation monitoring (QCM‐D) induced by the adsorption of rigid spheres to the resonator surface. The comparison with the experimental values of Δ<jats:italic>f</jats:italic> and ΔΓ allows to estimate the stiffness of the contacts between the spheres and the resonator surface. The contact stiffness is of interest in contact mechanics, but also in sensing because it depends on the properties of thin films situated between the resonator surface and the sphere. The simulation differs from previous implementations of FreqD‐LBM insofar, as the material inside the particles is not included in the FreqD‐LBM algorithm. Rather, the particle surface is configured to be an oscillating boundary. The amplitude of the particles' motions (displacement and rotation) is governed by the force balance at the surface of the particle. Because the contact stiffness enters this balance, it can be derived from experimental values of Δ<jats:italic>f</jats:italic> and ΔΓ. The simulation reproduces experiments by the Krakow group. For sufficiently small spheres, a contact stiffness can be derived from the comparison of the simulation with the experiment.</jats:p>","lang":"eng"}],"publication":"Advanced Theory and Simulations","language":[{"iso":"eng"}],"year":"2023","quality_controlled":"1","issue":"11","title":"Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation","publisher":"Wiley","date_created":"2025-12-18T17:03:12Z","status":"public","type":"journal_article","article_number":"2300190","article_type":"original","extern":"1","_id":"63228","user_id":"117722","citation":{"apa":"Johannsmann, D., Leppin, C., &#38; Langhoff, A. (2023). Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation. <i>Advanced Theory and Simulations</i>, <i>6</i>(11), Article 2300190. <a href=\"https://doi.org/10.1002/adts.202300190\">https://doi.org/10.1002/adts.202300190</a>","bibtex":"@article{Johannsmann_Leppin_Langhoff_2023, title={Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation}, volume={6}, DOI={<a href=\"https://doi.org/10.1002/adts.202300190\">10.1002/adts.202300190</a>}, number={112300190}, journal={Advanced Theory and Simulations}, publisher={Wiley}, author={Johannsmann, Diethelm and Leppin, Christian and Langhoff, Arne}, year={2023} }","short":"D. Johannsmann, C. Leppin, A. Langhoff, Advanced Theory and Simulations 6 (2023).","mla":"Johannsmann, Diethelm, et al. “Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation.” <i>Advanced Theory and Simulations</i>, vol. 6, no. 11, 2300190, Wiley, 2023, doi:<a href=\"https://doi.org/10.1002/adts.202300190\">10.1002/adts.202300190</a>.","ama":"Johannsmann D, Leppin C, Langhoff A. Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation. <i>Advanced Theory and Simulations</i>. 2023;6(11). doi:<a href=\"https://doi.org/10.1002/adts.202300190\">10.1002/adts.202300190</a>","ieee":"D. Johannsmann, C. Leppin, and A. Langhoff, “Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation,” <i>Advanced Theory and Simulations</i>, vol. 6, no. 11, Art. no. 2300190, 2023, doi: <a href=\"https://doi.org/10.1002/adts.202300190\">10.1002/adts.202300190</a>.","chicago":"Johannsmann, Diethelm, Christian Leppin, and Arne Langhoff. “Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation.” <i>Advanced Theory and Simulations</i> 6, no. 11 (2023). <a href=\"https://doi.org/10.1002/adts.202300190\">https://doi.org/10.1002/adts.202300190</a>."},"intvolume":"         6","publication_status":"published","publication_identifier":{"issn":["2513-0390","2513-0390"]},"doi":"10.1002/adts.202300190","date_updated":"2025-12-18T17:41:08Z","author":[{"full_name":"Johannsmann, Diethelm","last_name":"Johannsmann","first_name":"Diethelm"},{"first_name":"Christian","full_name":"Leppin, Christian","id":"117722","last_name":"Leppin"},{"first_name":"Arne","full_name":"Langhoff, Arne","last_name":"Langhoff"}],"volume":6},{"quality_controlled":"1","publication_identifier":{"issn":["1424-8220"]},"publication_status":"published","issue":"3","year":"2023","intvolume":"        23","citation":{"ama":"Johannsmann D, Langhoff A, Leppin C, Reviakine I, Maan AMC. Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model. <i>Sensors</i>. 2023;23(3). doi:<a href=\"https://doi.org/10.3390/s23031348\">10.3390/s23031348</a>","chicago":"Johannsmann, Diethelm, Arne Langhoff, Christian Leppin, Ilya Reviakine, and Anna M. C. Maan. “Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model.” <i>Sensors</i> 23, no. 3 (2023). <a href=\"https://doi.org/10.3390/s23031348\">https://doi.org/10.3390/s23031348</a>.","ieee":"D. Johannsmann, A. Langhoff, C. Leppin, I. Reviakine, and A. M. C. Maan, “Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model,” <i>Sensors</i>, vol. 23, no. 3, Art. no. 1348, 2023, doi: <a href=\"https://doi.org/10.3390/s23031348\">10.3390/s23031348</a>.","apa":"Johannsmann, D., Langhoff, A., Leppin, C., Reviakine, I., &#38; Maan, A. M. C. (2023). Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model. <i>Sensors</i>, <i>23</i>(3), Article 1348. <a href=\"https://doi.org/10.3390/s23031348\">https://doi.org/10.3390/s23031348</a>","mla":"Johannsmann, Diethelm, et al. “Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model.” <i>Sensors</i>, vol. 23, no. 3, 1348, MDPI AG, 2023, doi:<a href=\"https://doi.org/10.3390/s23031348\">10.3390/s23031348</a>.","bibtex":"@article{Johannsmann_Langhoff_Leppin_Reviakine_Maan_2023, title={Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model}, volume={23}, DOI={<a href=\"https://doi.org/10.3390/s23031348\">10.3390/s23031348</a>}, number={31348}, journal={Sensors}, publisher={MDPI AG}, author={Johannsmann, Diethelm and Langhoff, Arne and Leppin, Christian and Reviakine, Ilya and Maan, Anna M. C.}, year={2023} }","short":"D. Johannsmann, A. Langhoff, C. Leppin, I. Reviakine, A.M.C. Maan, Sensors 23 (2023)."},"date_updated":"2025-12-18T17:39:52Z","publisher":"MDPI AG","volume":23,"author":[{"first_name":"Diethelm","full_name":"Johannsmann, Diethelm","last_name":"Johannsmann"},{"first_name":"Arne","last_name":"Langhoff","full_name":"Langhoff, Arne"},{"first_name":"Christian","last_name":"Leppin","id":"117722","full_name":"Leppin, Christian"},{"first_name":"Ilya","last_name":"Reviakine","full_name":"Reviakine, Ilya"},{"full_name":"Maan, Anna M. C.","last_name":"Maan","first_name":"Anna M. C."}],"date_created":"2025-12-18T17:05:00Z","title":"Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model","doi":"10.3390/s23031348","publication":"Sensors","type":"journal_article","abstract":[{"text":"<jats:p>Quartz crystal microbalance with dissipation monitoring (QCM-D) is a well-established technique for studying soft films. It can provide gravimetric as well as nongravimetric information about a film, such as its thickness and mechanical properties. The interpretation of sets of overtone-normalized frequency shifts, ∆f/n, and overtone-normalized shifts in half-bandwidth, ΔΓ/n, provided by QCM-D relies on a model that, in general, contains five independent parameters that are needed to describe film thickness and frequency-dependent viscoelastic properties. Here, we examine how noise inherent in experimental data affects the determination of these parameters. There are certain conditions where noise prevents the reliable determination of film thickness and the loss tangent. On the other hand, we show that there are conditions where it is possible to determine all five parameters. We relate these conditions to the mathematical properties of the model in terms of simple conceptual diagrams that can help users understand the model’s behavior. Finally, we present new open source software for QCM-D data analysis written in Python, PyQTM.</jats:p>","lang":"eng"}],"status":"public","_id":"63230","user_id":"117722","article_number":"1348","language":[{"iso":"eng"}],"extern":"1"},{"article_number":"106219","extern":"1","language":[{"iso":"eng"}],"_id":"63229","user_id":"117722","status":"public","type":"journal_article","publication":"Results in Physics","title":"Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method","doi":"10.1016/j.rinp.2023.106219","date_updated":"2025-12-18T17:40:25Z","publisher":"Elsevier BV","date_created":"2025-12-18T17:04:13Z","author":[{"last_name":"Johannsmann","full_name":"Johannsmann, Diethelm","first_name":"Diethelm"},{"last_name":"Petri","full_name":"Petri, Judith","first_name":"Judith"},{"full_name":"Leppin, Christian","id":"117722","last_name":"Leppin","first_name":"Christian"},{"first_name":"Arne","full_name":"Langhoff, Arne","last_name":"Langhoff"},{"first_name":"Hozan","full_name":"Ibrahim, Hozan","last_name":"Ibrahim"}],"volume":45,"year":"2023","citation":{"chicago":"Johannsmann, Diethelm, Judith Petri, Christian Leppin, Arne Langhoff, and Hozan Ibrahim. “Particle Fouling at Hot Reactor Walls Monitored In Situ with a QCM-D and Modeled with the Frequency-Domain Lattice Boltzmann Method.” <i>Results in Physics</i> 45 (2023). <a href=\"https://doi.org/10.1016/j.rinp.2023.106219\">https://doi.org/10.1016/j.rinp.2023.106219</a>.","ieee":"D. Johannsmann, J. Petri, C. Leppin, A. Langhoff, and H. Ibrahim, “Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method,” <i>Results in Physics</i>, vol. 45, Art. no. 106219, 2023, doi: <a href=\"https://doi.org/10.1016/j.rinp.2023.106219\">10.1016/j.rinp.2023.106219</a>.","ama":"Johannsmann D, Petri J, Leppin C, Langhoff A, Ibrahim H. Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method. <i>Results in Physics</i>. 2023;45. doi:<a href=\"https://doi.org/10.1016/j.rinp.2023.106219\">10.1016/j.rinp.2023.106219</a>","short":"D. Johannsmann, J. Petri, C. Leppin, A. Langhoff, H. Ibrahim, Results in Physics 45 (2023).","bibtex":"@article{Johannsmann_Petri_Leppin_Langhoff_Ibrahim_2023, title={Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method}, volume={45}, DOI={<a href=\"https://doi.org/10.1016/j.rinp.2023.106219\">10.1016/j.rinp.2023.106219</a>}, number={106219}, journal={Results in Physics}, publisher={Elsevier BV}, author={Johannsmann, Diethelm and Petri, Judith and Leppin, Christian and Langhoff, Arne and Ibrahim, Hozan}, year={2023} }","mla":"Johannsmann, Diethelm, et al. “Particle Fouling at Hot Reactor Walls Monitored In Situ with a QCM-D and Modeled with the Frequency-Domain Lattice Boltzmann Method.” <i>Results in Physics</i>, vol. 45, 106219, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.rinp.2023.106219\">10.1016/j.rinp.2023.106219</a>.","apa":"Johannsmann, D., Petri, J., Leppin, C., Langhoff, A., &#38; Ibrahim, H. (2023). Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method. <i>Results in Physics</i>, <i>45</i>, Article 106219. <a href=\"https://doi.org/10.1016/j.rinp.2023.106219\">https://doi.org/10.1016/j.rinp.2023.106219</a>"},"intvolume":"        45","publication_status":"published","publication_identifier":{"issn":["2211-3797"]}},{"intvolume":"        28","citation":{"ieee":"M. Winkler, “Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing,” <i>Advances in Differential Equations</i>, vol. 28, no. 11/12, 2023, doi: <a href=\"https://doi.org/10.57262/ade028-1112-921\">10.57262/ade028-1112-921</a>.","chicago":"Winkler, Michael. “Absence of Collapse into Persistent Dirac-Type Singularities in a Keller-Segel-Navier-Stokes System Involving Local Sensing.” <i>Advances in Differential Equations</i> 28, no. 11/12 (2023). <a href=\"https://doi.org/10.57262/ade028-1112-921\">https://doi.org/10.57262/ade028-1112-921</a>.","ama":"Winkler M. Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. <i>Advances in Differential Equations</i>. 2023;28(11/12). doi:<a href=\"https://doi.org/10.57262/ade028-1112-921\">10.57262/ade028-1112-921</a>","apa":"Winkler, M. (2023). Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing. <i>Advances in Differential Equations</i>, <i>28</i>(11/12). <a href=\"https://doi.org/10.57262/ade028-1112-921\">https://doi.org/10.57262/ade028-1112-921</a>","short":"M. Winkler, Advances in Differential Equations 28 (2023).","bibtex":"@article{Winkler_2023, title={Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing}, volume={28}, DOI={<a href=\"https://doi.org/10.57262/ade028-1112-921\">10.57262/ade028-1112-921</a>}, number={11/12}, journal={Advances in Differential Equations}, publisher={Khayyam Publishing, Inc}, author={Winkler, Michael}, year={2023} }","mla":"Winkler, Michael. “Absence of Collapse into Persistent Dirac-Type Singularities in a Keller-Segel-Navier-Stokes System Involving Local Sensing.” <i>Advances in Differential Equations</i>, vol. 28, no. 11/12, Khayyam Publishing, Inc, 2023, doi:<a href=\"https://doi.org/10.57262/ade028-1112-921\">10.57262/ade028-1112-921</a>."},"year":"2023","issue":"11/12","publication_identifier":{"issn":["1079-9389"]},"publication_status":"published","doi":"10.57262/ade028-1112-921","title":"Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing","volume":28,"date_created":"2025-12-18T19:18:31Z","author":[{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"publisher":"Khayyam Publishing, Inc","date_updated":"2025-12-18T20:07:12Z","status":"public","publication":"Advances in Differential Equations","type":"journal_article","language":[{"iso":"eng"}],"user_id":"31496","_id":"63285"},{"intvolume":"        21","citation":{"apa":"Winkler, M. (2023). Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. <i>Open Mathematics</i>, <i>21</i>(1), Article 20220578. <a href=\"https://doi.org/10.1515/math-2022-0578\">https://doi.org/10.1515/math-2022-0578</a>","bibtex":"@article{Winkler_2023, title={Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type}, volume={21}, DOI={<a href=\"https://doi.org/10.1515/math-2022-0578\">10.1515/math-2022-0578</a>}, number={120220578}, journal={Open Mathematics}, publisher={Walter de Gruyter GmbH}, author={Winkler, Michael}, year={2023} }","mla":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” <i>Open Mathematics</i>, vol. 21, no. 1, 20220578, Walter de Gruyter GmbH, 2023, doi:<a href=\"https://doi.org/10.1515/math-2022-0578\">10.1515/math-2022-0578</a>.","short":"M. Winkler, Open Mathematics 21 (2023).","ama":"Winkler M. Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type. <i>Open Mathematics</i>. 2023;21(1). doi:<a href=\"https://doi.org/10.1515/math-2022-0578\">10.1515/math-2022-0578</a>","chicago":"Winkler, Michael. “Classical Solutions to Cauchy Problems for Parabolic–Elliptic Systems of Keller-Segel Type.” <i>Open Mathematics</i> 21, no. 1 (2023). <a href=\"https://doi.org/10.1515/math-2022-0578\">https://doi.org/10.1515/math-2022-0578</a>.","ieee":"M. Winkler, “Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type,” <i>Open Mathematics</i>, vol. 21, no. 1, Art. no. 20220578, 2023, doi: <a href=\"https://doi.org/10.1515/math-2022-0578\">10.1515/math-2022-0578</a>."},"year":"2023","issue":"1","publication_identifier":{"issn":["2391-5455"]},"publication_status":"published","doi":"10.1515/math-2022-0578","title":"Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type","volume":21,"author":[{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:19:35Z","date_updated":"2025-12-18T20:07:34Z","publisher":"Walter de Gruyter GmbH","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>The Cauchy problem in <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_001.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:msup>\r\n                              <m:mrow>\r\n                                 <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>n</m:mi>\r\n                              </m:mrow>\r\n                           </m:msup>\r\n                        </m:math>\r\n                        <jats:tex-math>{{\\mathbb{R}}}^{n}</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>, <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_002.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mi>n</m:mi>\r\n                           <m:mo>≥</m:mo>\r\n                           <m:mn>2</m:mn>\r\n                        </m:math>\r\n                        <jats:tex-math>n\\ge 2</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>, for <jats:disp-formula id=\"j_math-2022-0578_eq_001\">\r\n                     <jats:alternatives>\r\n                        <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_003.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\r\n                           <m:mtable displaystyle=\"true\">\r\n                              <m:mtr>\r\n                                 <m:mtd columnalign=\"right\">\r\n                                    <m:mfenced open=\"{\" close=\"\">\r\n                                       <m:mrow>\r\n                                          <m:mspace depth=\"1.25em\"/>\r\n                                          <m:mtable displaystyle=\"true\">\r\n                                             <m:mtr>\r\n                                                <m:mtd columnalign=\"left\">\r\n                                                   <m:msub>\r\n                                                      <m:mrow>\r\n                                                         <m:mi>u</m:mi>\r\n                                                      </m:mrow>\r\n                                                      <m:mrow>\r\n                                                         <m:mi>t</m:mi>\r\n                                                      </m:mrow>\r\n                                                   </m:msub>\r\n                                                   <m:mo>=</m:mo>\r\n                                                   <m:mi mathvariant=\"normal\">Δ</m:mi>\r\n                                                   <m:mi>u</m:mi>\r\n                                                   <m:mo>−</m:mo>\r\n                                                   <m:mrow>\r\n                                                      <m:mo>∇</m:mo>\r\n                                                   </m:mrow>\r\n                                                   <m:mo>⋅</m:mo>\r\n                                                   <m:mrow>\r\n                                                      <m:mo>(</m:mo>\r\n                                                      <m:mrow>\r\n                                                         <m:mi>u</m:mi>\r\n                                                         <m:mi>S</m:mi>\r\n                                                         <m:mo>⋅</m:mo>\r\n                                                         <m:mrow>\r\n                                                            <m:mo>∇</m:mo>\r\n                                                         </m:mrow>\r\n                                                         <m:mi>v</m:mi>\r\n                                                      </m:mrow>\r\n                                                      <m:mo>)</m:mo>\r\n                                                   </m:mrow>\r\n                                                   <m:mo>,</m:mo>\r\n                                                </m:mtd>\r\n                                             </m:mtr>\r\n                                             <m:mtr>\r\n                                                <m:mtd columnalign=\"left\">\r\n                                                   <m:mn>0</m:mn>\r\n                                                   <m:mo>=</m:mo>\r\n                                                   <m:mi mathvariant=\"normal\">Δ</m:mi>\r\n                                                   <m:mi>v</m:mi>\r\n                                                   <m:mo>+</m:mo>\r\n                                                   <m:mi>u</m:mi>\r\n                                                   <m:mo>,</m:mo>\r\n                                                </m:mtd>\r\n                                             </m:mtr>\r\n                                          </m:mtable>\r\n                                       </m:mrow>\r\n                                    </m:mfenced>\r\n                                    <m:mspace width=\"2.0em\"/>\r\n                                    <m:mspace width=\"2.0em\"/>\r\n                                    <m:mspace width=\"2.0em\"/>\r\n                                    <m:mrow>\r\n                                       <m:mo>(</m:mo>\r\n                                       <m:mrow>\r\n                                          <m:mo>⋆</m:mo>\r\n                                       </m:mrow>\r\n                                       <m:mo>)</m:mo>\r\n                                    </m:mrow>\r\n                                 </m:mtd>\r\n                              </m:mtr>\r\n                           </m:mtable>\r\n                        </m:math>\r\n                        <jats:tex-math>\\begin{array}{r}\\left\\{\\phantom{\\rule[-1.25em]{}{0ex}}\\begin{array}{l}{u}_{t}=\\Delta u-\\nabla \\cdot \\left(uS\\cdot \\nabla v),\\\\ 0=\\Delta v+u,\\end{array}\\right.\\hspace{2.0em}\\hspace{2.0em}\\hspace{2.0em}\\left(\\star )\\end{array}</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:disp-formula> is considered for general matrices <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_004.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mi>S</m:mi>\r\n                           <m:mo>∈</m:mo>\r\n                           <m:msup>\r\n                              <m:mrow>\r\n                                 <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>n</m:mi>\r\n                                 <m:mo>×</m:mo>\r\n                                 <m:mi>n</m:mi>\r\n                              </m:mrow>\r\n                           </m:msup>\r\n                        </m:math>\r\n                        <jats:tex-math>S\\in {{\\mathbb{R}}}^{n\\times n}</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>. A theory of local-in-time classical existence and extensibility is developed in a framework that differs from those considered in large parts of the literature by involving bounded classical solutions. Specifically, it is shown that for all non-negative initial data belonging to <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_005.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mi mathvariant=\"normal\">BUC</m:mi>\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:msup>\r\n                                    <m:mrow>\r\n                                       <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>n</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msup>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                           <m:mo>∩</m:mo>\r\n                           <m:msup>\r\n                              <m:mrow>\r\n                                 <m:mi>L</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>p</m:mi>\r\n                              </m:mrow>\r\n                           </m:msup>\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:msup>\r\n                                    <m:mrow>\r\n                                       <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>n</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msup>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:tex-math>{\\rm{BUC}}\\left({{\\mathbb{R}}}^{n})\\cap {L}^{p}\\left({{\\mathbb{R}}}^{n})</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula> with some <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_006.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mi>p</m:mi>\r\n                           <m:mo>∈</m:mo>\r\n                           <m:mrow>\r\n                              <m:mo>[</m:mo>\r\n                              <m:mrow>\r\n                                 <m:mn>1</m:mn>\r\n                                 <m:mo>,</m:mo>\r\n                                 <m:mi>n</m:mi>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:tex-math>p\\in \\left[1,n)</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>, there exist <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_007.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:msub>\r\n                              <m:mrow>\r\n                                 <m:mi>T</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>max</m:mi>\r\n                              </m:mrow>\r\n                           </m:msub>\r\n                           <m:mo>∈</m:mo>\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:mn>0</m:mn>\r\n                                 <m:mo>,</m:mo>\r\n                                 <m:mi>∞</m:mi>\r\n                              </m:mrow>\r\n                              <m:mo>]</m:mo>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:tex-math>{T}_{\\max }\\in \\left(0,\\infty ]</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula> and a uniquely determined <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_008.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mi>u</m:mi>\r\n                           <m:mo>∈</m:mo>\r\n                           <m:msup>\r\n                              <m:mrow>\r\n                                 <m:mi>C</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mn>0</m:mn>\r\n                              </m:mrow>\r\n                           </m:msup>\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:mrow>\r\n                                    <m:mo>[</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:mn>0</m:mn>\r\n                                       <m:mo>,</m:mo>\r\n                                       <m:msub>\r\n                                          <m:mrow>\r\n                                             <m:mi>T</m:mi>\r\n                                          </m:mrow>\r\n                                          <m:mrow>\r\n                                             <m:mi>max</m:mi>\r\n                                          </m:mrow>\r\n                                       </m:msub>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                                 <m:mo>;</m:mo>\r\n                                 <m:mspace width=\"0.33em\"/>\r\n                                 <m:mi mathvariant=\"normal\">BUC</m:mi>\r\n                                 <m:mrow>\r\n                                    <m:mo>(</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:msup>\r\n                                          <m:mrow>\r\n                                             <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                                          </m:mrow>\r\n                                          <m:mrow>\r\n                                             <m:mi>n</m:mi>\r\n                                          </m:mrow>\r\n                                       </m:msup>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                           <m:mo>∩</m:mo>\r\n                           <m:msup>\r\n                              <m:mrow>\r\n                                 <m:mi>C</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mn>0</m:mn>\r\n                              </m:mrow>\r\n                           </m:msup>\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:mrow>\r\n                                    <m:mo>[</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:mn>0</m:mn>\r\n                                       <m:mo>,</m:mo>\r\n                                       <m:msub>\r\n                                          <m:mrow>\r\n                                             <m:mi>T</m:mi>\r\n                                          </m:mrow>\r\n                                          <m:mrow>\r\n                                             <m:mi>max</m:mi>\r\n                                          </m:mrow>\r\n                                       </m:msub>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                                 <m:mo>;</m:mo>\r\n                                 <m:mspace width=\"0.33em\"/>\r\n                                 <m:msup>\r\n                                    <m:mrow>\r\n                                       <m:mi>L</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>p</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msup>\r\n                                 <m:mrow>\r\n                                    <m:mo>(</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:msup>\r\n                                          <m:mrow>\r\n                                             <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                                          </m:mrow>\r\n                                          <m:mrow>\r\n                                             <m:mi>n</m:mi>\r\n                                          </m:mrow>\r\n                                       </m:msup>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                           <m:mo>∩</m:mo>\r\n                           <m:msup>\r\n                              <m:mrow>\r\n                                 <m:mi>C</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>∞</m:mi>\r\n                              </m:mrow>\r\n                           </m:msup>\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:msup>\r\n                                    <m:mrow>\r\n                                       <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>n</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msup>\r\n                                 <m:mo>×</m:mo>\r\n                                 <m:mrow>\r\n                                    <m:mo>(</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:mn>0</m:mn>\r\n                                       <m:mo>,</m:mo>\r\n                                       <m:msub>\r\n                                          <m:mrow>\r\n                                             <m:mi>T</m:mi>\r\n                                          </m:mrow>\r\n                                          <m:mrow>\r\n                                             <m:mi>max</m:mi>\r\n                                          </m:mrow>\r\n                                       </m:msub>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:tex-math>u\\in {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{\\rm{BUC}}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{0}\\left(\\left[0,{T}_{\\max });\\hspace{0.33em}{L}^{p}\\left({{\\mathbb{R}}}^{n}))\\cap {C}^{\\infty }\\left({{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max }))</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula> such that with <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_009.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mi>v</m:mi>\r\n                           <m:mo>≔</m:mo>\r\n                           <m:mi mathvariant=\"normal\">Γ</m:mi>\r\n                           <m:mo>⋆</m:mo>\r\n                           <m:mi>u</m:mi>\r\n                        </m:math>\r\n                        <jats:tex-math>v:= \\Gamma \\star u</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>, and with <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_010.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mi mathvariant=\"normal\">Γ</m:mi>\r\n                        </m:math>\r\n                        <jats:tex-math>\\Gamma </jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula> denoting the Newtonian kernel on <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_011.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:msup>\r\n                              <m:mrow>\r\n                                 <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>n</m:mi>\r\n                              </m:mrow>\r\n                           </m:msup>\r\n                        </m:math>\r\n                        <jats:tex-math>{{\\mathbb{R}}}^{n}</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>, the pair <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_012.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:mi>u</m:mi>\r\n                                 <m:mo>,</m:mo>\r\n                                 <m:mi>v</m:mi>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:tex-math>\\left(u,v)</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula> forms a classical solution of (<jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_013.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mo>⋆</m:mo>\r\n                        </m:math>\r\n                        <jats:tex-math>\\star </jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>) in <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_014.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:msup>\r\n                              <m:mrow>\r\n                                 <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>n</m:mi>\r\n                              </m:mrow>\r\n                           </m:msup>\r\n                           <m:mo>×</m:mo>\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:mn>0</m:mn>\r\n                                 <m:mo>,</m:mo>\r\n                                 <m:msub>\r\n                                    <m:mrow>\r\n                                       <m:mi>T</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>max</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msub>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:tex-math>{{\\mathbb{R}}}^{n}\\times \\left(0,{T}_{\\max })</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>, which has the property that <jats:disp-formula id=\"j_math-2022-0578_eq_002\">\r\n                     <jats:alternatives>\r\n                        <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_015.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\r\n                           <m:mspace width=\"0.1em\"/>\r\n                           <m:mtext>if</m:mtext>\r\n                           <m:mspace width=\"0.1em\"/>\r\n                           <m:mspace width=\"0.33em\"/>\r\n                           <m:msub>\r\n                              <m:mrow>\r\n                                 <m:mi>T</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>max</m:mi>\r\n                              </m:mrow>\r\n                           </m:msub>\r\n                           <m:mo>&lt;</m:mo>\r\n                           <m:mi>∞</m:mi>\r\n                           <m:mo>,</m:mo>\r\n                           <m:mspace width=\"1.0em\"/>\r\n                           <m:mstyle>\r\n                              <m:mspace width=\"0.1em\"/>\r\n                              <m:mtext>then both</m:mtext>\r\n                              <m:mspace width=\"0.1em\"/>\r\n                           </m:mstyle>\r\n                           <m:mspace width=\"0.33em\"/>\r\n                           <m:munder>\r\n                              <m:mrow>\r\n                                 <m:mi>limsup</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>t</m:mi>\r\n                                 <m:mo>↗</m:mo>\r\n                                 <m:msub>\r\n                                    <m:mrow>\r\n                                       <m:mi>T</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>max</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msub>\r\n                              </m:mrow>\r\n                           </m:munder>\r\n                           <m:msub>\r\n                              <m:mrow>\r\n                                 <m:mo>‖</m:mo>\r\n                                 <m:mi>u</m:mi>\r\n                                 <m:mrow>\r\n                                    <m:mo>(</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:mo>⋅</m:mo>\r\n                                       <m:mo>,</m:mo>\r\n                                       <m:mi>t</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                                 <m:mo>‖</m:mo>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:msup>\r\n                                    <m:mrow>\r\n                                       <m:mi>L</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>∞</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msup>\r\n                                 <m:mrow>\r\n                                    <m:mo>(</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:msup>\r\n                                          <m:mrow>\r\n                                             <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                                          </m:mrow>\r\n                                          <m:mrow>\r\n                                             <m:mi>n</m:mi>\r\n                                          </m:mrow>\r\n                                       </m:msup>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                              </m:mrow>\r\n                           </m:msub>\r\n                           <m:mo>=</m:mo>\r\n                           <m:mi>∞</m:mi>\r\n                           <m:mspace width=\"1.0em\"/>\r\n                           <m:mspace width=\"0.1em\"/>\r\n                           <m:mtext>and</m:mtext>\r\n                           <m:mspace width=\"0.1em\"/>\r\n                           <m:mspace width=\"1.0em\"/>\r\n                           <m:munder>\r\n                              <m:mrow>\r\n                                 <m:mi>limsup</m:mi>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:mi>t</m:mi>\r\n                                 <m:mo>↗</m:mo>\r\n                                 <m:msub>\r\n                                    <m:mrow>\r\n                                       <m:mi>T</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>max</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msub>\r\n                              </m:mrow>\r\n                           </m:munder>\r\n                           <m:msub>\r\n                              <m:mrow>\r\n                                 <m:mo>‖</m:mo>\r\n                                 <m:mrow>\r\n                                    <m:mo>∇</m:mo>\r\n                                 </m:mrow>\r\n                                 <m:mi>v</m:mi>\r\n                                 <m:mrow>\r\n                                    <m:mo>(</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:mo>⋅</m:mo>\r\n                                       <m:mo>,</m:mo>\r\n                                       <m:mi>t</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                                 <m:mo>‖</m:mo>\r\n                              </m:mrow>\r\n                              <m:mrow>\r\n                                 <m:msup>\r\n                                    <m:mrow>\r\n                                       <m:mi>L</m:mi>\r\n                                    </m:mrow>\r\n                                    <m:mrow>\r\n                                       <m:mi>∞</m:mi>\r\n                                    </m:mrow>\r\n                                 </m:msup>\r\n                                 <m:mrow>\r\n                                    <m:mo>(</m:mo>\r\n                                    <m:mrow>\r\n                                       <m:msup>\r\n                                          <m:mrow>\r\n                                             <m:mi mathvariant=\"double-struck\">R</m:mi>\r\n                                          </m:mrow>\r\n                                          <m:mrow>\r\n                                             <m:mi>n</m:mi>\r\n                                          </m:mrow>\r\n                                       </m:msup>\r\n                                    </m:mrow>\r\n                                    <m:mo>)</m:mo>\r\n                                 </m:mrow>\r\n                              </m:mrow>\r\n                           </m:msub>\r\n                           <m:mo>=</m:mo>\r\n                           <m:mi>∞</m:mi>\r\n                           <m:mo>.</m:mo>\r\n                        </m:math>\r\n                        <jats:tex-math>\\hspace{0.1em}\\text{if}\\hspace{0.1em}\\hspace{0.33em}{T}_{\\max }\\lt \\infty ,\\hspace{1.0em}\\hspace{0.1em}\\text{then both}\\hspace{0.1em}\\hspace{0.33em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert u\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty \\hspace{1.0em}\\hspace{0.1em}\\text{and}\\hspace{0.1em}\\hspace{1.0em}\\mathop{\\mathrm{limsup}}\\limits_{t\\nearrow {T}_{\\max }}\\Vert \\nabla v\\left(\\cdot ,t){\\Vert }_{{L}^{\\infty }\\left({{\\mathbb{R}}}^{n})}=\\infty .</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:disp-formula> An exemplary application of this provides a result on global classical solvability in cases when <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_016.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mo>∣</m:mo>\r\n                           <m:mi>S</m:mi>\r\n                           <m:mo>+</m:mo>\r\n                           <m:mn mathvariant=\"bold\">1</m:mn>\r\n                           <m:mo>∣</m:mo>\r\n                        </m:math>\r\n                        <jats:tex-math>| S+{\\bf{1}}| </jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula> is sufficiently small, where <jats:inline-formula>\r\n                     <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_math-2022-0578_eq_017.png\"/>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mn mathvariant=\"bold\">1</m:mn>\r\n                           <m:mo>=</m:mo>\r\n                           <m:mi mathvariant=\"normal\">diag</m:mi>\r\n                           <m:mspace width=\"0.33em\"/>\r\n                           <m:mrow>\r\n                              <m:mo>(</m:mo>\r\n                              <m:mrow>\r\n                                 <m:mn>1</m:mn>\r\n                                 <m:mo>,</m:mo>\r\n                                 <m:mrow>\r\n                                    <m:mo>…</m:mo>\r\n                                 </m:mrow>\r\n                                 <m:mo>,</m:mo>\r\n                                 <m:mn>1</m:mn>\r\n                              </m:mrow>\r\n                              <m:mo>)</m:mo>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:tex-math>{\\bf{1}}={\\rm{diag}}\\hspace{0.33em}\\left(1,\\ldots ,1)</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>.</jats:p>"}],"publication":"Open Mathematics","type":"journal_article","language":[{"iso":"eng"}],"article_number":"20220578","user_id":"31496","_id":"63288"}]
