[{"language":[{"iso":"eng"}],"article_number":"44","doi":"10.1007/s00245-025-10243-9","publication_identifier":{"issn":["0095-4616","1432-0606"]},"author":[{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"year":"2025","title":"Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters","intvolume":"        91","publication_status":"published","date_updated":"2026-02-26T15:59:30Z","date_created":"2025-04-02T11:23:25Z","department":[{"_id":"90"}],"type":"journal_article","issue":"2","publication":"Applied Mathematics & Optimization","publisher":"Springer Science and Business Media LLC","_id":"59258","volume":91,"user_id":"11829","status":"public","citation":{"short":"M. Winkler, Applied Mathematics &#38; Optimization 91 (2025).","chicago":"Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters.” <i>Applied Mathematics &#38; Optimization</i> 91, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00245-025-10243-9\">https://doi.org/10.1007/s00245-025-10243-9</a>.","apa":"Winkler, M. (2025). Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters. <i>Applied Mathematics &#38; Optimization</i>, <i>91</i>(2), Article 44. <a href=\"https://doi.org/10.1007/s00245-025-10243-9\">https://doi.org/10.1007/s00245-025-10243-9</a>","ieee":"M. Winkler, “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters,” <i>Applied Mathematics &#38; Optimization</i>, vol. 91, no. 2, Art. no. 44, 2025, doi: <a href=\"https://doi.org/10.1007/s00245-025-10243-9\">10.1007/s00245-025-10243-9</a>.","ama":"Winkler M. Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters. <i>Applied Mathematics &#38; Optimization</i>. 2025;91(2). doi:<a href=\"https://doi.org/10.1007/s00245-025-10243-9\">10.1007/s00245-025-10243-9</a>","bibtex":"@article{Winkler_2025, title={Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}, volume={91}, DOI={<a href=\"https://doi.org/10.1007/s00245-025-10243-9\">10.1007/s00245-025-10243-9</a>}, number={244}, journal={Applied Mathematics &#38; Optimization}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }","mla":"Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters.” <i>Applied Mathematics &#38; Optimization</i>, vol. 91, no. 2, 44, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00245-025-10243-9\">10.1007/s00245-025-10243-9</a>."},"project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}]},{"quality_controlled":"1","citation":{"mla":"Frahm, Jan, et al., editors. “Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday.” <i>J. Lie Theory</i>, vol. 35, no. 4, 2025.","bibtex":"@book{Frahm_Glöckner_Hilgert_Olafsson_2025, title={Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday}, volume={35}, number={4}, journal={J. Lie Theory}, year={2025} }","ama":"Frahm J, Glöckner H, Hilgert J, Olafsson G, eds. <i>Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday</i>. Vol 35.; 2025.","ieee":"J. Frahm, H. Glöckner, J. Hilgert, and G. Olafsson, Eds., <i>Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday</i>, vol. 35, no. 4. 2025.","apa":"Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday. (2025). In J. Frahm, H. Glöckner, J. Hilgert, &#38; G. Olafsson (Eds.), <i>J. Lie Theory</i> (Vol. 35, Issue 4).","chicago":"Frahm, Jan, Helge Glöckner, Joachim Hilgert, and Gestur Olafsson, eds. <i>Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday</i>. <i>J. Lie Theory</i>. Vol. 35, 2025.","short":"J. Frahm, H. Glöckner, J. Hilgert, G. Olafsson, eds., Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday, 2025."},"issue":"4","publication":"J. Lie Theory","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"journal_editor","date_created":"2026-02-26T17:42:01Z","intvolume":"        35","date_updated":"2026-02-26T17:51:43Z","year":"2025","title":"Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday","status":"public","volume":35,"editor":[{"full_name":"Frahm, Jan","last_name":"Frahm","first_name":"Jan"},{"last_name":"Glöckner","first_name":"Helge","full_name":"Glöckner, Helge","id":"178"},{"full_name":"Hilgert, Joachim","last_name":"Hilgert","first_name":"Joachim","id":"220"},{"full_name":"Olafsson, Gestur","first_name":"Gestur","last_name":"Olafsson"}],"user_id":"178","_id":"64736","language":[{"iso":"eng"}]},{"status":"public","title":"Manifold of mappings and regularity properties of half-Lie groups","year":"2025","author":[{"last_name":"Pinaud","first_name":"Matthieu","full_name":"Pinaud, Matthieu"}],"date_updated":"2026-02-26T21:58:36Z","main_file_link":[{"url":"https://nbn-resolving.org/urn:nbn:de:hbz:466:2-54221","open_access":"1"}],"_id":"64770","language":[{"iso":"eng"}],"user_id":"178","doi":"10.17619/UNIPB/1-2211","citation":{"apa":"Pinaud, M. (2025). <i>Manifold of mappings and regularity properties of half-Lie groups</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-2211\">https://doi.org/10.17619/UNIPB/1-2211</a>","mla":"Pinaud, Matthieu. <i>Manifold of Mappings and Regularity Properties of Half-Lie Groups</i>. 2025, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2211\">10.17619/UNIPB/1-2211</a>.","ieee":"M. Pinaud, <i>Manifold of mappings and regularity properties of half-Lie groups</i>. 2025.","ama":"Pinaud M. <i>Manifold of Mappings and Regularity Properties of Half-Lie Groups</i>.; 2025. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2211\">10.17619/UNIPB/1-2211</a>","short":"M. Pinaud, Manifold of Mappings and Regularity Properties of Half-Lie Groups, 2025.","chicago":"Pinaud, Matthieu. <i>Manifold of Mappings and Regularity Properties of Half-Lie Groups</i>, 2025. <a href=\"https://doi.org/10.17619/UNIPB/1-2211\">https://doi.org/10.17619/UNIPB/1-2211</a>.","bibtex":"@book{Pinaud_2025, title={Manifold of mappings and regularity properties of half-Lie groups}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-2211\">10.17619/UNIPB/1-2211</a>}, author={Pinaud, Matthieu}, year={2025} }"},"supervisor":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"}],"date_created":"2026-02-26T21:58:22Z","type":"dissertation","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"oa":"1"},{"abstract":[{"lang":"eng","text":"The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep networks are often unable to handle time-series data appearing at irregular intervals. These issues can be resolved by considering continuous-depth networks based on the neural ODE framework in combination with reversible integration methods that allow for variable time-steps. Reversibility of the method ensures that the memory requirement for training is independent of network depth, while variable time-steps are required for assimilating time-series data on irregular intervals. However, at present, there are no known higher-order reversible methods with this property. High-order methods are especially important when a high level of accuracy in learning is required or when small time-steps are necessary due to large errors in time integration of neural ODEs, for instance in context of complex dynamical systems such as Kepler systems and molecular dynamics. The requirement of small time-steps when using a low-order method can significantly increase the computational cost of training as well as inference. In this work, we present an approach for constructing high-order reversible methods that allow adaptive time-stepping. Our numerical tests show the advantages in computational speed when applied to the task of learning dynamical systems."}],"file_date_updated":"2025-05-05T09:28:02Z","citation":{"bibtex":"@article{Maslovskaya_Ober-Blöbaum_Offen_Singh_Wembe Moafo_2025, title={Adaptive higher order reversible integrators for memory efficient deep learning}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina and Offen, Christian and Singh, Pranav and Wembe Moafo, Boris Edgar}, year={2025} }","ama":"Maslovskaya S, Ober-Blöbaum S, Offen C, Singh P, Wembe Moafo BE. Adaptive higher order reversible integrators for memory efficient deep learning. Published online 2025.","mla":"Maslovskaya, Sofya, et al. <i>Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning</i>. 2025.","chicago":"Maslovskaya, Sofya, Sina Ober-Blöbaum, Christian Offen, Pranav Singh, and Boris Edgar Wembe Moafo. “Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning,” 2025.","short":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).","ieee":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, and B. E. Wembe Moafo, “Adaptive higher order reversible integrators for memory efficient deep learning.” 2025.","apa":"Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., &#38; Wembe Moafo, B. E. (2025). <i>Adaptive higher order reversible integrators for memory efficient deep learning</i>."},"type":"preprint","department":[{"_id":"636"}],"file":[{"access_level":"closed","file_size":1830758,"file_name":"2410.09537v2.pdf","date_updated":"2025-05-05T09:28:02Z","relation":"main_file","content_type":"application/pdf","success":1,"file_id":"59795","creator":"sofyam","date_created":"2025-05-05T09:28:02Z"}],"external_id":{"arxiv":["2410.09537"]},"date_created":"2025-05-05T09:25:28Z","date_updated":"2025-09-30T15:16:09Z","has_accepted_license":"1","status":"public","title":"Adaptive higher order reversible integrators for memory efficient deep learning","year":"2025","author":[{"id":"87909","first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"id":"85279","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen"},{"full_name":"Singh, Pranav","last_name":"Singh","first_name":"Pranav"},{"first_name":"Boris Edgar","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394"}],"user_id":"85279","ddc":["510"],"_id":"59794","language":[{"iso":"eng"}]},{"volume":46,"user_id":"72183","_id":"61518","publisher":"Springer Science and Business Media LLC","status":"public","citation":{"bibtex":"@article{Richter_Bruns_Gasteiger_2025, title={Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften}, volume={46}, DOI={<a href=\"https://doi.org/10.1007/s13138-025-00259-7\">10.1007/s13138-025-00259-7</a>}, number={18}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science and Business Media LLC}, author={Richter, Alix and Bruns, Julia and Gasteiger, Hedwig}, year={2025} }","ama":"Richter A, Bruns J, Gasteiger H. Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften. <i>Journal für Mathematik-Didaktik</i>. 2025;46(1). doi:<a href=\"https://doi.org/10.1007/s13138-025-00259-7\">10.1007/s13138-025-00259-7</a>","mla":"Richter, Alix, et al. “Interaction- or Material-Centred Implementation of Teacher Professional Development: A Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung Interaktions- Oder Materialzentriert Implementieren: Ein Vergleich Hinsichtlich Der Kompetenzentwicklung Sowie Der Potentiellen Unterrichtsplanung von Lehrkräften.” <i>Journal Für Mathematik-Didaktik</i>, vol. 46, no. 1, 8, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s13138-025-00259-7\">10.1007/s13138-025-00259-7</a>.","short":"A. Richter, J. Bruns, H. Gasteiger, Journal Für Mathematik-Didaktik 46 (2025).","chicago":"Richter, Alix, Julia Bruns, and Hedwig Gasteiger. “Interaction- or Material-Centred Implementation of Teacher Professional Development: A Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung Interaktions- Oder Materialzentriert Implementieren: Ein Vergleich Hinsichtlich Der Kompetenzentwicklung Sowie Der Potentiellen Unterrichtsplanung von Lehrkräften.” <i>Journal Für Mathematik-Didaktik</i> 46, no. 1 (2025). <a href=\"https://doi.org/10.1007/s13138-025-00259-7\">https://doi.org/10.1007/s13138-025-00259-7</a>.","ieee":"A. Richter, J. Bruns, and H. Gasteiger, “Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften,” <i>Journal für Mathematik-Didaktik</i>, vol. 46, no. 1, Art. no. 8, 2025, doi: <a href=\"https://doi.org/10.1007/s13138-025-00259-7\">10.1007/s13138-025-00259-7</a>.","apa":"Richter, A., Bruns, J., &#38; Gasteiger, H. (2025). Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften. <i>Journal Für Mathematik-Didaktik</i>, <i>46</i>(1), Article 8. <a href=\"https://doi.org/10.1007/s13138-025-00259-7\">https://doi.org/10.1007/s13138-025-00259-7</a>"},"doi":"10.1007/s13138-025-00259-7","language":[{"iso":"eng"}],"article_number":"8","intvolume":"        46","date_updated":"2025-10-05T17:55:53Z","publication_status":"published","publication_identifier":{"issn":["0173-5322","1869-2699"]},"author":[{"first_name":"Alix","last_name":"Richter","full_name":"Richter, Alix","id":"93186"},{"id":"72183","full_name":"Bruns, Julia","first_name":"Julia","orcid":"https://orcid.org/0000-0002-6604-5864","last_name":"Bruns"},{"first_name":"Hedwig","last_name":"Gasteiger","full_name":"Gasteiger, Hedwig"}],"title":"Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften","year":"2025","department":[{"_id":"611"}],"type":"journal_article","date_created":"2025-10-05T17:55:20Z","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>Teacher professional development (TPD) is a crucial support mechanism for mathematics teachers. Strategies for implementing TPD include disseminating educative curriculum materials or conducting TPD courses. However, it remains unclear whether different implementations of the same TPD support mathematics teachers in distinct ways. This study investigated two implementations of the TPD <jats:italic>EmMa-FS</jats:italic> which focuses early mathematics education (EME) for German vocational school (VS) teachers who instruct prospective early childhood (EC) educators. One group of teachers received an in-person TPD course along with educative curriculum materials (<jats:italic>n</jats:italic>\r\n            <jats:sub>\r\n              <jats:italic>PM</jats:italic>\r\n            </jats:sub> = 26), whereas the other received only the educative curriculum materials (<jats:italic>n</jats:italic>\r\n            <jats:sub>\r\n              <jats:italic>M</jats:italic>\r\n            </jats:sub> = 15). The effects on VS teachers’ beliefs and knowledge concerning EME were examined using a <jats:italic>t</jats:italic>-test and repeated measures ANOVA. To assess how teachers in the different implementation groups made use of the TPD in their lesson planning, participants submitted hypothetical lesson sequences on early numeracy, which were analysed for instructional quality, covered content, and the visible implementation of the provided educative curriculum materials using qualitative content analysis. The results indicated that both TPD implementations positively affected VS teachers’ knowledge related to EME but not their beliefs. While the instructional quality of the lesson sequences varied across both groups, participants who received the TPD course appeared to use the educative curriculum materials more often and to cover more content.</jats:p>","lang":"eng"}],"issue":"1","publication":"Journal für Mathematik-Didaktik"},{"status":"public","_id":"61519","publisher":"Hogrefe Publishing Group","page":"193-200","volume":14,"user_id":"72183","citation":{"mla":"Bruns, Julia, and Tessa Mette. “Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?” <i>Frühe Bildung</i>, vol. 14, no. 4, Hogrefe Publishing Group, 2025, pp. 193–200, doi:<a href=\"https://doi.org/10.1026/2191-9186/a000730\">10.1026/2191-9186/a000730</a>.","bibtex":"@article{Bruns_Mette_2025, title={Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?}, volume={14}, DOI={<a href=\"https://doi.org/10.1026/2191-9186/a000730\">10.1026/2191-9186/a000730</a>}, number={4}, journal={Frühe Bildung}, publisher={Hogrefe Publishing Group}, author={Bruns, Julia and Mette, Tessa}, year={2025}, pages={193–200} }","ama":"Bruns J, Mette T. Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden? <i>Frühe Bildung</i>. 2025;14(4):193-200. doi:<a href=\"https://doi.org/10.1026/2191-9186/a000730\">10.1026/2191-9186/a000730</a>","ieee":"J. Bruns and T. Mette, “Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?,” <i>Frühe Bildung</i>, vol. 14, no. 4, pp. 193–200, 2025, doi: <a href=\"https://doi.org/10.1026/2191-9186/a000730\">10.1026/2191-9186/a000730</a>.","apa":"Bruns, J., &#38; Mette, T. (2025). Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden? <i>Frühe Bildung</i>, <i>14</i>(4), 193–200. <a href=\"https://doi.org/10.1026/2191-9186/a000730\">https://doi.org/10.1026/2191-9186/a000730</a>","short":"J. Bruns, T. Mette, Frühe Bildung 14 (2025) 193–200.","chicago":"Bruns, Julia, and Tessa Mette. “Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?” <i>Frühe Bildung</i> 14, no. 4 (2025): 193–200. <a href=\"https://doi.org/10.1026/2191-9186/a000730\">https://doi.org/10.1026/2191-9186/a000730</a>."},"author":[{"id":"72183","full_name":"Bruns, Julia","first_name":"Julia","orcid":"https://orcid.org/0000-0002-6604-5864","last_name":"Bruns"},{"full_name":"Mette, Tessa","last_name":"Mette","first_name":"Tessa"}],"publication_identifier":{"issn":["2191-9186","2191-9194"]},"title":"Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?","year":"2025","intvolume":"        14","date_updated":"2025-10-05T17:56:50Z","publication_status":"published","language":[{"iso":"ger"}],"alternative_title":["Analyse von Gelegenheiten zur frühen mathematischen Bildung im Alltag einer Kindertagesstätte"],"doi":"10.1026/2191-9186/a000730","issue":"4","publication":"Frühe Bildung","abstract":[{"text":"<jats:p> Zusammenfassung: Frühe mathematische Bildung, die ihren Ausgangspunkt in den (Spiel-)Situationen der Kindertagesstätte nimmt, kann breite mathematische Erfahrungen ermöglichen, wenn die (Spiel-)Situationen entsprechende Möglichkeiten bieten. Erste Studien weisen darauf hin, dass in diesen Situationen verschiedene mathematische Inhalte angesprochen werden können. Allerdings konzentrieren sich bisherige Studien auf ausgewählte Kontexte oder Inhaltsbereiche. Diese Studie zielt daher auf eine vertiefte Analyse der Gelegenheiten für mathematische Erfahrungen, die in verschiedenen (Spiel-)Situationen im Alltag der Kindertagesstätte entstehen können. Dazu wurde eine videobasierte Beobachtungsstudie mittels einer Action-Kamera in einer Kindertagesstätte durchgeführt. Die Ergebnisse zeigen, dass eine Vielfalt von mathematischen Inhalten in (Spiel-)Situationen in der Kindertagesstätte beobachtet werden kann, einzelne Inhalte jedoch nur in formellen Lernsituationen auftreten. </jats:p>","lang":"eng"}],"date_created":"2025-10-05T17:56:06Z","department":[{"_id":"611"}],"type":"journal_article"},{"file_date_updated":"2024-11-28T08:58:00Z","citation":{"bibtex":"@article{Bot_Sonntag_2025, title={Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}, journal={Journal of Mathematical Analysis and Applications}, author={Bot, Radu Ioan and Sonntag, Konstantin}, year={2025} }","ama":"Bot RI, Sonntag K. Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>. Published online 2025.","mla":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","chicago":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","short":"R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (2025).","ieee":"R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization,” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","apa":"Bot, R. I., &#38; Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>."},"oa":"1","external_id":{"arxiv":["2411.18422"]},"has_accepted_license":"1","status":"public","user_id":"56399","ddc":["510"],"_id":"57472","abstract":[{"lang":"eng","text":"In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting."}],"publication":"Journal of Mathematical Analysis and Applications","keyword":["Pareto optimization","Lyapunov analysis","gradient-like dynamical systems","inertial dynamics","asymptotic vanishing damping","Tikhonov regularization","strong convergence"],"type":"journal_article","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"file":[{"date_created":"2024-11-28T08:58:00Z","creator":"sonntagk","content_type":"application/pdf","file_id":"57473","date_updated":"2024-11-28T08:58:00Z","relation":"main_file","access_level":"open_access","file_size":4291134,"file_name":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization.pdf"}],"date_created":"2024-11-28T08:58:17Z","date_updated":"2025-10-16T11:56:36Z","title":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization","year":"2025","author":[{"full_name":"Bot, Radu Ioan","first_name":"Radu Ioan","last_name":"Bot"},{"full_name":"Sonntag, Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin","id":"56399"}],"main_file_link":[{"url":"https://arxiv.org/pdf/2411.18422"}],"language":[{"iso":"eng"}]},{"type":"journal_article","department":[{"_id":"360"}],"date_created":"2025-11-21T16:25:49Z","publication":"mathematik lehren","issue":"252","citation":{"ama":"Rezat S, Doligkeit N. Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken. <i>mathematik lehren</i>. 2025;(252):16–22.","bibtex":"@article{Rezat_Doligkeit_2025, title={Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken}, number={252}, journal={mathematik lehren}, author={Rezat, Sebastian and Doligkeit, Nadja}, year={2025}, pages={16–22} }","mla":"Rezat, Sebastian, and Nadja Doligkeit. “Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken.” <i>mathematik lehren</i>, no. 252, 2025, pp. 16–22.","short":"S. Rezat, N. Doligkeit, mathematik lehren (2025) 16–22.","chicago":"Rezat, Sebastian, and Nadja Doligkeit. “Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken.” <i>mathematik lehren</i>, no. 252 (2025): 16–22.","apa":"Rezat, S., &#38; Doligkeit, N. (2025). Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken. <i>mathematik lehren</i>, <i>252</i>, 16–22.","ieee":"S. Rezat and N. Doligkeit, “Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken,” <i>mathematik lehren</i>, no. 252, pp. 16–22, 2025."},"user_id":"31132","page":"16–22","language":[{"iso":"ger"}],"_id":"62283","publication_status":"published","date_updated":"2025-11-21T16:26:27Z","status":"public","title":"Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken","year":"2025","author":[{"id":"31132","last_name":"Rezat","first_name":"Sebastian","full_name":"Rezat, Sebastian"},{"first_name":"Nadja","last_name":"Doligkeit","full_name":"Doligkeit, Nadja"}]},{"page":"549-555","_id":"62645","publisher":"Klinkhardt","language":[{"iso":"ger"}],"edition":"2","doi":"10.35468/hblb2025-070","user_id":"44184","editor":[{"full_name":"Cramer, C.","first_name":"C.","last_name":"Cramer"},{"full_name":"König, J.","last_name":"König","first_name":"J."},{"first_name":"M.","last_name":"Rothland","full_name":"Rothland, M."}],"title":" Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule","status":"public","year":"2025","author":[{"first_name":"Uta","orcid":"0000-0001-6278-4240","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta","id":"60267"},{"last_name":"Nührenbörger","first_name":"Marcus","full_name":"Nührenbörger, Marcus"}],"date_updated":"2025-11-27T10:53:52Z","date_created":"2025-11-27T10:53:30Z","type":"book_chapter","department":[{"_id":"543"}],"publication":"Handbuch Lehrerinnen- und Lehrerbildung","citation":{"ama":"Häsel-Weide U, Nührenbörger M.  Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule. In: Cramer C, König J, Rothland M, eds. <i>Handbuch Lehrerinnen- und Lehrerbildung</i>. 2nd ed. Klinkhardt; 2025:549-555. doi:<a href=\"https://doi.org/10.35468/hblb2025-070\">10.35468/hblb2025-070</a>","bibtex":"@inbook{Häsel-Weide_Nührenbörger_2025, edition={2}, title={ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule}, DOI={<a href=\"https://doi.org/10.35468/hblb2025-070\">10.35468/hblb2025-070</a>}, booktitle={Handbuch Lehrerinnen- und Lehrerbildung}, publisher={Klinkhardt}, author={Häsel-Weide, Uta and Nührenbörger, Marcus}, editor={Cramer, C. and König, J. and Rothland, M.}, year={2025}, pages={549–555} }","mla":"Häsel-Weide, Uta, and Marcus Nührenbörger. “ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule.” <i>Handbuch Lehrerinnen- und Lehrerbildung</i>, edited by C. Cramer et al., 2nd ed., Klinkhardt, 2025, pp. 549–55, doi:<a href=\"https://doi.org/10.35468/hblb2025-070\">10.35468/hblb2025-070</a>.","chicago":"Häsel-Weide, Uta, and Marcus Nührenbörger. “ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule.” In <i>Handbuch Lehrerinnen- und Lehrerbildung</i>, edited by C. Cramer, J. König, and M. Rothland, 2nd ed., 549–55. Klinkhardt, 2025. <a href=\"https://doi.org/10.35468/hblb2025-070\">https://doi.org/10.35468/hblb2025-070</a>.","short":"U. Häsel-Weide, M. Nührenbörger, in: C. Cramer, J. König, M. Rothland (Eds.), Handbuch Lehrerinnen- und Lehrerbildung, 2nd ed., Klinkhardt, 2025, pp. 549–555.","apa":"Häsel-Weide, U., &#38; Nührenbörger, M. (2025).  Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule. In C. Cramer, J. König, &#38; M. Rothland (Eds.), <i>Handbuch Lehrerinnen- und Lehrerbildung</i> (2nd ed., pp. 549–555). Klinkhardt. <a href=\"https://doi.org/10.35468/hblb2025-070\">https://doi.org/10.35468/hblb2025-070</a>","ieee":"U. Häsel-Weide and M. Nührenbörger, “ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule,” in <i>Handbuch Lehrerinnen- und Lehrerbildung</i>, 2nd ed., C. Cramer, J. König, and M. Rothland, Eds. Klinkhardt, 2025, pp. 549–555."}},{"status":"public","has_accepted_license":"1","_id":"62750","publisher":"Paderborn University","user_id":"56399","ddc":["510"],"citation":{"ieee":"K. Sonntag, <i>First-order methods and gradient dynamical systems for multiobjective optimization</i>. Paderborn University, 2025.","apa":"Sonntag, K. (2025). <i>First-order methods and gradient dynamical systems for multiobjective optimization</i>. Paderborn University. <a href=\"https://doi.org/10.17619/UNIPB/1-2457\">https://doi.org/10.17619/UNIPB/1-2457</a>","chicago":"Sonntag, Konstantin. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University, 2025. <a href=\"https://doi.org/10.17619/UNIPB/1-2457\">https://doi.org/10.17619/UNIPB/1-2457</a>.","short":"K. Sonntag, First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization, Paderborn University, 2025.","mla":"Sonntag, Konstantin. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University, 2025, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>.","bibtex":"@book{Sonntag_2025, title={First-order methods and gradient dynamical systems for multiobjective optimization}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>}, publisher={Paderborn University}, author={Sonntag, Konstantin}, year={2025} }","ama":"Sonntag K. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University; 2025. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>"},"supervisor":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"}],"oa":"1","title":"First-order methods and gradient dynamical systems for multiobjective optimization","year":"2025","author":[{"full_name":"Sonntag, Konstantin","first_name":"Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","id":"56399"}],"date_updated":"2025-12-03T07:04:36Z","main_file_link":[{"open_access":"1","url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/8141881"}],"language":[{"iso":"eng"}],"doi":"10.17619/UNIPB/1-2457","abstract":[{"lang":"eng","text":"Diese Dissertation enthält Beiträge zum Bereich der Mehrzieloptimierung mit einem Fokus auf unbeschränkten Problemen, die auf einem allgemeinen Hilbertraum definiert sind. Für Mehrzieloptimierungsprobleme mit lokal Lipschitz-stetigen Zielfunktionen definieren wir ein multikriterielles Subdifferential, das wir erstmals im Kontext allgemeiner Hilberträume analysieren. Aufbauend auf diesen theoretischen Untersuchungen präsentieren wir ein Abstiegsverfahren, bei welchem in jeder Iteration eine Abstiegsrichtung mittels einer numerischen Approximation des multikriteriellen Subdifferentials bestimmt wird. Im Kontext konvexer, stetig differenzierbarer Zielfunktionen mit Lipschitz-stetigen Gradienten, führen wir eine Familie von dynamischen Gradientensystemen mit Trägheitsterm ein, die bekannte kontinuierliche Systeme aus der skalaren Optimierung verallgemeinern. Wir stellen drei neue Systeme vor: eines mit konstanter Dämpfung, eines mit asymptotisch abnehmender Dämpfung und eines, das zusätzlich eine zeitabhängige Tikhonov-Regularisierung beinhaltet. Aufbauend auf den Untersuchungen der neuen dynamischen Gradientensysteme, entwickeln wir ein beschleunigtes Gradientenverfahren zur Mehrzieloptimierung, das auf einer Diskretisierung des multikriteriellen Gradientensystems mit asymptotisch abnehmender Dämpfung beruht. Das hergeleitete Verfahren bewahrt die günstigen Konvergenzeigenschaften des kontinuierlichen Systems und erreicht eine schnellere Konvergenz als klassische Verfahren."},{"text":"This dissertation contributes to the field of multiobjective optimization, with a focus on unconstrained problems formulated in a general Hilbert space. For multiobjective optimization problems with locally Lipschitz continuous objective functions, we define a multiobjective subdifferential, which we analyze for the first time in the context of general Hilbert spaces. Building on these theoretical investigations, we present a descent method in which, at each iteration, a descent direction is determined via a numerical approximation of the multiobjective subdifferential. In the setting of convex, continuously differentiable objective functions with Lipschitz continuous gradients, we introduce a family of inertial gradient dynamical systems that generalize well-known continuous-time systems from scalar optimization. We present three novel systems: one with constant damping, one with asymptotic vanishing damping, and one combining vanishing damping with time-dependent Tikhonov regularization. Building on the investigation of the novel gradient dynamical systems, we develop an accelerated gradient method for multiobjective optimization via discretization of the multiobjective gradient system with asymptotic vanishing damping. The proposed method retains the favorable convergence properties of the continuous system while achieving faster convergence than standard approaches, such as classical methods.","lang":"eng"}],"date_created":"2025-12-03T06:55:01Z","type":"dissertation","department":[{"_id":"101"},{"_id":"530"}]},{"doi":"10.1103/sv6z-v1gk","language":[{"iso":"eng"}],"article_number":"033062","intvolume":"         7","date_updated":"2025-12-09T09:10:01Z","publication_status":"published","author":[{"first_name":"Denis A.","last_name":"Kopylov","full_name":"Kopylov, Denis A."},{"id":"85279","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian"},{"last_name":"Ares","first_name":"Laura","full_name":"Ares, Laura"},{"full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar","id":"95394"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"full_name":"Meier, Torsten","last_name":"Meier","orcid":"0000-0001-8864-2072","first_name":"Torsten","id":"344"},{"id":"60286","last_name":"Sharapova","first_name":"Polina R.","full_name":"Sharapova, Polina R."},{"id":"75127","last_name":"Sperling","first_name":"Jan","orcid":"0000-0002-5844-3205","full_name":"Sperling, Jan"}],"publication_identifier":{"issn":["2643-1564"]},"title":"Multiphoton, multimode state classification for nonlinear optical circuits","year":"2025","department":[{"_id":"15"},{"_id":"569"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"35"},{"_id":"230"},{"_id":"429"},{"_id":"623"}],"type":"journal_article","date_created":"2025-12-09T09:08:39Z","abstract":[{"lang":"eng","text":"<jats:p>We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.</jats:p>"}],"publication":"Physical Review Research","issue":"3","volume":7,"user_id":"16199","_id":"62980","publisher":"American Physical Society (APS)","status":"public","project":[{"name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen","_id":"53"},{"name":"TRR 142 - Project Area C","_id":"56"},{"_id":"174","name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse"},{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"citation":{"ama":"Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>. 2025;7(3). doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, volume={7}, DOI={<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>}, number={3033062}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Kopylov, Denis A. and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina R. and Sperling, Jan}, year={2025} }","mla":"Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i>, vol. 7, no. 3, 033062, American Physical Society (APS), 2025, doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","chicago":"Kopylov, Denis A., Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina R. Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i> 7, no. 3 (2025). <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>.","short":"D.A. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P.R. Sharapova, J. Sperling, Physical Review Research 7 (2025).","apa":"Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P. R., &#38; Sperling, J. (2025). Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>, <i>7</i>(3), Article 033062. <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>","ieee":"D. A. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits,” <i>Physical Review Research</i>, vol. 7, no. 3, Art. no. 033062, 2025, doi: <a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>."}},{"page":"72–91","_id":"63036","publisher":"Norwegian University of Science and Technology.","ddc":["370"],"user_id":"31132","editor":[{"last_name":"Pepin","first_name":"Birgit","full_name":"Pepin, Birgit"},{"last_name":"Kohanová","first_name":"Iveta","full_name":"Kohanová, Iveta"},{"full_name":"Langfeldt, Marit Buset","first_name":"Marit Buset","last_name":"Langfeldt"}],"status":"public","conference":{"name":"Fifth International Conference on Mathematics Textbook Research and Development (ICMT5)","start_date":"2025-06-17","location":"Trondheim, Norway","end_date":"2025-06-20"},"has_accepted_license":"1","file_date_updated":"2025-12-11T15:39:27Z","citation":{"short":"S. Rezat, D. Glasnović Gracin, H. Van Steenbrugge, H. Sievert, in: B. Pepin, I. Kohanová, M.B. Langfeldt (Eds.), Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development., Norwegian University of Science and Technology., 2025, pp. 72–91.","chicago":"Rezat, Sebastian, Dubravka Glasnović Gracin, Hendrik Van Steenbrugge, and Henning Sievert. “The Quality of Print and Digital Mathematics Curriculum Resources.” In <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development.</i>, edited by Birgit Pepin, Iveta Kohanová, and Marit Buset Langfeldt, 72–91. Norwegian University of Science and Technology., 2025.","ieee":"S. Rezat, D. Glasnović Gracin, H. Van Steenbrugge, and H. Sievert, “The quality of print and digital mathematics curriculum resources,” in <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development.</i>, Trondheim, Norway, 2025, pp. 72–91.","apa":"Rezat, S., Glasnović Gracin, D., Van Steenbrugge, H., &#38; Sievert, H. (2025). The quality of print and digital mathematics curriculum resources. In B. Pepin, I. Kohanová, &#38; M. B. Langfeldt (Eds.), <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development.</i> (pp. 72–91). Norwegian University of Science and Technology.","bibtex":"@inproceedings{Rezat_Glasnović Gracin_Van Steenbrugge_Sievert_2025, title={The quality of print and digital mathematics curriculum resources}, booktitle={Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development.}, publisher={Norwegian University of Science and Technology.}, author={Rezat, Sebastian and Glasnović Gracin, Dubravka and Van Steenbrugge, Hendrik and Sievert, Henning}, editor={Pepin, Birgit and Kohanová, Iveta and Langfeldt, Marit Buset}, year={2025}, pages={72–91} }","ama":"Rezat S, Glasnović Gracin D, Van Steenbrugge H, Sievert H. The quality of print and digital mathematics curriculum resources. In: Pepin B, Kohanová I, Langfeldt MB, eds. <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development.</i> Norwegian University of Science and Technology.; 2025:72–91.","mla":"Rezat, Sebastian, et al. “The Quality of Print and Digital Mathematics Curriculum Resources.” <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development.</i>, edited by Birgit Pepin et al., Norwegian University of Science and Technology., 2025, pp. 72–91."},"language":[{"iso":"eng"}],"year":"2025","title":"The quality of print and digital mathematics curriculum resources","author":[{"id":"31132","last_name":"Rezat","first_name":"Sebastian","full_name":"Rezat, Sebastian"},{"full_name":"Glasnović Gracin, Dubravka","first_name":"Dubravka","last_name":"Glasnović Gracin"},{"full_name":"Van Steenbrugge, Hendrik","last_name":"Van Steenbrugge","first_name":"Hendrik"},{"full_name":"Sievert, Henning","last_name":"Sievert","first_name":"Henning"}],"publication_identifier":{"isbn":["978-82-691902-2-9"]},"date_updated":"2025-12-12T10:15:57Z","publication_status":"published","file":[{"date_updated":"2025-12-11T15:39:27Z","relation":"main_file","access_level":"closed","file_size":724455,"file_name":"Proceedings ICMT5 december 2026 Seiten 85-104.pdf","success":1,"content_type":"application/pdf","file_id":"63037","creator":"srezat","date_created":"2025-12-11T15:39:27Z"}],"date_created":"2025-12-11T15:36:37Z","type":"conference","department":[{"_id":"360"}],"publication":"Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development."},{"main_file_link":[{"open_access":"1","url":"https://www.ntnu.edu/documents/1317903369/0/Proceedings+ICMT5+december+2026.pdf"}],"_id":"63034","publisher":"Norwegian University of Science and Technology","language":[{"iso":"eng"}],"user_id":"31132","editor":[{"last_name":"Pepin","first_name":"Birgit","full_name":"Pepin, Birgit"},{"full_name":"Kohanová, Iveta","first_name":"Iveta","last_name":"Kohanová"},{"full_name":"Langfeldt, Marit Buset","last_name":"Langfeldt","first_name":"Marit Buset"}],"status":"public","title":"Students’ use of different material resources for specific purposes in the process of learning mathematics","year":"2025","conference":{"end_date":"2025-06-20","name":"Fifth International Conference on Mathematics Textbook Research and Development","start_date":"2025-06-17","location":"Trondheim, Norway"},"publication_identifier":{"isbn":["978-82-691902-2-9"]},"author":[{"id":"63369","first_name":"Lea","last_name":"Stallmeister","full_name":"Stallmeister, Lea"},{"last_name":"Rezat","first_name":"Sebastian","full_name":"Rezat, Sebastian","id":"31132"}],"date_updated":"2025-12-12T10:17:46Z","publication_status":"published","date_created":"2025-12-11T13:15:07Z","type":"conference","oa":"1","department":[{"_id":"98"}],"publication":"Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development","citation":{"apa":"Stallmeister, L., &#38; Rezat, S. (2025). Students’ use of different material resources for specific purposes in the process of learning mathematics. In B. Pepin, I. Kohanová, &#38; M. B. Langfeldt (Eds.), <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development</i>. Norwegian University of Science and Technology.","ieee":"L. Stallmeister and S. Rezat, “Students’ use of different material resources for specific purposes in the process of learning mathematics,” in <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development</i>, Trondheim, Norway, 2025.","short":"L. Stallmeister, S. Rezat, in: B. Pepin, I. Kohanová, M.B. Langfeldt (Eds.), Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development, Norwegian University of Science and Technology, 2025.","chicago":"Stallmeister, Lea, and Sebastian Rezat. “Students’ Use of Different Material Resources for Specific Purposes in the Process of Learning Mathematics.” In <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development</i>, edited by Birgit Pepin, Iveta Kohanová, and Marit Buset Langfeldt. Norwegian University of Science and Technology, 2025.","mla":"Stallmeister, Lea, and Sebastian Rezat. “Students’ Use of Different Material Resources for Specific Purposes in the Process of Learning Mathematics.” <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development</i>, edited by Birgit Pepin et al., Norwegian University of Science and Technology, 2025.","ama":"Stallmeister L, Rezat S. Students’ use of different material resources for specific purposes in the process of learning mathematics. In: Pepin B, Kohanová I, Langfeldt MB, eds. <i>Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development</i>. Norwegian University of Science and Technology; 2025.","bibtex":"@inproceedings{Stallmeister_Rezat_2025, title={Students’ use of different material resources for specific purposes in the process of learning mathematics}, booktitle={Proceedings of the Fifth International Conference on Mathematics Textbook Research and Development}, publisher={Norwegian University of Science and Technology}, author={Stallmeister, Lea and Rezat, Sebastian}, editor={Pepin, Birgit and Kohanová, Iveta and Langfeldt, Marit Buset}, year={2025} }"}},{"file_date_updated":"2025-06-12T14:23:07Z","citation":{"short":"S. Rezat, ZDM – Mathematics Education 57 (2025) 891–904.","chicago":"Rezat, Sebastian. “The Quality of Digital Curriculum Resources for Mathematics in German Educational Policy.” <i>ZDM – Mathematics Education</i> 57 (2025): 891–904. <a href=\"https://doi.org/10.1007/s11858-025-01708-w\">https://doi.org/10.1007/s11858-025-01708-w</a>.","ieee":"S. Rezat, “The quality of digital curriculum resources for mathematics in German educational policy,” <i>ZDM – Mathematics Education</i>, vol. 57, pp. 891–904, 2025, doi: <a href=\"https://doi.org/10.1007/s11858-025-01708-w\">10.1007/s11858-025-01708-w</a>.","apa":"Rezat, S. (2025). The quality of digital curriculum resources for mathematics in German educational policy. <i>ZDM – Mathematics Education</i>, <i>57</i>, 891–904. <a href=\"https://doi.org/10.1007/s11858-025-01708-w\">https://doi.org/10.1007/s11858-025-01708-w</a>","bibtex":"@article{Rezat_2025, title={The quality of digital curriculum resources for mathematics in German educational policy}, volume={57}, DOI={<a href=\"https://doi.org/10.1007/s11858-025-01708-w\">10.1007/s11858-025-01708-w</a>}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Rezat, Sebastian}, year={2025}, pages={891–904} }","ama":"Rezat S. The quality of digital curriculum resources for mathematics in German educational policy. <i>ZDM – Mathematics Education</i>. 2025;57:891–904. doi:<a href=\"https://doi.org/10.1007/s11858-025-01708-w\">10.1007/s11858-025-01708-w</a>","mla":"Rezat, Sebastian. “The Quality of Digital Curriculum Resources for Mathematics in German Educational Policy.” <i>ZDM – Mathematics Education</i>, vol. 57, Springer Science and Business Media LLC, 2025, pp. 891–904, doi:<a href=\"https://doi.org/10.1007/s11858-025-01708-w\">10.1007/s11858-025-01708-w</a>."},"quality_controlled":"1","status":"public","has_accepted_license":"1","page":" 891–904","publisher":"Springer Science and Business Media LLC","_id":"60196","ddc":["370"],"user_id":"31132","volume":57,"publication":"ZDM – Mathematics Education","abstract":[{"lang":"eng","text":"This paper examines the governance and quality control of digital curriculum resources (DCR) for K-12 mathematics education in Germany. It focuses on approval processes and criteria set by the 16 federal states, arguing that these have the potential to influence the development of DCR. Using qualitative content analysis, the study explores three research questions: which DCR require official approval, the criteria applied for approval, and the extent to which these criteria are mathematics-specific. Findings indicate that 10 federal states maintain official approval systems, covering digital equivalents of printed textbooks and selected supplemental materials. However, most DCR fall outside these regulated processes, leaving their evaluation largely to individual schools and teachers. The study identifies 17 categories of quality criteria, but reveals a lack of detailed, mathematics-specific requirements. Instead, many criteria are broad references to didactical principles and educational goals, leaving the interpretation and application of these quality standards open-ended. Subject-specific criteria are included but remain limited in specificity. The study underscores the need for research-informed, mathematics-specific quality standards to guide DCR development and approval, emphasizing their importance amidst challenges like artificial intelligence. Policymakers are urged to adopt clearer criteria to ensure high-quality DCR to be used in schools."}],"file":[{"date_updated":"2025-06-12T14:23:07Z","relation":"main_file","file_size":1296774,"access_level":"closed","file_name":"s11858-025-01708-w.pdf","content_type":"application/pdf","success":1,"file_id":"60197","creator":"srezat","date_created":"2025-06-12T14:23:07Z"}],"date_created":"2025-06-12T14:21:07Z","type":"journal_article","keyword":["governance","digital curriculum resources","digital textbooks","digital curriculum materials","quality"],"department":[{"_id":"360"}],"year":"2025","title":"The quality of digital curriculum resources for mathematics in German educational policy","author":[{"full_name":"Rezat, Sebastian","last_name":"Rezat","first_name":"Sebastian","id":"31132"}],"publication_identifier":{"issn":["1863-9690","1863-9704"]},"date_updated":"2025-12-16T14:32:27Z","publication_status":"published","intvolume":"        57","article_type":"original","language":[{"iso":"eng"}],"doi":"10.1007/s11858-025-01708-w"},{"department":[{"_id":"10"}],"type":"preprint","date_created":"2025-12-16T14:38:59Z","related_material":{"link":[{"url":"https://arxiv.org/abs/2510.24642","relation":"confirmation"}]},"citation":{"mla":"Cummings, Charley, et al. <i>An Equivalence Linking CM-Types $A_\\infty$ and $D_\\infty$</i>. 2025, pp. 1–9.","ama":"Cummings C, Gratz S, Kirkman E, Letz JC, Rock JD, Špenko Š. An equivalence linking CM-types $A_\\infty$ and $D_\\infty$. Published online 2025:1-9.","bibtex":"@article{Cummings_Gratz_Kirkman_Letz_Rock_Špenko_2025, title={An equivalence linking CM-types $A_\\infty$ and $D_\\infty$}, author={Cummings, Charley and Gratz, Sira and Kirkman, Ellen and Letz, Janina Carmen and Rock, J. Daisie and Špenko, Špela}, year={2025}, pages={1–9} }","apa":"Cummings, C., Gratz, S., Kirkman, E., Letz, J. C., Rock, J. D., &#38; Špenko, Š. (2025). <i>An equivalence linking CM-types $A_\\infty$ and $D_\\infty$</i> (pp. 1–9).","ieee":"C. Cummings, S. Gratz, E. Kirkman, J. C. Letz, J. D. Rock, and Š. Špenko, “An equivalence linking CM-types $A_\\infty$ and $D_\\infty$.” pp. 1–9, 2025.","chicago":"Cummings, Charley, Sira Gratz, Ellen Kirkman, Janina Carmen Letz, J. Daisie Rock, and Špela Špenko. “An Equivalence Linking CM-Types $A_\\infty$ and $D_\\infty$,” 2025.","short":"C. Cummings, S. Gratz, E. Kirkman, J.C. Letz, J.D. Rock, Š. Špenko, (2025) 1–9."},"user_id":"121953","_id":"63150","language":[{"iso":"eng"}],"page":"1-9","date_updated":"2025-12-16T14:40:06Z","author":[{"full_name":"Cummings, Charley","last_name":"Cummings","first_name":"Charley"},{"first_name":"Sira","last_name":"Gratz","full_name":"Gratz, Sira"},{"first_name":"Ellen","last_name":"Kirkman","full_name":"Kirkman, Ellen"},{"id":"121953","full_name":"Letz, Janina Carmen","last_name":"Letz","first_name":"Janina Carmen","orcid":"0000-0002-5497-8296"},{"full_name":"Rock, J. Daisie","first_name":"J. Daisie","last_name":"Rock"},{"full_name":"Špenko, Špela","last_name":"Špenko","first_name":"Špela"}],"status":"public","title":"An equivalence linking CM-types $A_\\infty$ and $D_\\infty$","year":"2025"},{"type":"preprint","department":[{"_id":"10"}],"date_created":"2025-12-16T14:38:56Z","related_material":{"link":[{"url":"https://arxiv.org/abs/2509.09941","relation":"confirmation"}]},"extern":"1","citation":{"ieee":"A. Kekkou, J. C. Letz, and M. Stephan, “Regular sequences for triangulated categories.” pp. 1–37, 2025.","apa":"Kekkou, A., Letz, J. C., &#38; Stephan, M. (2025). <i>Regular sequences for triangulated categories</i> (pp. 1–37).","chicago":"Kekkou, Antonia, Janina Carmen Letz, and Marc Stephan. “Regular Sequences for Triangulated Categories,” 2025.","short":"A. Kekkou, J.C. Letz, M. Stephan, (2025) 1–37.","mla":"Kekkou, Antonia, et al. <i>Regular Sequences for Triangulated Categories</i>. 2025, pp. 1–37.","bibtex":"@article{Kekkou_Letz_Stephan_2025, title={Regular sequences for triangulated categories}, author={Kekkou, Antonia and Letz, Janina Carmen and Stephan, Marc}, year={2025}, pages={1–37} }","ama":"Kekkou A, Letz JC, Stephan M. Regular sequences for triangulated categories. Published online 2025:1-37."},"user_id":"121953","page":"1-37","language":[{"iso":"eng"}],"_id":"63149","date_updated":"2025-12-16T14:42:14Z","year":"2025","title":"Regular sequences for triangulated categories","status":"public","author":[{"first_name":"Antonia","last_name":"Kekkou","full_name":"Kekkou, Antonia"},{"last_name":"Letz","first_name":"Janina Carmen","orcid":"0000-0002-5497-8296","full_name":"Letz, Janina Carmen","id":"121953"},{"first_name":"Marc","last_name":"Stephan","full_name":"Stephan, Marc"}]},{"date_created":"2025-12-16T14:38:52Z","type":"preprint","department":[{"_id":"10"}],"citation":{"ama":"Letz JC. The Rouquier dimension of the category of perfect complexes over a regular ring. Published online 2025:1-7.","bibtex":"@article{Letz_2025, title={The Rouquier dimension of the category of perfect complexes over a regular ring}, author={Letz, Janina Carmen}, year={2025}, pages={1–7} }","mla":"Letz, Janina Carmen. <i>The Rouquier Dimension of the Category of Perfect Complexes over a Regular Ring</i>. 2025, pp. 1–7.","chicago":"Letz, Janina Carmen. “The Rouquier Dimension of the Category of Perfect Complexes over a Regular Ring,” 2025.","short":"J.C. Letz, (2025) 1–7.","apa":"Letz, J. C. (2025). <i>The Rouquier dimension of the category of perfect complexes over a regular ring</i> (pp. 1–7).","ieee":"J. C. Letz, “The Rouquier dimension of the category of perfect complexes over a regular ring.” pp. 1–7, 2025."},"extern":"1","related_material":{"link":[{"relation":"confirmation","url":"https://arxiv.org/abs/2506.24038"}]},"page":"1-7","_id":"63148","language":[{"iso":"eng"}],"user_id":"121953","title":"The Rouquier dimension of the category of perfect complexes over a regular ring","status":"public","year":"2025","author":[{"full_name":"Letz, Janina Carmen","orcid":"0000-0002-5497-8296","first_name":"Janina Carmen","last_name":"Letz","id":"121953"}],"date_updated":"2025-12-16T14:47:53Z"},{"date_updated":"2025-12-16T15:17:27Z","publication_status":"submitted","intvolume":"       477","status":"public","year":"2025","title":"Commutator-free Cayley methods","author":[{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"last_name":"Offen","first_name":"Cristian ","full_name":"Offen, Cristian "},{"id":"87909","last_name":"Maslovskaya","first_name":"Sofya","full_name":"Maslovskaya, Sofya"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Singh","first_name":"Pranav","full_name":"Singh, Pranav"}],"doi":"10.1016/j.cam.2025.117184","user_id":"95394","volume":477,"_id":"59507","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they respect important physical laws of the dynamical system, such as unitarity and energy conservation in the context of quantum dynamical systems, for instance. In this article we develop a high-order commutator free Lie group integrator for non-autonomous differential equations evolving on quadratic Lie groups. Instead of matrix exponentials, which are expensive to evaluate and need to be approximated by appropriate rational functions in order to preserve the Lie group structure, the proposed method is obtained as a composition of Cayley transforms which naturally respect the structure of quadratic Lie groups while being computationally efficient to evaluate. Unlike Cayley-Magnus methods the method is also free from nested matrix commutators."}],"publication":"J. Comput. Appl. Math","issue":"15","citation":{"chicago":"Wembe Moafo, Boris Edgar, Cristian  Offen, Sofya Maslovskaya, Sina Ober-Blöbaum, and Pranav Singh. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i> 477, no. 15 (n.d.). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>.","short":"B.E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, P. Singh, J. Comput. Appl. Math 477 (n.d.).","apa":"Wembe Moafo, B. E., Offen, C., Maslovskaya, S., Ober-Blöbaum, S., &#38; Singh, P. (n.d.). Commutator-free Cayley methods. <i>J. Comput. Appl. Math</i>, <i>477</i>(15). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>","ieee":"B. E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, and P. Singh, “Commutator-free Cayley methods,” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi: <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>.","ama":"Wembe Moafo BE, Offen C, Maslovskaya S, Ober-Blöbaum S, Singh P. Commutator-free Cayley methods. <i>J Comput Appl Math</i>. 477(15). doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>","bibtex":"@article{Wembe Moafo_Offen_Maslovskaya_Ober-Blöbaum_Singh, title={Commutator-free Cayley methods}, volume={477}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>}, number={15}, journal={J. Comput. Appl. Math}, author={Wembe Moafo, Boris Edgar and Offen, Cristian  and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Singh, Pranav} }","mla":"Wembe Moafo, Boris Edgar, et al. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>."},"type":"journal_article","department":[{"_id":"94"}],"date_created":"2025-04-10T14:42:52Z"},{"language":[{"iso":"eng"}],"_id":"63187","user_id":"15540","author":[{"id":"111755","full_name":"Kidner, Arnott Jeffery Joel","first_name":"Arnott Jeffery Joel","last_name":"Kidner"},{"full_name":"Steffen, Eckhard","last_name":"Steffen","first_name":"Eckhard","orcid":"0000-0002-9808-7401","id":"15548"},{"id":"117508","last_name":"Yu","first_name":"Weiqiang","full_name":"Yu, Weiqiang"}],"status":"public","year":"2025","title":"Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor","date_updated":"2025-12-18T13:17:18Z","date_created":"2025-12-17T14:40:23Z","external_id":{"arxiv":["2512.14285"]},"department":[{"_id":"542"}],"type":"preprint","citation":{"short":"A.J.J. Kidner, E. Steffen, W. Yu, ArXiv:2512.14285 (2025).","chicago":"Kidner, Arnott Jeffery Joel, Eckhard Steffen, and Weiqiang Yu. “Edge-Coloring 4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025.","apa":"Kidner, A. J. J., Steffen, E., &#38; Yu, W. (2025). Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. In <i>arXiv:2512.14285</i>.","ieee":"A. J. J. Kidner, E. Steffen, and W. Yu, “Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor,” <i>arXiv:2512.14285</i>. 2025.","ama":"Kidner AJJ, Steffen E, Yu W. Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor. <i>arXiv:251214285</i>. Published online 2025.","bibtex":"@article{Kidner_Steffen_Yu_2025, title={Edge-coloring 4- and 5-regular projective planar graphs with no Petersen-minor}, journal={arXiv:2512.14285}, author={Kidner, Arnott Jeffery Joel and Steffen, Eckhard and Yu, Weiqiang}, year={2025} }","mla":"Kidner, Arnott Jeffery Joel, et al. “Edge-Coloring 4- and 5-Regular Projective Planar Graphs with No Petersen-Minor.” <i>ArXiv:2512.14285</i>, 2025."},"publication":"arXiv:2512.14285"},{"title":"Linear dimension of group actions","year":"2025","status":"public","author":[{"full_name":"Devillers, Alice","first_name":"Alice","last_name":"Devillers"},{"full_name":"Giudici, Michael","first_name":"Michael","last_name":"Giudici"},{"first_name":"Daniel R.","last_name":"Hawtin","full_name":"Hawtin, Daniel R."},{"id":"91965","full_name":"Klawuhn, Lukas-André Dominik","orcid":"0009-0009-7736-4885","first_name":"Lukas-André Dominik","last_name":"Klawuhn"},{"first_name":"Luke","last_name":"Morgan","full_name":"Morgan, Luke"}],"date_updated":"2025-12-19T11:23:41Z","language":[{"iso":"eng"}],"_id":"63384","user_id":"91965","citation":{"bibtex":"@article{Devillers_Giudici_Hawtin_Klawuhn_Morgan_2025, title={Linear dimension of group actions}, author={Devillers, Alice and Giudici, Michael and Hawtin, Daniel R. and Klawuhn, Lukas-André Dominik and Morgan, Luke}, year={2025} }","ama":"Devillers A, Giudici M, Hawtin DR, Klawuhn L-AD, Morgan L. Linear dimension of group actions. Published online 2025.","mla":"Devillers, Alice, et al. <i>Linear Dimension of Group Actions</i>. 2025.","short":"A. Devillers, M. Giudici, D.R. Hawtin, L.-A.D. Klawuhn, L. Morgan, (2025).","chicago":"Devillers, Alice, Michael Giudici, Daniel R. Hawtin, Lukas-André Dominik Klawuhn, and Luke Morgan. “Linear Dimension of Group Actions,” 2025.","ieee":"A. Devillers, M. Giudici, D. R. Hawtin, L.-A. D. Klawuhn, and L. Morgan, “Linear dimension of group actions.” 2025.","apa":"Devillers, A., Giudici, M., Hawtin, D. R., Klawuhn, L.-A. D., &#38; Morgan, L. (2025). <i>Linear dimension of group actions</i>."},"abstract":[{"text":"Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how small the matrices in such a linear representation can be. The minimal dimension of such a representation is the \\emph{linear dimension of the group action} and this has applications in cryptography and cryptosystems.\r\n\r\nWe develop the idea of linear dimension from an algebraic point of view by using the theory of permutation modules. We give structural results about representations of minimal dimension and investigate the implications of faithfulness, transitivity and primitivity on the linear dimension. Furthermore, we compute the linear dimension of several classes of finite primitive permutation groups. We also study wreath products, allowing us to determine the linear dimension of imprimitive group actions. Finally, we give the linear dimension of almost simple finite $2$-transitive groups, some of which may be used for further applications in cryptography. Our results also open up many new questions about linear representations of group actions.","lang":"eng"}],"external_id":{"arxiv":["2512.16079"]},"date_created":"2025-12-19T11:20:46Z","type":"preprint","department":[{"_id":"100"}]}]