[{"title":"„Tolle lege! Aber was liest man eigentlich, wenn man englische Romane deutscher Schulbuchverlage liest?“","date_created":"2024-03-07T00:53:28Z","author":[{"first_name":"Julie","last_name":"Intveen","full_name":"Intveen, Julie","id":"56558"},{"full_name":"Hohwiller, Peter","last_name":"Hohwiller","first_name":"Peter"}],"date_updated":"2024-04-04T13:27:01Z","publisher":"Universitätsbibliothek Heidelberg","citation":{"apa":"Intveen, J., &#38; Hohwiller, P. (n.d.). „Tolle lege! Aber was liest man eigentlich, wenn man englische Romane deutscher Schulbuchverlage liest?“. <i>HeLix Dossiers zur romanischen Literaturwissenschaft</i>.","short":"J. Intveen, P. Hohwiller, HeLix Dossiers zur romanischen Literaturwissenschaft (n.d.).","bibtex":"@article{Intveen_Hohwiller, title={„Tolle lege! Aber was liest man eigentlich, wenn man englische Romane deutscher Schulbuchverlage liest?“}, journal={HeLix Dossiers zur romanischen Literaturwissenschaft}, publisher={Universitätsbibliothek Heidelberg}, author={Intveen, Julie and Hohwiller, Peter} }","mla":"Intveen, Julie, and Peter Hohwiller. “„Tolle lege! Aber was liest man eigentlich, wenn man englische Romane deutscher Schulbuchverlage liest?“.” <i>HeLix Dossiers zur romanischen Literaturwissenschaft</i>, Universitätsbibliothek Heidelberg.","ieee":"J. Intveen and P. Hohwiller, “„Tolle lege! Aber was liest man eigentlich, wenn man englische Romane deutscher Schulbuchverlage liest?“,” <i>HeLix Dossiers zur romanischen Literaturwissenschaft</i>.","chicago":"Intveen, Julie, and Peter Hohwiller. “„Tolle lege! Aber was liest man eigentlich, wenn man englische Romane deutscher Schulbuchverlage liest?“.” <i>HeLix Dossiers zur romanischen Literaturwissenschaft</i>, n.d.","ama":"Intveen J, Hohwiller P. „Tolle lege! Aber was liest man eigentlich, wenn man englische Romane deutscher Schulbuchverlage liest?“. <i>HeLix Dossiers zur romanischen Literaturwissenschaft</i>."},"year":"2024","publication_status":"accepted","quality_controlled":"1","language":[{"iso":"ger"}],"user_id":"56558","_id":"52338","status":"public","type":"journal_article","publication":"HeLix Dossiers zur romanischen Literaturwissenschaft"},{"title":"Leveraging Business Modeling Tools For Ecosystemic Business Model Design","volume":12,"author":[{"first_name":"Christian","full_name":"Vorbohle, Christian","id":"29951","last_name":"Vorbohle"},{"full_name":"Kundisch, Dennis","id":"21117","last_name":"Kundisch","first_name":"Dennis"}],"date_created":"2024-04-05T09:09:56Z","date_updated":"2024-04-05T09:10:01Z","intvolume":"        12","page":"100-112","citation":{"apa":"Vorbohle, C., &#38; Kundisch, D. (2024). Leveraging Business Modeling Tools For Ecosystemic Business Model Design. <i>Journal of Business Models</i>, <i>12</i>(1), 100–112.","bibtex":"@article{Vorbohle_Kundisch_2024, title={Leveraging Business Modeling Tools For Ecosystemic Business Model Design}, volume={12}, number={1}, journal={Journal of Business Models}, author={Vorbohle, Christian and Kundisch, Dennis}, year={2024}, pages={100–112} }","short":"C. Vorbohle, D. Kundisch, Journal of Business Models 12 (2024) 100–112.","mla":"Vorbohle, Christian, and Dennis Kundisch. “Leveraging Business Modeling Tools For Ecosystemic Business Model Design.” <i>Journal of Business Models</i>, vol. 12, no. 1, 2024, pp. 100–12.","ama":"Vorbohle C, Kundisch D. Leveraging Business Modeling Tools For Ecosystemic Business Model Design. <i>Journal of Business Models</i>. 2024;12(1):100-112.","ieee":"C. Vorbohle and D. Kundisch, “Leveraging Business Modeling Tools For Ecosystemic Business Model Design,” <i>Journal of Business Models</i>, vol. 12, no. 1, pp. 100–112, 2024.","chicago":"Vorbohle, Christian, and Dennis Kundisch. “Leveraging Business Modeling Tools For Ecosystemic Business Model Design.” <i>Journal of Business Models</i> 12, no. 1 (2024): 100–112."},"year":"2024","issue":"1","publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"276"}],"user_id":"16205","_id":"53277","status":"public","publication":"Journal of Business Models","type":"journal_article"},{"title":"Anwendung von System Dynamics zur Geschäftsmodellinnovation in einem B2B-Ökosystem","author":[{"full_name":"Ksouri-Gerwien, Christoph","last_name":"Ksouri-Gerwien","first_name":"Christoph"},{"first_name":"Christian","full_name":"Vorbohle, Christian","id":"29951","last_name":"Vorbohle"}],"date_created":"2023-01-20T10:57:37Z","publisher":"Springer Gabler","date_updated":"2024-04-05T09:31:10Z","citation":{"short":"C. Ksouri-Gerwien, C. Vorbohle, in: D.R.A. Schallmo, D. Kundisch, K. Lang (Eds.), Digitale Plattformen und Ökosysteme im B2B-Bereich, Springer Gabler, Wiesbaden, 2024.","bibtex":"@inbook{Ksouri-Gerwien_Vorbohle_2024, place={Wiesbaden}, title={Anwendung von System Dynamics zur Geschäftsmodellinnovation in einem B2B-Ökosystem}, booktitle={Digitale Plattformen und Ökosysteme im B2B-Bereich}, publisher={Springer Gabler}, author={Ksouri-Gerwien, Christoph and Vorbohle, Christian}, editor={Schallmo, D.R.A. and Kundisch, Dennis and Lang, K.}, year={2024} }","mla":"Ksouri-Gerwien, Christoph, and Christian Vorbohle. “Anwendung von System Dynamics zur Geschäftsmodellinnovation in einem B2B-Ökosystem.” <i>Digitale Plattformen und Ökosysteme im B2B-Bereich</i>, edited by D.R.A. Schallmo et al., Springer Gabler, 2024.","apa":"Ksouri-Gerwien, C., &#38; Vorbohle, C. (2024). Anwendung von System Dynamics zur Geschäftsmodellinnovation in einem B2B-Ökosystem. In D. R. A. Schallmo, D. Kundisch, &#38; K. Lang (Eds.), <i>Digitale Plattformen und Ökosysteme im B2B-Bereich</i>. Springer Gabler.","chicago":"Ksouri-Gerwien, Christoph, and Christian Vorbohle. “Anwendung von System Dynamics zur Geschäftsmodellinnovation in einem B2B-Ökosystem.” In <i>Digitale Plattformen und Ökosysteme im B2B-Bereich</i>, edited by D.R.A. Schallmo, Dennis Kundisch, and K. Lang. Wiesbaden: Springer Gabler, 2024.","ieee":"C. Ksouri-Gerwien and C. Vorbohle, “Anwendung von System Dynamics zur Geschäftsmodellinnovation in einem B2B-Ökosystem,” in <i>Digitale Plattformen und Ökosysteme im B2B-Bereich</i>, D. R. A. Schallmo, D. Kundisch, and K. Lang, Eds. Wiesbaden: Springer Gabler, 2024.","ama":"Ksouri-Gerwien C, Vorbohle C. Anwendung von System Dynamics zur Geschäftsmodellinnovation in einem B2B-Ökosystem. In: Schallmo DRA, Kundisch D, Lang K, eds. <i>Digitale Plattformen und Ökosysteme im B2B-Bereich</i>. Springer Gabler; 2024."},"place":"Wiesbaden","year":"2024","language":[{"iso":"ger"}],"department":[{"_id":"276"}],"user_id":"29951","_id":"37704","project":[{"_id":"1","name":"SFB 901: SFB 901","grant_number":"160364472"},{"_id":"4","name":"SFB 901 - C: SFB 901 - Project Area C"},{"_id":"17","name":"SFB 901 - C5: SFB 901 - Subproject C5"}],"status":"public","editor":[{"last_name":"Schallmo","full_name":"Schallmo, D.R.A.","first_name":"D.R.A."},{"first_name":"Dennis","full_name":"Kundisch, Dennis","last_name":"Kundisch"},{"full_name":"Lang, K.","last_name":"Lang","first_name":"K."}],"publication":"Digitale Plattformen und Ökosysteme im B2B-Bereich","type":"book_chapter"},{"language":[{"iso":"eng"}],"department":[{"_id":"263"}],"user_id":"67076","_id":"53282","external_id":{"arxiv":["2402.16434"]},"status":"public","abstract":[{"text":"Modern wireless communication systems are expected to provide improved\r\nlatency and reliability. To meet these expectations, a short packet length is\r\nneeded, which makes the first-order Shannon rate an inaccurate performance\r\nmetric for such communication systems. A more accurate approximation of the\r\nachievable rates of finite-block-length (FBL) coding regimes is known as the\r\nnormal approximation (NA). It is therefore of substantial interest to study the\r\noptimization of the FBL rate in multi-user multiple-input multiple-output\r\n(MIMO) systems, in which each user may transmit and/or receive multiple data\r\nstreams. Hence, we formulate a general optimization problem for improving the\r\nspectral and energy efficiency of multi-user MIMO-aided ultra-reliable\r\nlow-latency communication (URLLC) systems, which are assisted by reconfigurable\r\nintelligent surfaces (RISs). We show that a RIS is capable of substantially\r\nimproving the performance of multi-user MIMO-aided URLLC systems. Moreover, the\r\nbenefits of RIS increase as the packet length and/or the tolerable bit error\r\nrate are reduced. This reveals that RISs can be even more beneficial in URLLC\r\nsystems for improving the FBL rates than in conventional systems approaching\r\nShannon rates.","lang":"eng"}],"publication":"arXiv:2402.16434","type":"preprint","title":"Optimization of the Downlink Spectral- and Energy-Efficiency of  RIS-aided Multi-user URLLC MIMO Systems","author":[{"first_name":"Mohammad","last_name":"Soleymani","full_name":"Soleymani, Mohammad"},{"first_name":"Ignacio","full_name":"Santamaria, Ignacio","last_name":"Santamaria"},{"first_name":"Eduard","last_name":"Jorswieck","full_name":"Jorswieck, Eduard"},{"first_name":"Robert","last_name":"Schober","full_name":"Schober, Robert"},{"last_name":"Hanzo","full_name":"Hanzo, Lajos","first_name":"Lajos"}],"date_created":"2024-04-05T09:16:32Z","date_updated":"2024-04-05T13:18:19Z","citation":{"apa":"Soleymani, M., Santamaria, I., Jorswieck, E., Schober, R., &#38; Hanzo, L. (2024). Optimization of the Downlink Spectral- and Energy-Efficiency of  RIS-aided Multi-user URLLC MIMO Systems. In <i>arXiv:2402.16434</i>.","mla":"Soleymani, Mohammad, et al. “Optimization of the Downlink Spectral- and Energy-Efficiency of  RIS-Aided Multi-User URLLC MIMO Systems.” <i>ArXiv:2402.16434</i>, 2024.","bibtex":"@article{Soleymani_Santamaria_Jorswieck_Schober_Hanzo_2024, title={Optimization of the Downlink Spectral- and Energy-Efficiency of  RIS-aided Multi-user URLLC MIMO Systems}, journal={arXiv:2402.16434}, author={Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard and Schober, Robert and Hanzo, Lajos}, year={2024} }","short":"M. Soleymani, I. Santamaria, E. Jorswieck, R. Schober, L. Hanzo, ArXiv:2402.16434 (2024).","ama":"Soleymani M, Santamaria I, Jorswieck E, Schober R, Hanzo L. Optimization of the Downlink Spectral- and Energy-Efficiency of  RIS-aided Multi-user URLLC MIMO Systems. <i>arXiv:240216434</i>. Published online 2024.","ieee":"M. Soleymani, I. Santamaria, E. Jorswieck, R. Schober, and L. Hanzo, “Optimization of the Downlink Spectral- and Energy-Efficiency of  RIS-aided Multi-user URLLC MIMO Systems,” <i>arXiv:2402.16434</i>. 2024.","chicago":"Soleymani, Mohammad, Ignacio Santamaria, Eduard Jorswieck, Robert Schober, and Lajos Hanzo. “Optimization of the Downlink Spectral- and Energy-Efficiency of  RIS-Aided Multi-User URLLC MIMO Systems.” <i>ArXiv:2402.16434</i>, 2024."},"year":"2024"},{"_id":"53259","user_id":"67076","department":[{"_id":"263"}],"language":[{"iso":"eng"}],"type":"conference","publication":"2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","status":"public","publisher":"IEEE","date_updated":"2024-04-05T13:20:28Z","author":[{"first_name":"Mohammad","full_name":"Soleymani, Mohammad","last_name":"Soleymani"},{"last_name":"Santamaria","full_name":"Santamaria, Ignacio","first_name":"Ignacio"},{"first_name":"Aydin","full_name":"Sezgin, Aydin","last_name":"Sezgin"},{"first_name":"Eduard","last_name":"Jorswieck","full_name":"Jorswieck, Eduard"}],"date_created":"2024-04-05T09:00:06Z","title":"Maximization of Minimum Rate in MIMO OFDM RIS-Assisted Broadcast Channels","doi":"10.1109/camsap58249.2023.10403459","publication_status":"published","year":"2024","citation":{"ama":"Soleymani M, Santamaria I, Sezgin A, Jorswieck E. Maximization of Minimum Rate in MIMO OFDM RIS-Assisted Broadcast Channels. In: <i>2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)</i>. IEEE; 2024. doi:<a href=\"https://doi.org/10.1109/camsap58249.2023.10403459\">10.1109/camsap58249.2023.10403459</a>","ieee":"M. Soleymani, I. Santamaria, A. Sezgin, and E. Jorswieck, “Maximization of Minimum Rate in MIMO OFDM RIS-Assisted Broadcast Channels,” 2024, doi: <a href=\"https://doi.org/10.1109/camsap58249.2023.10403459\">10.1109/camsap58249.2023.10403459</a>.","chicago":"Soleymani, Mohammad, Ignacio Santamaria, Aydin Sezgin, and Eduard Jorswieck. “Maximization of Minimum Rate in MIMO OFDM RIS-Assisted Broadcast Channels.” In <i>2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)</i>. IEEE, 2024. <a href=\"https://doi.org/10.1109/camsap58249.2023.10403459\">https://doi.org/10.1109/camsap58249.2023.10403459</a>.","mla":"Soleymani, Mohammad, et al. “Maximization of Minimum Rate in MIMO OFDM RIS-Assisted Broadcast Channels.” <i>2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)</i>, IEEE, 2024, doi:<a href=\"https://doi.org/10.1109/camsap58249.2023.10403459\">10.1109/camsap58249.2023.10403459</a>.","short":"M. Soleymani, I. Santamaria, A. Sezgin, E. Jorswieck, in: 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), IEEE, 2024.","bibtex":"@inproceedings{Soleymani_Santamaria_Sezgin_Jorswieck_2024, title={Maximization of Minimum Rate in MIMO OFDM RIS-Assisted Broadcast Channels}, DOI={<a href=\"https://doi.org/10.1109/camsap58249.2023.10403459\">10.1109/camsap58249.2023.10403459</a>}, booktitle={2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)}, publisher={IEEE}, author={Soleymani, Mohammad and Santamaria, Ignacio and Sezgin, Aydin and Jorswieck, Eduard}, year={2024} }","apa":"Soleymani, M., Santamaria, I., Sezgin, A., &#38; Jorswieck, E. (2024). Maximization of Minimum Rate in MIMO OFDM RIS-Assisted Broadcast Channels. <i>2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)</i>. <a href=\"https://doi.org/10.1109/camsap58249.2023.10403459\">https://doi.org/10.1109/camsap58249.2023.10403459</a>"}},{"language":[{"iso":"eng"}],"user_id":"67076","department":[{"_id":"263"}],"_id":"53258","status":"public","type":"conference","publication":"GLOBECOM 2023 - 2023 IEEE Global Communications Conference","doi":"10.1109/globecom54140.2023.10437458","title":"NOMA-Based Improper Signaling for MIMO STAR-RIS-Assisted Broadcast Channels with Hardware Impairments","date_created":"2024-04-05T08:59:35Z","author":[{"first_name":"Mohammad","last_name":"Soleymani","full_name":"Soleymani, Mohammad"},{"first_name":"Ignacio","full_name":"Santamaria, Ignacio","last_name":"Santamaria"},{"first_name":"Eduard","full_name":"Jorswieck, Eduard","last_name":"Jorswieck"}],"date_updated":"2024-04-05T13:21:21Z","publisher":"IEEE","citation":{"ieee":"M. Soleymani, I. Santamaria, and E. Jorswieck, “NOMA-Based Improper Signaling for MIMO STAR-RIS-Assisted Broadcast Channels with Hardware Impairments,” 2024, doi: <a href=\"https://doi.org/10.1109/globecom54140.2023.10437458\">10.1109/globecom54140.2023.10437458</a>.","chicago":"Soleymani, Mohammad, Ignacio Santamaria, and Eduard Jorswieck. “NOMA-Based Improper Signaling for MIMO STAR-RIS-Assisted Broadcast Channels with Hardware Impairments.” In <i>GLOBECOM 2023 - 2023 IEEE Global Communications Conference</i>. IEEE, 2024. <a href=\"https://doi.org/10.1109/globecom54140.2023.10437458\">https://doi.org/10.1109/globecom54140.2023.10437458</a>.","ama":"Soleymani M, Santamaria I, Jorswieck E. NOMA-Based Improper Signaling for MIMO STAR-RIS-Assisted Broadcast Channels with Hardware Impairments. In: <i>GLOBECOM 2023 - 2023 IEEE Global Communications Conference</i>. IEEE; 2024. doi:<a href=\"https://doi.org/10.1109/globecom54140.2023.10437458\">10.1109/globecom54140.2023.10437458</a>","apa":"Soleymani, M., Santamaria, I., &#38; Jorswieck, E. (2024). NOMA-Based Improper Signaling for MIMO STAR-RIS-Assisted Broadcast Channels with Hardware Impairments. <i>GLOBECOM 2023 - 2023 IEEE Global Communications Conference</i>. <a href=\"https://doi.org/10.1109/globecom54140.2023.10437458\">https://doi.org/10.1109/globecom54140.2023.10437458</a>","mla":"Soleymani, Mohammad, et al. “NOMA-Based Improper Signaling for MIMO STAR-RIS-Assisted Broadcast Channels with Hardware Impairments.” <i>GLOBECOM 2023 - 2023 IEEE Global Communications Conference</i>, IEEE, 2024, doi:<a href=\"https://doi.org/10.1109/globecom54140.2023.10437458\">10.1109/globecom54140.2023.10437458</a>.","bibtex":"@inproceedings{Soleymani_Santamaria_Jorswieck_2024, title={NOMA-Based Improper Signaling for MIMO STAR-RIS-Assisted Broadcast Channels with Hardware Impairments}, DOI={<a href=\"https://doi.org/10.1109/globecom54140.2023.10437458\">10.1109/globecom54140.2023.10437458</a>}, booktitle={GLOBECOM 2023 - 2023 IEEE Global Communications Conference}, publisher={IEEE}, author={Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard}, year={2024} }","short":"M. Soleymani, I. Santamaria, E. Jorswieck, in: GLOBECOM 2023 - 2023 IEEE Global Communications Conference, IEEE, 2024."},"year":"2024","publication_status":"published"},{"user_id":"56070","department":[{"_id":"263"}],"_id":"53304","language":[{"iso":"eng"}],"type":"conference","publication":"ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","status":"public","date_created":"2024-04-05T14:40:34Z","author":[{"first_name":"Maurice","last_name":"Kuschel","full_name":"Kuschel, Maurice","id":"56070"},{"last_name":"Hasija","full_name":"Hasija, Tanuj","id":"43497","first_name":"Tanuj"},{"first_name":"Timothy","last_name":"Marrinan","full_name":"Marrinan, Timothy"}],"publisher":"IEEE","date_updated":"2024-04-05T14:50:14Z","doi":"10.1109/icassp48485.2024.10446173","title":"Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning","publication_status":"published","citation":{"chicago":"Kuschel, Maurice, Tanuj Hasija, and Timothy Marrinan. “Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning.” In <i>ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</i>. IEEE, 2024. <a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">https://doi.org/10.1109/icassp48485.2024.10446173</a>.","ieee":"M. Kuschel, T. Hasija, and T. Marrinan, “Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning,” 2024, doi: <a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">10.1109/icassp48485.2024.10446173</a>.","ama":"Kuschel M, Hasija T, Marrinan T. Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning. In: <i>ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</i>. IEEE; 2024. doi:<a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">10.1109/icassp48485.2024.10446173</a>","short":"M. Kuschel, T. Hasija, T. Marrinan, in: ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2024.","bibtex":"@inproceedings{Kuschel_Hasija_Marrinan_2024, title={Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning}, DOI={<a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">10.1109/icassp48485.2024.10446173</a>}, booktitle={ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, publisher={IEEE}, author={Kuschel, Maurice and Hasija, Tanuj and Marrinan, Timothy}, year={2024} }","mla":"Kuschel, Maurice, et al. “Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning.” <i>ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</i>, IEEE, 2024, doi:<a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">10.1109/icassp48485.2024.10446173</a>.","apa":"Kuschel, M., Hasija, T., &#38; Marrinan, T. (2024). Rademacher Complexity Regularization for Correlation-Based Multiview Representation Learning. <i>ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</i>. <a href=\"https://doi.org/10.1109/icassp48485.2024.10446173\">https://doi.org/10.1109/icassp48485.2024.10446173</a>"},"year":"2024"},{"publication_identifier":{"issn":["1424-3199","1424-3202"]},"publication_status":"published","issue":"2","year":"2024","intvolume":"        24","citation":{"ama":"Stinner C, Winkler M. A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. <i>Journal of Evolution Equations</i>. 2024;24(2). doi:<a href=\"https://doi.org/10.1007/s00028-024-00954-x\">10.1007/s00028-024-00954-x</a>","chicago":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” <i>Journal of Evolution Equations</i> 24, no. 2 (2024). <a href=\"https://doi.org/10.1007/s00028-024-00954-x\">https://doi.org/10.1007/s00028-024-00954-x</a>.","ieee":"C. Stinner and M. Winkler, “A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects,” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, Art. no. 26, 2024, doi: <a href=\"https://doi.org/10.1007/s00028-024-00954-x\">10.1007/s00028-024-00954-x</a>.","apa":"Stinner, C., &#38; Winkler, M. (2024). A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects. <i>Journal of Evolution Equations</i>, <i>24</i>(2), Article 26. <a href=\"https://doi.org/10.1007/s00028-024-00954-x\">https://doi.org/10.1007/s00028-024-00954-x</a>","bibtex":"@article{Stinner_Winkler_2024, title={A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects}, volume={24}, DOI={<a href=\"https://doi.org/10.1007/s00028-024-00954-x\">10.1007/s00028-024-00954-x</a>}, number={226}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Stinner, Christian and Winkler, Michael}, year={2024} }","mla":"Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for Volume-Filling Effects.” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, 26, Springer Science and Business Media LLC, 2024, doi:<a href=\"https://doi.org/10.1007/s00028-024-00954-x\">10.1007/s00028-024-00954-x</a>.","short":"C. Stinner, M. Winkler, Journal of Evolution Equations 24 (2024)."},"publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-07T12:36:21Z","volume":24,"author":[{"full_name":"Stinner, Christian","last_name":"Stinner","first_name":"Christian"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-04-07T12:29:25Z","title":"A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects","doi":"10.1007/s00028-024-00954-x","publication":"Journal of Evolution Equations","type":"journal_article","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>The quasilinear Keller–Segel system <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t=\\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (S(u)\\nabla v), \\\\ v_t=\\Delta v-v+u, \\end{array}\\right. \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mfenced>\r\n                            <mml:mrow>\r\n                              <mml:mtable>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:msub>\r\n                                        <mml:mi>u</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>=</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n                                        <mml:mi>D</mml:mi>\r\n                                        <mml:mrow>\r\n                                          <mml:mo>(</mml:mo>\r\n                                          <mml:mi>u</mml:mi>\r\n                                          <mml:mo>)</mml:mo>\r\n                                        </mml:mrow>\r\n                                        <mml:mi>∇</mml:mi>\r\n                                        <mml:mi>u</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mo>-</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n                                      <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n                                        <mml:mi>S</mml:mi>\r\n                                        <mml:mrow>\r\n                                          <mml:mo>(</mml:mo>\r\n                                          <mml:mi>u</mml:mi>\r\n                                          <mml:mo>)</mml:mo>\r\n                                        </mml:mrow>\r\n                                        <mml:mi>∇</mml:mi>\r\n                                        <mml:mi>v</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                                <mml:mtr>\r\n                                  <mml:mtd>\r\n                                    <mml:mrow>\r\n                                      <mml:mrow />\r\n                                      <mml:msub>\r\n                                        <mml:mi>v</mml:mi>\r\n                                        <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n                                      <mml:mo>=</mml:mo>\r\n                                      <mml:mi>Δ</mml:mi>\r\n                                      <mml:mi>v</mml:mi>\r\n                                      <mml:mo>-</mml:mo>\r\n                                      <mml:mi>v</mml:mi>\r\n                                      <mml:mo>+</mml:mo>\r\n                                      <mml:mi>u</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n                                  </mml:mtd>\r\n                                </mml:mtr>\r\n                              </mml:mtable>\r\n                            </mml:mrow>\r\n                          </mml:mfenced>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>endowed with homogeneous Neumann boundary conditions is considered in a bounded domain <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Omega \\subset {\\mathbb {R}}^n$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>Ω</mml:mi>\r\n                    <mml:mo>⊂</mml:mo>\r\n                    <mml:msup>\r\n                      <mml:mrow>\r\n                        <mml:mi>R</mml:mi>\r\n                      </mml:mrow>\r\n                      <mml:mi>n</mml:mi>\r\n                    </mml:msup>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \\ge 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, with smooth boundary for sufficiently regular functions <jats:italic>D</jats:italic> and <jats:italic>S</jats:italic> satisfying <jats:inline-formula><jats:alternatives><jats:tex-math>$$D&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>D</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> on <jats:inline-formula><jats:alternatives><jats:tex-math>$$[0,\\infty )$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>[</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>,</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$S&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> on <jats:inline-formula><jats:alternatives><jats:tex-math>$$(0,\\infty )$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>,</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$S(0)=0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                    <mml:mo>)</mml:mo>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. On the one hand, it is shown that if <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\frac{S}{D}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mfrac>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>D</mml:mi>\r\n                  </mml:mfrac>\r\n                </mml:math></jats:alternatives></jats:inline-formula> satisfies the subcritical growth condition <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\frac{S(s)}{D(s)} \\le C s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha &lt; \\frac{2}{n} \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mrow>\r\n                            <mml:mfrac>\r\n                              <mml:mrow>\r\n                                <mml:mi>S</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                              <mml:mrow>\r\n                                <mml:mi>D</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                            </mml:mfrac>\r\n                            <mml:mo>≤</mml:mo>\r\n                            <mml:mi>C</mml:mi>\r\n                            <mml:msup>\r\n                              <mml:mi>s</mml:mi>\r\n                              <mml:mi>α</mml:mi>\r\n                            </mml:msup>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>for</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>all</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mi>s</mml:mi>\r\n                            <mml:mo>≥</mml:mo>\r\n                            <mml:mn>1</mml:mn>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>with</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>some</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mi>α</mml:mi>\r\n                            <mml:mo>&lt;</mml:mo>\r\n                            <mml:mfrac>\r\n                              <mml:mn>2</mml:mn>\r\n                              <mml:mi>n</mml:mi>\r\n                            </mml:mfrac>\r\n                          </mml:mrow>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>and <jats:inline-formula><jats:alternatives><jats:tex-math>$$C&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>C</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, then for any sufficiently regular initial data there exists a global weak energy solution such that <jats:inline-formula><jats:alternatives><jats:tex-math>$${ \\mathrm{{ess}}} \\sup _{t&gt;0} \\Vert u(t) \\Vert _{L^p(\\Omega )}&lt;\\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>ess</mml:mi>\r\n                    <mml:msub>\r\n                      <mml:mo>sup</mml:mo>\r\n                      <mml:mrow>\r\n                        <mml:mi>t</mml:mi>\r\n                        <mml:mo>&gt;</mml:mo>\r\n                        <mml:mn>0</mml:mn>\r\n                      </mml:mrow>\r\n                    </mml:msub>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mo>‖</mml:mo>\r\n                        <mml:mi>u</mml:mi>\r\n                        <mml:mrow>\r\n                          <mml:mo>(</mml:mo>\r\n                          <mml:mi>t</mml:mi>\r\n                          <mml:mo>)</mml:mo>\r\n                        </mml:mrow>\r\n                        <mml:mo>‖</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mrow>\r\n                        <mml:msup>\r\n                          <mml:mi>L</mml:mi>\r\n                          <mml:mi>p</mml:mi>\r\n                        </mml:msup>\r\n                        <mml:mrow>\r\n                          <mml:mo>(</mml:mo>\r\n                          <mml:mi>Ω</mml:mi>\r\n                          <mml:mo>)</mml:mo>\r\n                        </mml:mrow>\r\n                      </mml:mrow>\r\n                    </mml:msub>\r\n                    <mml:mo>&lt;</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> for some <jats:inline-formula><jats:alternatives><jats:tex-math>$$p &gt; \\frac{2n}{n+2}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>p</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mfrac>\r\n                      <mml:mrow>\r\n                        <mml:mn>2</mml:mn>\r\n                        <mml:mi>n</mml:mi>\r\n                      </mml:mrow>\r\n                      <mml:mrow>\r\n                        <mml:mi>n</mml:mi>\r\n                        <mml:mo>+</mml:mo>\r\n                        <mml:mn>2</mml:mn>\r\n                      </mml:mrow>\r\n                    </mml:mfrac>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. On the other hand, if <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\frac{S}{D}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mfrac>\r\n                    <mml:mi>S</mml:mi>\r\n                    <mml:mi>D</mml:mi>\r\n                  </mml:mfrac>\r\n                </mml:math></jats:alternatives></jats:inline-formula> satisfies the supercritical growth condition <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\frac{S(s)}{D(s)} \\ge c s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge 1 \\qquad \\text{ with } \\text{ some } \\alpha &gt; \\frac{2}{n} \\end{aligned}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mrow>\r\n                            <mml:mfrac>\r\n                              <mml:mrow>\r\n                                <mml:mi>S</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                              <mml:mrow>\r\n                                <mml:mi>D</mml:mi>\r\n                                <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n                                <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n                            </mml:mfrac>\r\n                            <mml:mo>≥</mml:mo>\r\n                            <mml:mi>c</mml:mi>\r\n                            <mml:msup>\r\n                              <mml:mi>s</mml:mi>\r\n                              <mml:mi>α</mml:mi>\r\n                            </mml:msup>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>for</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>all</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mi>s</mml:mi>\r\n                            <mml:mo>≥</mml:mo>\r\n                            <mml:mn>1</mml:mn>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>with</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mspace />\r\n                            <mml:mtext>some</mml:mtext>\r\n                            <mml:mspace />\r\n                            <mml:mi>α</mml:mi>\r\n                            <mml:mo>&gt;</mml:mo>\r\n                            <mml:mfrac>\r\n                              <mml:mn>2</mml:mn>\r\n                              <mml:mi>n</mml:mi>\r\n                            </mml:mfrac>\r\n                          </mml:mrow>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>and <jats:inline-formula><jats:alternatives><jats:tex-math>$$c&gt;0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>c</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha = \\frac{2}{n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>α</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mfrac>\r\n                      <mml:mn>2</mml:mn>\r\n                      <mml:mi>n</mml:mi>\r\n                    </mml:mfrac>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> for <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \\ge 3$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n                    <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, without any additional assumption on the behavior of <jats:italic>D</jats:italic>(<jats:italic>s</jats:italic>) as <jats:inline-formula><jats:alternatives><jats:tex-math>$$s \\rightarrow \\infty $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>s</mml:mi>\r\n                    <mml:mo>→</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, in particular without requiring any algebraic lower bound for <jats:italic>D</jats:italic>. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type <jats:inline-formula><jats:alternatives><jats:tex-math>$$Q(s) = \\exp (-s^\\beta )$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>Q</mml:mi>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mi>s</mml:mi>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mo>exp</mml:mo>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mo>-</mml:mo>\r\n                      <mml:msup>\r\n                        <mml:mi>s</mml:mi>\r\n                        <mml:mi>β</mml:mi>\r\n                      </mml:msup>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$s \\ge 0$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>s</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, for global solvability the exponent <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta = \\frac{n-2}{n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mi>β</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n                    <mml:mfrac>\r\n                      <mml:mrow>\r\n                        <mml:mi>n</mml:mi>\r\n                        <mml:mo>-</mml:mo>\r\n                        <mml:mn>2</mml:mn>\r\n                      </mml:mrow>\r\n                      <mml:mi>n</mml:mi>\r\n                    </mml:mfrac>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula> is seen to be critical.\r\n</jats:p>","lang":"eng"}],"status":"public","_id":"53316","user_id":"31496","keyword":["Mathematics (miscellaneous)"],"article_number":"26","language":[{"iso":"eng"}]},{"type":"journal_article","publication":"Journal of the London Mathematical Society","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional domain  and for a given nondecreasing positive unbounded , for each  and  the inequality\r\n<jats:disp-formula />is shown to hold for any positive  fulfilling\r\n<jats:disp-formula />This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over  near its explosion time.</jats:p>"}],"user_id":"31496","_id":"53315","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"issue":"3","publication_status":"published","publication_identifier":{"issn":["0024-6107","1469-7750"]},"citation":{"chicago":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i> 109, no. 3 (2024). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>.","ieee":"Y. Wang and M. Winkler, “An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, 2024, doi: <a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","ama":"Wang Y, Winkler M. An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>. 2024;109(3). doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>","apa":"Wang, Y., &#38; Winkler, M. (2024). An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>, <i>109</i>(3). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>","bibtex":"@article{Wang_Winkler_2024, title={An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>}, number={3}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }","mla":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, Wiley, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024)."},"intvolume":"       109","year":"2024","date_created":"2024-04-07T12:27:28Z","author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"volume":109,"date_updated":"2024-04-07T12:36:25Z","publisher":"Wiley","doi":"10.1112/jlms.12885","title":"An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system"},{"publication":"Mitteilungen des Instituts für Europäische Kulturgeschichte","type":"journal_article","status":"public","_id":"53375","user_id":"42693","language":[{"iso":"eng"}],"year":"2024","citation":{"short":"F. Voß, Mitteilungen Des Instituts Für Europäische Kulturgeschichte (2024).","bibtex":"@article{Voß_2024, title={Rezension zu Anna-Victoria Bognár: Der Architekt in der Frühen Neuzeit. 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Eine qualitative Studie im Kontext von Sachunterrichtsdidaktik.” <i>Jahrbuch für Tod und Gesellschaft</i>, edited by Thorsten Benkel and Matthias Meitzler, vol. 3, Beltz Juventa, 2024, pp. 147–49."},"_id":"53397","user_id":"47572","series_title":"Jahrbuch für Tod und Gesellschaft","language":[{"iso":"ger"}],"publication":"Jahrbuch für Tod und Gesellschaft","type":"book_chapter","editor":[{"last_name":"Benkel","full_name":"Benkel, Thorsten","first_name":"Thorsten"},{"last_name":"Meitzler","full_name":"Meitzler, Matthias","first_name":"Matthias"}],"status":"public"},{"publication":"Zeitschrift des Aachener Geschichtsvereins ","type":"journal_article","status":"public","department":[{"_id":"512"}],"user_id":"54666","_id":"52096","language":[{"iso":"ger"}],"publication_identifier":{"unknown":["978-3-87707-300-1"]},"publication_status":"published","page":"137-167","citation":{"mla":"Kamp, Hermann. “Zwischen Beutesuche und politischen Ambitionen. Die Normannen an Rhein und Maas zwischen 880 und 892.” <i>Zeitschrift des Aachener Geschichtsvereins </i>, vol. 123/124, 2021–2022, VERLAGSDRUCKEREI SCHMIDT GMBH, 2024, pp. 137–67.","bibtex":"@article{Kamp_2024, title={Zwischen Beutesuche und politischen Ambitionen. Die Normannen an Rhein und Maas zwischen 880 und 892}, volume={123/124, 2021–2022}, journal={Zeitschrift des Aachener Geschichtsvereins }, publisher={VERLAGSDRUCKEREI SCHMIDT GMBH}, author={Kamp, Hermann}, year={2024}, pages={137–167} }","short":"H. Kamp, Zeitschrift des Aachener Geschichtsvereins  123/124, 2021–2022 (2024) 137–167.","apa":"Kamp, H. (2024). Zwischen Beutesuche und politischen Ambitionen. Die Normannen an Rhein und Maas zwischen 880 und 892. <i>Zeitschrift des Aachener Geschichtsvereins </i>, <i>123/124, 2021–2022</i>, 137–167.","ieee":"H. Kamp, “Zwischen Beutesuche und politischen Ambitionen. 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Zeitschrift für Geschlecht, Kultur und Gesellschaft }, title={Reproduktionspolitiken und Selbstbestimmung}, volume={16}, year={2024}, collection={GENDER. Zeitschrift für Geschlecht, Kultur und Gesellschaft } }","short":"O. Eremin, A. Langer, A. Mattei, C. Mahs, eds., Reproduktionspolitiken Und Selbstbestimmung, 2024.","ama":"Eremin O, Langer A, Mattei A, Mahs C, eds. <i>Reproduktionspolitiken Und Selbstbestimmung</i>. Vol 16.; 2024.","chicago":"Eremin, Oxana, Antje Langer, Annalisa Mattei, and Claudia Mahs, eds. <i>Reproduktionspolitiken Und Selbstbestimmung</i>. Vol. 16. GENDER. Zeitschrift Für Geschlecht, Kultur Und Gesellschaft , 2024.","ieee":"O. Eremin, A. Langer, A. Mattei, and C. Mahs, Eds., <i>Reproduktionspolitiken und Selbstbestimmung</i>, vol. 16. 2024."},"intvolume":"        16","year":"2024","title":"Reproduktionspolitiken und Selbstbestimmung","date_created":"2024-03-27T10:28:27Z","volume":16,"date_updated":"2024-04-11T08:32:17Z"},{"citation":{"chicago":"Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and Feliks Nüske. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>Applied and Computational Harmonic Analysis </i> 71 (2024). <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">https://doi.org/10.1016/j.acha.2024.101657</a>.","ieee":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error bounds for kernel-based approximations of the Koopman operator,” <i>Applied and Computational Harmonic Analysis </i>, vol. 71, Art. no. 101657, 2024, doi: <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>.","ama":"Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error bounds for kernel-based approximations of the Koopman operator. <i>Applied and Computational Harmonic Analysis </i>. 2024;71. doi:<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>","mla":"Philipp, Friedrich, et al. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.” <i>Applied and Computational Harmonic Analysis </i>, vol. 71, 101657, Springer , 2024, doi:<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>.","bibtex":"@article{Philipp_Schaller_Worthmann_Peitz_Nüske_2024, title={Error bounds for kernel-based approximations of the Koopman operator}, volume={71}, DOI={<a href=\"https://doi.org/10.1016/j.acha.2024.101657\">10.1016/j.acha.2024.101657</a>}, number={101657}, journal={Applied and Computational Harmonic Analysis }, publisher={Springer }, author={Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl and Peitz, Sebastian and Nüske, Feliks}, year={2024} }","short":"F. Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, Applied and Computational Harmonic Analysis  71 (2024).","apa":"Philipp, F., Schaller, M., Worthmann, K., Peitz, S., &#38; Nüske, F. (2024). Error bounds for kernel-based approximations of the Koopman operator. <i>Applied and Computational Harmonic Analysis </i>, <i>71</i>, Article 101657. <a href=\"https://doi.org/10.1016/j.acha.2024.101657\">https://doi.org/10.1016/j.acha.2024.101657</a>"},"intvolume":"        71","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2301.08637"}],"doi":"10.1016/j.acha.2024.101657","date_updated":"2024-04-11T12:41:13Z","oa":"1","author":[{"first_name":"Friedrich","last_name":"Philipp","full_name":"Philipp, Friedrich"},{"last_name":"Schaller","full_name":"Schaller, Manuel","first_name":"Manuel"},{"first_name":"Karl","full_name":"Worthmann, Karl","last_name":"Worthmann"},{"orcid":"0000-0002-3389-793X","last_name":"Peitz","id":"47427","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"first_name":"Feliks","last_name":"Nüske","full_name":"Nüske, Feliks"}],"volume":71,"status":"public","type":"journal_article","article_number":"101657","_id":"38031","user_id":"47427","department":[{"_id":"655"}],"year":"2024","title":"Error bounds for kernel-based approximations of the Koopman operator","publisher":"Springer ","date_created":"2023-01-23T07:03:39Z","abstract":[{"text":"We consider the data-driven approximation of the Koopman operator for\r\nstochastic differential equations on reproducing kernel Hilbert spaces (RKHS).\r\nOur focus is on the estimation error if the data are collected from long-term\r\nergodic simulations. We derive both an exact expression for the variance of the\r\nkernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and\r\nprobabilistic bounds for the finite-data estimation error. Moreover, we derive\r\na bound on the prediction error of observables in the RKHS using a finite\r\nMercer series expansion. Further, assuming Koopman-invariance of the RKHS, we\r\nprovide bounds on the full approximation error. Numerical experiments using the\r\nOrnstein-Uhlenbeck process illustrate our results.","lang":"eng"}],"publication":"Applied and Computational Harmonic Analysis ","language":[{"iso":"eng"}],"external_id":{"arxiv":["2301.08637"]}},{"issue":"2","intvolume":"        39","page":"167–184","citation":{"chicago":"Sharma ,  Umesh ,  Tim  Loreman ,  Fiona  May ,  Alessandra  Romano , Caroline Sahli Lozano ,  Elias  Avramidis ,  Stuart  Woodcock ,  Pearl  Subban , and Harry Kullmann. “Measuring Collective Efficacy for Inclusion in a Global Context.” <i>European Journal of Special Needs Education</i> 39, no. 2 (2024): 167–184. <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">https://doi.org/10.1080/08856257.2023.2195075</a>.","ieee":"Umesh  Sharma  <i>et al.</i>, “Measuring collective efficacy for inclusion in a global context,” <i>European Journal of Special Needs Education</i>, vol. 39, no. 2, pp. 167–184, 2024, doi: <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>.","ama":"Sharma   Umesh , Loreman   Tim , May   Fiona , et al. Measuring collective efficacy for inclusion in a global context. <i>European Journal of Special Needs Education</i>. 2024;39(2):167–184. doi:<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>","apa":"Sharma ,  Umesh , Loreman ,  Tim , May ,  Fiona , Romano ,  Alessandra , Lozano , C. S., Avramidis ,  Elias , Woodcock ,  Stuart , Subban ,  Pearl , &#38; Kullmann, H. (2024). Measuring collective efficacy for inclusion in a global context. <i>European Journal of Special Needs Education</i>, <i>39</i>(2), 167–184. <a href=\"https://doi.org/10.1080/08856257.2023.2195075\">https://doi.org/10.1080/08856257.2023.2195075</a>","short":"Umesh  Sharma ,  Tim  Loreman ,  Fiona  May ,  Alessandra  Romano , C.S. Lozano ,  Elias  Avramidis ,  Stuart  Woodcock ,  Pearl  Subban , H. Kullmann, European Journal of Special Needs Education 39 (2024) 167–184.","mla":"Sharma ,  Umesh , et al. “Measuring Collective Efficacy for Inclusion in a Global Context.” <i>European Journal of Special Needs Education</i>, vol. 39, no. 2, 2024, pp. 167–184, doi:<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>.","bibtex":"@article{Sharma _Loreman _May _Romano _Lozano _Avramidis _Woodcock _Subban _Kullmann_2024, title={Measuring collective efficacy for inclusion in a global context}, volume={39}, DOI={<a href=\"https://doi.org/10.1080/08856257.2023.2195075\">10.1080/08856257.2023.2195075</a>}, number={2}, journal={European Journal of Special Needs Education}, author={Sharma ,  Umesh  and Loreman ,  Tim  and May ,  Fiona  and Romano ,  Alessandra  and Lozano , Caroline Sahli and Avramidis ,  Elias  and Woodcock ,  Stuart  and Subban ,  Pearl  and Kullmann, Harry}, year={2024}, pages={167–184} }"},"year":"2024","volume":39,"date_created":"2023-03-28T13:01:09Z","author":[{"full_name":"Sharma ,  Umesh ","last_name":"Sharma ","first_name":" Umesh "},{"last_name":"Loreman ","full_name":"Loreman ,  Tim ","first_name":" Tim "},{"last_name":"May ","full_name":"May ,  Fiona ","first_name":" Fiona "},{"last_name":"Romano ","full_name":"Romano ,  Alessandra ","first_name":" Alessandra "},{"last_name":"Lozano ","full_name":"Lozano , Caroline Sahli","first_name":"Caroline Sahli"},{"last_name":"Avramidis ","full_name":"Avramidis ,  Elias ","first_name":" Elias "},{"last_name":"Woodcock ","full_name":"Woodcock ,  Stuart ","first_name":" Stuart "},{"first_name":" Pearl ","last_name":"Subban ","full_name":"Subban ,  Pearl "},{"first_name":"Harry","full_name":"Kullmann, Harry","id":"77972","last_name":"Kullmann"}],"date_updated":"2024-04-11T13:17:29Z","doi":"10.1080/08856257.2023.2195075","title":"Measuring collective efficacy for inclusion in a global context","publication":"European Journal of Special Needs Education","type":"journal_article","status":"public","department":[{"_id":"556"}],"user_id":"65969","_id":"43135","language":[{"iso":"eng"}]},{"citation":{"ama":"Pritom TH, Welzel S, Klingler F. Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks. In: <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>. ; 2024.","ieee":"T. H. Pritom, S. Welzel, and F. Klingler, “Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks,” 2024.","chicago":"Pritom, Touhid Hossain, Simon Welzel, and Florian Klingler. “Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks.” In <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>. Big Island, HI, 2024.","short":"T.H. Pritom, S. Welzel, F. Klingler, in: 11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024), Big Island, HI, 2024.","mla":"Pritom, Touhid Hossain, et al. “Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks.” <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>, 2024.","bibtex":"@inproceedings{Pritom_Welzel_Klingler_2024, place={Big Island, HI}, title={Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks}, booktitle={11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)}, author={Pritom, Touhid Hossain and Welzel, Simon and Klingler, Florian}, year={2024} }","apa":"Pritom, T. H., Welzel, S., &#38; Klingler, F. (2024). Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks. <i>11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)</i>."},"place":"Big Island, HI","year":"2024","author":[{"first_name":"Touhid Hossain","full_name":"Pritom, Touhid Hossain","last_name":"Pritom"},{"full_name":"Welzel, Simon","last_name":"Welzel","first_name":"Simon"},{"last_name":"Klingler","full_name":"Klingler, Florian","first_name":"Florian"}],"date_created":"2024-04-11T18:26:09Z","date_updated":"2024-04-11T18:29:47Z","title":"Cuckoos United: Extending Cuckoo Filters for Message Dissemination in Vehicular Networks","publication":"11th IEEE International Conference on Computing, Networking and Communications (ICNC 2024)","type":"conference","status":"public","user_id":"49153","_id":"53437","language":[{"iso":"eng"}]}]