[{"publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","year":"2022","citation":{"ama":"Kovács B, Li B. Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. IMA Journal of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac033","ieee":"B. Kovács and B. Li, “Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems,” IMA Journal of Numerical Analysis, 2022, doi: 10.1093/imanum/drac033.","chicago":"Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac033.","apa":"Kovács, B., & Li, B. (2022). Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac033","mla":"Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.” IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac033.","short":"B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).","bibtex":"@article{Kovács_Li_2022, title={Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems}, DOI={10.1093/imanum/drac033}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }"},"date_updated":"2024-04-03T09:17:59Z","publisher":"Oxford University Press (OUP)","date_created":"2023-07-10T11:45:14Z","author":[{"id":"100441","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs"},{"first_name":"Buyang","full_name":"Li, Buyang","last_name":"Li"}],"title":"Maximal regularity of backward difference time discretization for evolving surface PDEs and its application to nonlinear problems","doi":"10.1093/imanum/drac033","publication":"IMA Journal of Numerical Analysis","type":"journal_article","abstract":[{"lang":"eng","text":"Abstract\r\n Maximal parabolic $L^p$-regularity of linear parabolic equations on an evolving surface is shown by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity on a fixed surface. By freezing the coefficients in the parabolic equations at a fixed time and utilizing a perturbation argument around the freezed time, it is shown that backward difference time discretizations of linear parabolic equations on an evolving surface along characteristic trajectories can preserve maximal $L^p$-regularity in the discrete setting. The result is applied to prove the stability and convergence of time discretizations of nonlinear parabolic equations on an evolving surface, with linearly implicit backward differentiation formulae characteristic trajectories of the surface, for general locally Lipschitz nonlinearities. The discrete maximal $L^p$-regularity is used to prove the boundedness and stability of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is used to bound the nonlinear terms in the stability analysis. Optimal-order error estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm is obtained by combining the stability analysis with the consistency estimates."}],"status":"public","_id":"45964","department":[{"_id":"841"}],"user_id":"100441","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}]},{"title":"Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions","doi":"10.1093/imanum/drac002","date_updated":"2024-04-03T09:16:47Z","publisher":"Oxford University Press (OUP)","date_created":"2023-07-10T11:45:49Z","author":[{"first_name":"Robert","full_name":"Altmann, Robert","last_name":"Altmann"},{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","last_name":"Kovács","orcid":"0000-0001-9872-3474"},{"last_name":"Zimmer","full_name":"Zimmer, Christoph","first_name":"Christoph"}],"volume":43,"year":"2022","citation":{"ama":"Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical Analysis. 2022;43(2):950-975. doi:10.1093/imanum/drac002","chicago":"Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis 43, no. 2 (2022): 950–75. https://doi.org/10.1093/imanum/drac002.","ieee":"R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions,” IMA Journal of Numerical Analysis, vol. 43, no. 2, pp. 950–975, 2022, doi: 10.1093/imanum/drac002.","mla":"Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol. 43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:10.1093/imanum/drac002.","short":"R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022) 950–975.","bibtex":"@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={10.1093/imanum/drac002}, number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022}, pages={950–975} }","apa":"Altmann, R., Kovács, B., & Zimmer, C. (2022). Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical Analysis, 43(2), 950–975. https://doi.org/10.1093/imanum/drac002"},"intvolume":" 43","page":"950-975","publication_status":"published","publication_identifier":{"issn":["0272-4979","1464-3642"]},"issue":"2","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"_id":"45966","user_id":"100441","department":[{"_id":"841"}],"abstract":[{"text":"Abstract\r\n This paper studies bulk–surface splitting methods of first order for (semilinear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a coupled partial differential–algebraic equation system, i.e., the boundary conditions are considered as a second dynamic equation that is coupled to the bulk problem. The splitting approach is combined with bulk–surface finite elements and an implicit Euler discretization of the two subsystems. We prove first-order convergence of the resulting fully discrete scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c h$ for some constant $c&gt;0$. The convergence is also illustrated numerically using dynamic boundary conditions of Allen–Cahn type.","lang":"eng"}],"status":"public","type":"journal_article","publication":"IMA Journal of Numerical Analysis"},{"publication":"IMA Journal of Numerical Analysis","type":"journal_article","status":"public","abstract":[{"text":"Abstract\r\n We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.","lang":"eng"}],"department":[{"_id":"841"}],"user_id":"100441","_id":"45968","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"publication_status":"published","citation":{"ieee":"P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator for abstract semilinear boundary coupled systems,” IMA Journal of Numerical Analysis, 2022, doi: 10.1093/imanum/drac079.","chicago":"Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac079.","ama":"Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac079","mla":"Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac079.","bibtex":"@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting integrator for abstract semilinear boundary coupled systems}, DOI={10.1093/imanum/drac079}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022} }","short":"P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).","apa":"Csomós, P., Farkas, B., & Kovács, B. (2022). Error estimates for a splitting integrator for abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac079"},"year":"2022","date_created":"2023-07-10T11:46:54Z","author":[{"last_name":"Csomós","full_name":"Csomós, Petra","first_name":"Petra"},{"first_name":"Bálint","full_name":"Farkas, Bálint","last_name":"Farkas"},{"first_name":"Balázs","full_name":"Kovács, Balázs","id":"100441","orcid":"0000-0001-9872-3474","last_name":"Kovács"}],"publisher":"Oxford University Press (OUP)","date_updated":"2024-04-03T09:15:52Z","doi":"10.1093/imanum/drac079","title":"Error estimates for a splitting integrator for abstract semilinear boundary coupled systems"},{"intvolume":" 151","page":"1-48","citation":{"ieee":"C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces,” Numerische Mathematik, vol. 151, no. 1, pp. 1–48, 2022, doi: 10.1007/s00211-022-01280-5.","chicago":"Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische Mathematik 151, no. 1 (2022): 1–48. https://doi.org/10.1007/s00211-022-01280-5.","ama":"Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces. Numerische Mathematik. 2022;151(1):1-48. doi:10.1007/s00211-022-01280-5","apa":"Beschle, C. A., & Kovács, B. (2022). Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces. Numerische Mathematik, 151(1), 1–48. https://doi.org/10.1007/s00211-022-01280-5","short":"C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.","mla":"Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische Mathematik, vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:10.1007/s00211-022-01280-5.","bibtex":"@article{Beschle_Kovács_2022, title={Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={10.1007/s00211-022-01280-5}, number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48} }"},"year":"2022","issue":"1","publication_identifier":{"issn":["0029-599X","0945-3245"]},"publication_status":"published","doi":"10.1007/s00211-022-01280-5","title":"Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces","volume":151,"author":[{"first_name":"Cedric Aaron","last_name":"Beschle","full_name":"Beschle, Cedric Aaron"},{"id":"100441","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","first_name":"Balázs"}],"date_created":"2023-07-10T11:43:44Z","date_updated":"2024-04-03T09:19:34Z","publisher":"Springer Science and Business Media LLC","status":"public","abstract":[{"text":"AbstractIn this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.","lang":"eng"}],"publication":"Numerische Mathematik","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics"],"department":[{"_id":"841"}],"user_id":"100441","_id":"45958"},{"publication_status":"published","publication_identifier":{"issn":["1609-4840","1609-9389"]},"citation":{"chicago":"Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.” Computational Methods in Applied Mathematics 23, no. 1 (2022): 19–48. https://doi.org/10.1515/cmam-2022-0145.","ieee":"J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation,” Computational Methods in Applied Mathematics, vol. 23, no. 1, pp. 19–48, 2022, doi: 10.1515/cmam-2022-0145.","ama":"Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational Methods in Applied Mathematics. 2022;23(1):19-48. doi:10.1515/cmam-2022-0145","apa":"Bohn, J., Feischl, M., & Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational Methods in Applied Mathematics, 23(1), 19–48. https://doi.org/10.1515/cmam-2022-0145","short":"J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics 23 (2022) 19–48.","bibtex":"@article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation}, volume={23}, DOI={10.1515/cmam-2022-0145}, number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs}, year={2022}, pages={19–48} }","mla":"Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.” Computational Methods in Applied Mathematics, vol. 23, no. 1, Walter de Gruyter GmbH, 2022, pp. 19–48, doi:10.1515/cmam-2022-0145."},"intvolume":" 23","page":"19-48","author":[{"last_name":"Bohn","full_name":"Bohn, Jan","first_name":"Jan"},{"last_name":"Feischl","full_name":"Feischl, Michael","first_name":"Michael"},{"first_name":"Balázs","id":"100441","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács"}],"volume":23,"date_updated":"2024-04-03T09:20:30Z","doi":"10.1515/cmam-2022-0145","type":"journal_article","status":"public","user_id":"100441","department":[{"_id":"841"}],"_id":"45956","issue":"1","year":"2022","date_created":"2023-07-10T11:43:13Z","publisher":"Walter de Gruyter GmbH","title":"FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation","publication":"Computational Methods in Applied Mathematics","abstract":[{"lang":"eng","text":"Abstract\r\n The full Maxwell equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials.\r\nWe propose a weak formulation of the coupled system based on the boundary integral formulation of the exterior Maxwell equations.\r\nWe show existence and partial uniqueness of a weak solution and propose a new numerical algorithm based on finite elements and boundary elements as spatial discretization with backward Euler and convolution quadrature for the time domain.\r\nThis is the first numerical algorithm which is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and full Maxwell’s equations without any simplifications like quasi-static approximations (e.g. eddy current model) and without restrictions on the shape of the domain (e.g. convexity).\r\nWe show well-posedness and convergence of the numerical algorithm under minimal assumptions on the regularity of the solution.\r\nThis is particularly important as there are few regularity results available and one generally expects the solution to be non-smooth.\r\nNumerical experiments illustrate and expand on the theoretical results."}],"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Numerical Analysis"]},{"user_id":"105654","author":[{"id":"105654","full_name":"Krause, Ina","orcid":"0000-0003-0170-7713","last_name":"Krause","first_name":"Ina"}],"date_created":"2024-04-03T11:27:03Z","_id":"53174","date_updated":"2024-04-03T11:27:18Z","language":[{"iso":"eng"}],"title":"Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie","publication":"ZBW-Beiheft: Betriebliche Berufsbildungsforschung","type":"book_chapter","status":"public","citation":{"mla":"Krause, Ina. “Distanzarbeit Als Impulsgeber Beruflicher Weiterbildung. Zur Bedeutung von Neuen Schlüsselkompetenzen Und Weiterbildung Im Strukturwandels von Büroarbeitswelten in Und Nach Der Corona-Pandemie.” ZBW-Beiheft: Betriebliche Berufsbildungsforschung, edited by Lutz Bellmann et al., 2022.","short":"I. Krause, in: L. Bellmann, H. Ertl, C. Gerhards, P. Sloane (Eds.), ZBW-Beiheft: Betriebliche Berufsbildungsforschung, 2022.","bibtex":"@inbook{Krause_2022, title={Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie}, booktitle={ZBW-Beiheft: Betriebliche Berufsbildungsforschung}, author={Krause, Ina}, editor={Bellmann, Lutz and Ertl, Hubert and Gerhards, Christian and Sloane, Peter}, year={2022} }","apa":"Krause, I. (2022). Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie. In L. Bellmann, H. Ertl, C. Gerhards, & P. Sloane (Eds.), ZBW-Beiheft: Betriebliche Berufsbildungsforschung.","ieee":"I. Krause, “Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie,” in ZBW-Beiheft: Betriebliche Berufsbildungsforschung, L. Bellmann, H. Ertl, C. Gerhards, and P. Sloane, Eds. 2022.","chicago":"Krause, Ina. “Distanzarbeit Als Impulsgeber Beruflicher Weiterbildung. Zur Bedeutung von Neuen Schlüsselkompetenzen Und Weiterbildung Im Strukturwandels von Büroarbeitswelten in Und Nach Der Corona-Pandemie.” In ZBW-Beiheft: Betriebliche Berufsbildungsforschung, edited by Lutz Bellmann, Hubert Ertl, Christian Gerhards, and Peter Sloane, 2022.","ama":"Krause I. Distanzarbeit als Impulsgeber beruflicher Weiterbildung. Zur Bedeutung von neuen Schlüsselkompetenzen und Weiterbildung im Strukturwandels von Büroarbeitswelten in und nach der Corona-Pandemie. In: Bellmann L, Ertl H, Gerhards C, Sloane P, eds. ZBW-Beiheft: Betriebliche Berufsbildungsforschung. ; 2022."},"editor":[{"first_name":"Lutz ","last_name":"Bellmann","full_name":"Bellmann, Lutz "},{"first_name":"Hubert","full_name":"Ertl, Hubert","last_name":"Ertl"},{"last_name":"Gerhards","full_name":"Gerhards, Christian","first_name":"Christian"},{"first_name":"Peter","last_name":"Sloane","full_name":"Sloane, Peter"}],"year":"2022"},{"publication_identifier":{"issn":["0302-9743","1611-3349"],"isbn":["9783031069802","9783031069819"]},"publication_status":"published","related_material":{"link":[{"relation":"confirmation","url":"https://link.springer.com/chapter/10.1007/978-3-031-06981-9_14"}]},"place":"Cham","year":"2022","citation":{"apa":"KOUAGOU, N. J., Heindorf, S., Demir, C., & Ngonga Ngomo, A.-C. (2022). Learning Concept Lengths Accelerates Concept Learning in ALC. In The Semantic Web. Springer International Publishing. https://doi.org/10.1007/978-3-031-06981-9_14","short":"N.J. KOUAGOU, S. Heindorf, C. Demir, A.-C. Ngonga Ngomo, in: The Semantic Web, Springer International Publishing, Cham, 2022.","bibtex":"@inbook{KOUAGOU_Heindorf_Demir_Ngonga Ngomo_2022, place={Cham}, title={Learning Concept Lengths Accelerates Concept Learning in ALC}, DOI={10.1007/978-3-031-06981-9_14}, booktitle={The Semantic Web}, publisher={Springer International Publishing}, author={KOUAGOU, N’Dah Jean and Heindorf, Stefan and Demir, Caglar and Ngonga Ngomo, Axel-Cyrille}, year={2022} }","mla":"KOUAGOU, N’Dah Jean, et al. “Learning Concept Lengths Accelerates Concept Learning in ALC.” The Semantic Web, Springer International Publishing, 2022, doi:10.1007/978-3-031-06981-9_14.","ama":"KOUAGOU NJ, Heindorf S, Demir C, Ngonga Ngomo A-C. Learning Concept Lengths Accelerates Concept Learning in ALC. In: The Semantic Web. Springer International Publishing; 2022. doi:10.1007/978-3-031-06981-9_14","chicago":"KOUAGOU, N’Dah Jean, Stefan Heindorf, Caglar Demir, and Axel-Cyrille Ngonga Ngomo. “Learning Concept Lengths Accelerates Concept Learning in ALC.” In The Semantic Web. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-031-06981-9_14.","ieee":"N. J. KOUAGOU, S. Heindorf, C. Demir, and A.-C. Ngonga Ngomo, “Learning Concept Lengths Accelerates Concept Learning in ALC,” in The Semantic Web, Cham: Springer International Publishing, 2022."},"publisher":"Springer International Publishing","oa":"1","date_updated":"2024-04-03T13:26:10Z","date_created":"2022-10-15T19:34:41Z","author":[{"last_name":"KOUAGOU","full_name":"KOUAGOU, N'Dah Jean","id":"87189","first_name":"N'Dah Jean"},{"last_name":"Heindorf","orcid":"0000-0002-4525-6865","id":"11871","full_name":"Heindorf, Stefan","first_name":"Stefan"},{"first_name":"Caglar","id":"43817","full_name":"Demir, Caglar","last_name":"Demir"},{"id":"65716","full_name":"Ngonga Ngomo, Axel-Cyrille","last_name":"Ngonga Ngomo","first_name":"Axel-Cyrille"}],"title":"Learning Concept Lengths Accelerates Concept Learning in ALC","doi":"10.1007/978-3-031-06981-9_14","main_file_link":[{"url":"https://arxiv.org/abs/2107.04911","open_access":"1"}],"publication":"The Semantic Web","type":"book_chapter","status":"public","_id":"33740","department":[{"_id":"574"},{"_id":"760"}],"user_id":"11871","language":[{"iso":"eng"}]},{"publication_identifier":{"issn":["0018-9545","1939-9359"]},"publication_status":"published","issue":"4","year":"2022","page":"4580-4597","intvolume":" 72","citation":{"mla":"Soleymani, Mohammad, et al. “Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling.” IEEE Transactions on Vehicular Technology, vol. 72, no. 4, Institute of Electrical and Electronics Engineers (IEEE), 2022, pp. 4580–97, doi:10.1109/tvt.2022.3222633.","bibtex":"@article{Soleymani_Santamaria_Jorswieck_2022, title={Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling}, volume={72}, DOI={10.1109/tvt.2022.3222633}, number={4}, journal={IEEE Transactions on Vehicular Technology}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Soleymani, Mohammad and Santamaria, Ignacio and Jorswieck, Eduard A.}, year={2022}, pages={4580–4597} }","short":"M. Soleymani, I. Santamaria, E.A. Jorswieck, IEEE Transactions on Vehicular Technology 72 (2022) 4580–4597.","apa":"Soleymani, M., Santamaria, I., & Jorswieck, E. A. (2022). Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling. IEEE Transactions on Vehicular Technology, 72(4), 4580–4597. https://doi.org/10.1109/tvt.2022.3222633","chicago":"Soleymani, Mohammad, Ignacio Santamaria, and Eduard A. Jorswieck. “Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling.” IEEE Transactions on Vehicular Technology 72, no. 4 (2022): 4580–97. https://doi.org/10.1109/tvt.2022.3222633.","ieee":"M. Soleymani, I. Santamaria, and E. A. Jorswieck, “Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling,” IEEE Transactions on Vehicular Technology, vol. 72, no. 4, pp. 4580–4597, 2022, doi: 10.1109/tvt.2022.3222633.","ama":"Soleymani M, Santamaria I, Jorswieck EA. Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling. IEEE Transactions on Vehicular Technology. 2022;72(4):4580-4597. doi:10.1109/tvt.2022.3222633"},"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","date_updated":"2024-04-05T13:21:31Z","volume":72,"author":[{"full_name":"Soleymani, Mohammad","last_name":"Soleymani","first_name":"Mohammad"},{"first_name":"Ignacio","full_name":"Santamaria, Ignacio","last_name":"Santamaria"},{"first_name":"Eduard A.","full_name":"Jorswieck, Eduard A.","last_name":"Jorswieck"}],"date_created":"2024-04-05T09:04:01Z","title":"Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling","doi":"10.1109/tvt.2022.3222633","publication":"IEEE Transactions on Vehicular Technology","type":"journal_article","status":"public","_id":"53266","department":[{"_id":"263"}],"user_id":"67076","keyword":["Electrical and Electronic Engineering","Computer Networks and Communications","Aerospace Engineering","Automotive Engineering"],"language":[{"iso":"eng"}]},{"keyword":["Computer Networks and Communications","Renewable Energy","Sustainability and the Environment"],"language":[{"iso":"eng"}],"_id":"53267","user_id":"67076","department":[{"_id":"263"}],"status":"public","type":"journal_article","publication":"IEEE Transactions on Green Communications and Networking","title":"Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance","doi":"10.1109/tgcn.2021.3140150","date_updated":"2024-04-05T13:21:41Z","publisher":"Institute of Electrical and Electronics Engineers (IEEE)","author":[{"first_name":"Mohammad","last_name":"Soleymani","full_name":"Soleymani, Mohammad"},{"full_name":"Santamaria, Ignacio","last_name":"Santamaria","first_name":"Ignacio"},{"first_name":"Peter J.","full_name":"Schreier, Peter J.","last_name":"Schreier"}],"date_created":"2024-04-05T09:04:25Z","volume":6,"year":"2022","citation":{"apa":"Soleymani, M., Santamaria, I., & Schreier, P. J. (2022). Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance. IEEE Transactions on Green Communications and Networking, 6(2), 723–738. https://doi.org/10.1109/tgcn.2021.3140150","bibtex":"@article{Soleymani_Santamaria_Schreier_2022, title={Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance}, volume={6}, DOI={10.1109/tgcn.2021.3140150}, number={2}, journal={IEEE Transactions on Green Communications and Networking}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Soleymani, Mohammad and Santamaria, Ignacio and Schreier, Peter J.}, year={2022}, pages={723–738} }","short":"M. Soleymani, I. Santamaria, P.J. Schreier, IEEE Transactions on Green Communications and Networking 6 (2022) 723–738.","mla":"Soleymani, Mohammad, et al. “Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance.” IEEE Transactions on Green Communications and Networking, vol. 6, no. 2, Institute of Electrical and Electronics Engineers (IEEE), 2022, pp. 723–38, doi:10.1109/tgcn.2021.3140150.","ama":"Soleymani M, Santamaria I, Schreier PJ. Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance. IEEE Transactions on Green Communications and Networking. 2022;6(2):723-738. doi:10.1109/tgcn.2021.3140150","chicago":"Soleymani, Mohammad, Ignacio Santamaria, and Peter J. Schreier. “Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance.” IEEE Transactions on Green Communications and Networking 6, no. 2 (2022): 723–38. https://doi.org/10.1109/tgcn.2021.3140150.","ieee":"M. Soleymani, I. Santamaria, and P. J. Schreier, “Improper Signaling for Multicell MIMO RIS-Assisted Broadcast Channels With I/Q Imbalance,” IEEE Transactions on Green Communications and Networking, vol. 6, no. 2, pp. 723–738, 2022, doi: 10.1109/tgcn.2021.3140150."},"intvolume":" 6","page":"723-738","publication_status":"published","publication_identifier":{"issn":["2473-2400"]},"issue":"2"},{"status":"public","type":"book_chapter","publication":"Communications in Computer and Information Science","language":[{"iso":"eng"}],"user_id":"56070","_id":"53306","citation":{"ieee":"H. G. Mohammadi et al., “FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics,” in Communications in Computer and Information Science, Cham: Springer International Publishing, 2022.","chicago":"Mohammadi, Hassan Ghasemzadeh, Felix Paul Jentzsch, Maurice Kuschel, Rahil Arshad, Sneha Rautmare, Suraj Manjunatha, Marco Platzner, Alexander Boschmann, and Dirk Schollbach. “FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics.” In Communications in Computer and Information Science. Cham: Springer International Publishing, 2022. https://doi.org/10.1007/978-3-030-93736-2_27.","ama":"Mohammadi HG, Jentzsch FP, Kuschel M, et al. FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics. In: Communications in Computer and Information Science. Springer International Publishing; 2022. doi:10.1007/978-3-030-93736-2_27","apa":"Mohammadi, H. G., Jentzsch, F. P., Kuschel, M., Arshad, R., Rautmare, S., Manjunatha, S., Platzner, M., Boschmann, A., & Schollbach, D. (2022). FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics. In Communications in Computer and Information Science. Springer International Publishing. https://doi.org/10.1007/978-3-030-93736-2_27","bibtex":"@inbook{Mohammadi_Jentzsch_Kuschel_Arshad_Rautmare_Manjunatha_Platzner_Boschmann_Schollbach_2022, place={Cham}, title={FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics}, DOI={10.1007/978-3-030-93736-2_27}, booktitle={Communications in Computer and Information Science}, publisher={Springer International Publishing}, author={Mohammadi, Hassan Ghasemzadeh and Jentzsch, Felix Paul and Kuschel, Maurice and Arshad, Rahil and Rautmare, Sneha and Manjunatha, Suraj and Platzner, Marco and Boschmann, Alexander and Schollbach, Dirk}, year={2022} }","mla":"Mohammadi, Hassan Ghasemzadeh, et al. “FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics.” Communications in Computer and Information Science, Springer International Publishing, 2022, doi:10.1007/978-3-030-93736-2_27.","short":"H.G. Mohammadi, F.P. Jentzsch, M. Kuschel, R. Arshad, S. Rautmare, S. Manjunatha, M. Platzner, A. Boschmann, D. Schollbach, in: Communications in Computer and Information Science, Springer International Publishing, Cham, 2022."},"place":"Cham","year":"2022","publication_status":"published","publication_identifier":{"issn":["1865-0929","1865-0937"],"isbn":["9783030937355","9783030937362"]},"doi":"10.1007/978-3-030-93736-2_27","title":"FLight: FPGA Acceleration of Lightweight DNN Model Inference in Industrial Analytics","date_created":"2024-04-05T14:43:07Z","author":[{"full_name":"Mohammadi, Hassan Ghasemzadeh","last_name":"Mohammadi","first_name":"Hassan Ghasemzadeh"},{"full_name":"Jentzsch, Felix Paul","last_name":"Jentzsch","first_name":"Felix Paul"},{"last_name":"Kuschel","id":"56070","full_name":"Kuschel, Maurice","first_name":"Maurice"},{"first_name":"Rahil","last_name":"Arshad","full_name":"Arshad, Rahil"},{"first_name":"Sneha","full_name":"Rautmare, Sneha","last_name":"Rautmare"},{"first_name":"Suraj","full_name":"Manjunatha, Suraj","last_name":"Manjunatha"},{"first_name":"Marco","last_name":"Platzner","full_name":"Platzner, Marco"},{"last_name":"Boschmann","full_name":"Boschmann, Alexander","first_name":"Alexander"},{"first_name":"Dirk","full_name":"Schollbach, Dirk","last_name":"Schollbach"}],"date_updated":"2024-04-05T14:50:26Z","publisher":"Springer International Publishing"},{"title":"A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System","doi":"10.1093/imrn/rnac286","publisher":"Oxford University Press (OUP)","date_updated":"2024-04-07T12:36:06Z","volume":2023,"author":[{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}],"date_created":"2024-04-07T12:33:44Z","year":"2022","page":"16336-16393","intvolume":" 2023","citation":{"short":"M. Winkler, International Mathematics Research Notices 2023 (2022) 16336–16393.","mla":"Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System.” International Mathematics Research Notices, vol. 2023, no. 19, Oxford University Press (OUP), 2022, pp. 16336–93, doi:10.1093/imrn/rnac286.","bibtex":"@article{Winkler_2022, title={A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System}, volume={2023}, DOI={10.1093/imrn/rnac286}, number={19}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Winkler, Michael}, year={2022}, pages={16336–16393} }","apa":"Winkler, M. (2022). A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System. International Mathematics Research Notices, 2023(19), 16336–16393. https://doi.org/10.1093/imrn/rnac286","ama":"Winkler M. A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System. International Mathematics Research Notices. 2022;2023(19):16336-16393. doi:10.1093/imrn/rnac286","ieee":"M. Winkler, “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System,” International Mathematics Research Notices, vol. 2023, no. 19, pp. 16336–16393, 2022, doi: 10.1093/imrn/rnac286.","chicago":"Winkler, Michael. “A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System.” International Mathematics Research Notices 2023, no. 19 (2022): 16336–93. https://doi.org/10.1093/imrn/rnac286."},"publication_identifier":{"issn":["1073-7928","1687-0247"]},"publication_status":"published","issue":"19","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"53319","user_id":"31496","abstract":[{"lang":"eng","text":"Abstract\r\n The Neumann problem for (0.1)$$ \\begin{align}& V_t = \\Delta V-aV+f(x,t) \\end{align}$$is considered in bounded domains $\\Omega \\subset {\\mathbb {R}}^n$ with smooth boundary, where $n\\ge 1$ and $a\\in {\\mathbb {R}}$. By means of a variational approach, a statement on boundedness of the quantities $$ \\begin{eqnarray*} \\sup_{t\\in (0,T)} \\int_\\Omega \\big|\\nabla V(\\cdot,t)\\big|^p L^{\\frac{n+p}{n+2}} \\Big( \\big|\\nabla V(\\cdot,t)\\big| \\Big) \\end{eqnarray*}$$in dependence on the expressions (0.2)$$ \\begin{align}& \\sup_{t\\in (0,T-\\tau)} \\int_t^{t+\\tau} \\int_\\Omega |f|^{\\frac{(n+2)p}{n+p}} L\\big( |f|\\big) \\end{align}$$is derived for $p\\ge 2$, $\\tau&gt;0$, and $T\\ge 2\\tau $, provided that $L\\in C^0([0,\\infty ))$ is positive, strictly increasing, unbounded, and slowly growing in the sense that $\\limsup _{s\\to \\infty } \\frac {L(s^{\\lambda _0})}{L(s)} &lt;\\infty $ for some $\\lambda _0&gt;1$. In the particular case when $p=n\\ge 2$, an additional condition on growth of $L$, particularly satisfied by $L(\\xi ):=\\ln ^\\alpha (\\xi +b)$ whenever $b&gt;0$ and $\\alpha&gt;\\frac {(n+2)(n-1)}{2n}$, is identified as sufficient to ensure that as a consequence of the above, bounds for theintegrals in (0.2) even imply estimates for the spatio-temporal modulus of continuity of solutions to (0.1). A subsequent application to the Keller–Segel system $$ \\begin{eqnarray*} \\left\\{ \\begin{array}{l} u_t = \\nabla \\cdot \\big( D(v)\\nabla u\\big) - \\nabla \\cdot \\big( uS(v)\\nabla v\\big) + ru - \\mu u^2, \\\\[1mm] v_t = \\Delta v-v+u, \\end{array} \\right. \\end{eqnarray*}$$shows that when $n=2$, $r\\in {\\mathbb {R}}$, $0&lt;D\\in C^2([0,\\infty ))$, and $S\\in C^2([0,\\infty )) \\cap W^{1,\\infty }((0,\\infty ))$ and thus especially in the presence of arbitrarily strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\\mu&gt;0$ excludes blowup in the sense that for all suitably regular nonnegative initial data, an associated initial-boundary value problem admits a global bounded classical solution."}],"status":"public","publication":"International Mathematics Research Notices","type":"journal_article"},{"user_id":"31496","_id":"53321","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Mathematics"],"publication":"Communications in Contemporary Mathematics","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":" The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text], [Formula: see text], where the positive function [Formula: see text] reflects suitably weak diffusion by satisfying [Formula: see text] for some [Formula: see text]. It is shown that whenever [Formula: see text] is positive and satisfies [Formula: see text] as [Formula: see text], one can find a suitably regular nonlinearity [Formula: see text] with the property that at each sufficiently large mass level [Formula: see text] there exists a globally defined radially symmetric classical solution to a Neumann-type boundary value problem for (⋆) which satisfies [Formula: see text] "}],"volume":25,"date_created":"2024-04-07T12:35:09Z","author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_updated":"2024-04-07T12:35:53Z","publisher":"World Scientific Pub Co Pte Ltd","doi":"10.1142/s0219199722500626","title":"Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems","issue":"10","publication_identifier":{"issn":["0219-1997","1793-6683"]},"publication_status":"published","intvolume":" 25","citation":{"ieee":"M. Winkler, “Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems,” Communications in Contemporary Mathematics, vol. 25, no. 10, 2022, doi: 10.1142/s0219199722500626.","chicago":"Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel Systems.” Communications in Contemporary Mathematics 25, no. 10 (2022). https://doi.org/10.1142/s0219199722500626.","ama":"Winkler M. Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. Communications in Contemporary Mathematics. 2022;25(10). doi:10.1142/s0219199722500626","apa":"Winkler, M. (2022). Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems. Communications in Contemporary Mathematics, 25(10). https://doi.org/10.1142/s0219199722500626","short":"M. Winkler, Communications in Contemporary Mathematics 25 (2022).","mla":"Winkler, Michael. “Arbitrarily Fast Grow-up Rates in Quasilinear Keller–Segel Systems.” Communications in Contemporary Mathematics, vol. 25, no. 10, World Scientific Pub Co Pte Ltd, 2022, doi:10.1142/s0219199722500626.","bibtex":"@article{Winkler_2022, title={Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems}, volume={25}, DOI={10.1142/s0219199722500626}, number={10}, journal={Communications in Contemporary Mathematics}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }"},"year":"2022"},{"publication":"Journal of Dynamics and Differential Equations","type":"journal_article","abstract":[{"text":"AbstractIn a ball $$\\Omega =B_R(0)\\subset \\mathbb {R}^n$$\r\n \r\n Ω\r\n =\r\n \r\n B\r\n R\r\n \r\n \r\n (\r\n 0\r\n )\r\n \r\n ⊂\r\n \r\n \r\n R\r\n \r\n n\r\n \r\n \r\n , $$n\\ge 2$$\r\n \r\n n\r\n ≥\r\n 2\r\n \r\n , the chemotaxis system $$\\begin{aligned} \\left\\{ \\begin{array}{l}u_t = \\nabla \\cdot \\big ( D(u) \\nabla u \\big ) - \\nabla \\cdot \\big ( uS(u)\\nabla v\\big ), \\\\ 0 = \\Delta v - \\mu + u, \\qquad \\mu =\\frac{1}{|\\Omega |} \\int _\\Omega u, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n =\r\n ∇\r\n ·\r\n \r\n (\r\n \r\n D\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n u\r\n \r\n )\r\n \r\n -\r\n ∇\r\n ·\r\n \r\n (\r\n \r\n u\r\n S\r\n \r\n (\r\n u\r\n )\r\n \r\n ∇\r\n v\r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n v\r\n -\r\n μ\r\n +\r\n u\r\n ,\r\n \r\n μ\r\n =\r\n \r\n 1\r\n \r\n |\r\n Ω\r\n |\r\n \r\n \r\n \r\n ∫\r\n Ω\r\n \r\n u\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n (\r\n ⋆\r\n )\r\n \r\n \r\n \r\n \r\n \r\n \r\n is considered under no-flux boundary conditions, with a focus on nonlinearities $$S\\in C^2([0,\\infty ))$$\r\n \r\n S\r\n ∈\r\n \r\n C\r\n 2\r\n \r\n \r\n (\r\n \r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n which exhibit super-algebraically fast decay in the sense that with some $$K_S>0, \\beta \\in [0,1)$$\r\n \r\n \r\n K\r\n S\r\n \r\n >\r\n 0\r\n ,\r\n β\r\n ∈\r\n \r\n [\r\n 0\r\n ,\r\n 1\r\n )\r\n \r\n \r\n and $$\\xi _0>0$$\r\n \r\n \r\n ξ\r\n 0\r\n \r\n >\r\n 0\r\n \r\n , $$\\begin{aligned} S(\\xi )>0 \\quad \\text{ and } \\quad S'(\\xi ) \\le -K_S\\xi ^{-\\beta } S(\\xi ) \\qquad \\text{ for } \\text{ all } \\xi \\ge \\xi _0. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n S\r\n \r\n (\r\n ξ\r\n )\r\n \r\n >\r\n 0\r\n \r\n \r\n and\r\n \r\n \r\n \r\n S\r\n ′\r\n \r\n \r\n (\r\n ξ\r\n )\r\n \r\n ≤\r\n -\r\n \r\n K\r\n S\r\n \r\n \r\n ξ\r\n \r\n -\r\n β\r\n \r\n \r\n S\r\n \r\n (\r\n ξ\r\n )\r\n \r\n \r\n \r\n for\r\n \r\n \r\n all\r\n \r\n ξ\r\n ≥\r\n \r\n ξ\r\n 0\r\n \r\n .\r\n \r\n \r\n \r\n \r\n \r\n It is, inter alia, shown that if furthermore $$D\\in C^2((0,\\infty ))$$\r\n \r\n D\r\n ∈\r\n \r\n C\r\n 2\r\n \r\n \r\n (\r\n \r\n (\r\n 0\r\n ,\r\n ∞\r\n )\r\n \r\n )\r\n \r\n \r\n is positive and suitably small in relation to S by satisfying $$\\begin{aligned} \\frac{\\xi S(\\xi )}{D(\\xi )} \\ge K_{SD}\\xi ^\\lambda \\qquad \\text{ for } \\text{ all } \\xi \\ge \\xi _0 \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n ξ\r\n S\r\n (\r\n ξ\r\n )\r\n \r\n \r\n D\r\n (\r\n ξ\r\n )\r\n \r\n \r\n ≥\r\n \r\n K\r\n \r\n SD\r\n \r\n \r\n \r\n ξ\r\n λ\r\n \r\n \r\n \r\n for\r\n \r\n \r\n all\r\n \r\n ξ\r\n ≥\r\n \r\n ξ\r\n 0\r\n \r\n \r\n \r\n \r\n \r\n \r\n with some $$K_{SD}>0$$\r\n \r\n \r\n K\r\n \r\n SD\r\n \r\n \r\n >\r\n 0\r\n \r\n and $$\\lambda >\\frac{2}{n}$$\r\n \r\n λ\r\n >\r\n \r\n 2\r\n n\r\n \r\n \r\n , then throughout a considerably large set of initial data, ($$\\star $$\r\n ⋆\r\n ) admits global classical solutions (u, v) fulfilling $$\\begin{aligned} \\frac{z(t)}{C} \\le \\Vert u(\\cdot ,t)\\Vert _{L^\\infty (\\Omega )} \\le Cz(t) \\qquad \\text{ for } \\text{ all } t>0, \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n z\r\n (\r\n t\r\n )\r\n \r\n C\r\n \r\n ≤\r\n \r\n \r\n ‖\r\n u\r\n \r\n (\r\n ·\r\n ,\r\n t\r\n )\r\n \r\n ‖\r\n \r\n \r\n \r\n L\r\n ∞\r\n \r\n \r\n (\r\n Ω\r\n )\r\n \r\n \r\n \r\n ≤\r\n C\r\n z\r\n \r\n (\r\n t\r\n )\r\n \r\n \r\n \r\n for\r\n \r\n \r\n all\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n with some $$C=C^{(u,v)}\\ge 1$$\r\n \r\n C\r\n =\r\n \r\n C\r\n \r\n (\r\n u\r\n ,\r\n v\r\n )\r\n \r\n \r\n ≥\r\n 1\r\n \r\n , where z denotes the solution of $$\\begin{aligned} \\left\\{ \\begin{array}{l}z'(t) = z^2(t) \\cdot S\\big ( z(t)\\big ), \\qquad t>0, \\\\ z(0)=\\xi _0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n z\r\n ′\r\n \r\n \r\n (\r\n t\r\n )\r\n \r\n =\r\n \r\n z\r\n 2\r\n \r\n \r\n (\r\n t\r\n )\r\n \r\n ·\r\n S\r\n \r\n (\r\n \r\n z\r\n \r\n (\r\n t\r\n )\r\n \r\n \r\n )\r\n \r\n ,\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n z\r\n \r\n (\r\n 0\r\n )\r\n \r\n =\r\n \r\n ξ\r\n 0\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n which is seen to exist globally, and to satisfy $$z(t)\\rightarrow +\\infty $$\r\n \r\n z\r\n (\r\n t\r\n )\r\n →\r\n +\r\n ∞\r\n \r\n as $$t\\rightarrow \\infty $$\r\n \r\n t\r\n →\r\n ∞\r\n \r\n . As particular examples, exponentially and doubly exponentially decaying S are found to imply corresponding infinite-time blow-up properties in ($$\\star $$\r\n ⋆\r\n ) at logarithmic and doubly logarithmic rates, respectively.","lang":"eng"}],"status":"public","_id":"53323","user_id":"31496","keyword":["Analysis"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1040-7294","1572-9222"]},"publication_status":"published","year":"2022","citation":{"short":"M. Winkler, Journal of Dynamics and Differential Equations (2022).","bibtex":"@article{Winkler_2022, title={Slow Grow-up in a Quasilinear Keller–Segel System}, DOI={10.1007/s10884-022-10167-w}, journal={Journal of Dynamics and Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2022} }","mla":"Winkler, Michael. “Slow Grow-up in a Quasilinear Keller–Segel System.” Journal of Dynamics and Differential Equations, Springer Science and Business Media LLC, 2022, doi:10.1007/s10884-022-10167-w.","apa":"Winkler, M. (2022). Slow Grow-up in a Quasilinear Keller–Segel System. Journal of Dynamics and Differential Equations. https://doi.org/10.1007/s10884-022-10167-w","ieee":"M. Winkler, “Slow Grow-up in a Quasilinear Keller–Segel System,” Journal of Dynamics and Differential Equations, 2022, doi: 10.1007/s10884-022-10167-w.","chicago":"Winkler, Michael. “Slow Grow-up in a Quasilinear Keller–Segel System.” Journal of Dynamics and Differential Equations, 2022. https://doi.org/10.1007/s10884-022-10167-w.","ama":"Winkler M. Slow Grow-up in a Quasilinear Keller–Segel System. Journal of Dynamics and Differential Equations. Published online 2022. doi:10.1007/s10884-022-10167-w"},"publisher":"Springer Science and Business Media LLC","date_updated":"2024-04-07T12:39:17Z","date_created":"2024-04-07T12:39:12Z","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"title":"Slow Grow-up in a Quasilinear Keller–Segel System","doi":"10.1007/s10884-022-10167-w"},{"status":"public","publication":"Journal of Differential Equations","type":"journal_article","language":[{"iso":"eng"}],"keyword":["Analysis","Applied Mathematics"],"user_id":"31496","_id":"53327","page":"390-418","intvolume":" 343","citation":{"short":"Y. Tao, M. Winkler, Journal of Differential Equations 343 (2022) 390–418.","bibtex":"@article{Tao_Winkler_2022, title={Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension}, volume={343}, DOI={10.1016/j.jde.2022.10.022}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Tao, Youshan and Winkler, Michael}, year={2022}, pages={390–418} }","mla":"Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary Dimension.” Journal of Differential Equations, vol. 343, Elsevier BV, 2022, pp. 390–418, doi:10.1016/j.jde.2022.10.022.","apa":"Tao, Y., & Winkler, M. (2022). Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Journal of Differential Equations, 343, 390–418. https://doi.org/10.1016/j.jde.2022.10.022","ieee":"Y. Tao and M. Winkler, “Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension,” Journal of Differential Equations, vol. 343, pp. 390–418, 2022, doi: 10.1016/j.jde.2022.10.022.","chicago":"Tao, Youshan, and Michael Winkler. “Global Solutions to a Keller-Segel-Consumption System Involving Singularly Signal-Dependent Motilities in Domains of Arbitrary Dimension.” Journal of Differential Equations 343 (2022): 390–418. https://doi.org/10.1016/j.jde.2022.10.022.","ama":"Tao Y, Winkler M. Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension. Journal of Differential Equations. 2022;343:390-418. doi:10.1016/j.jde.2022.10.022"},"year":"2022","publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","doi":"10.1016/j.jde.2022.10.022","title":"Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension","volume":343,"author":[{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:42:28Z","publisher":"Elsevier BV","date_updated":"2024-04-07T12:42:32Z"},{"_id":"53325","user_id":"31496","keyword":["Applied Mathematics","Analysis"],"article_number":"113153","language":[{"iso":"eng"}],"publication":"Nonlinear Analysis","type":"journal_article","status":"public","publisher":"Elsevier BV","date_updated":"2024-04-07T12:41:20Z","volume":226,"date_created":"2024-04-07T12:41:15Z","author":[{"first_name":"Laurent","full_name":"Desvillettes, Laurent","last_name":"Desvillettes"},{"last_name":"Laurençot","full_name":"Laurençot, Philippe","first_name":"Philippe"},{"first_name":"Ariane","full_name":"Trescases, Ariane","last_name":"Trescases"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"title":"Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing","doi":"10.1016/j.na.2022.113153","publication_identifier":{"issn":["0362-546X"]},"publication_status":"published","year":"2022","intvolume":" 226","citation":{"chicago":"Desvillettes, Laurent, Philippe Laurençot, Ariane Trescases, and Michael Winkler. “Weak Solutions to Triangular Cross Diffusion Systems Modeling Chemotaxis with Local Sensing.” Nonlinear Analysis 226 (2022). https://doi.org/10.1016/j.na.2022.113153.","ieee":"L. Desvillettes, P. Laurençot, A. Trescases, and M. Winkler, “Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing,” Nonlinear Analysis, vol. 226, Art. no. 113153, 2022, doi: 10.1016/j.na.2022.113153.","ama":"Desvillettes L, Laurençot P, Trescases A, Winkler M. Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. Nonlinear Analysis. 2022;226. doi:10.1016/j.na.2022.113153","bibtex":"@article{Desvillettes_Laurençot_Trescases_Winkler_2022, title={Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing}, volume={226}, DOI={10.1016/j.na.2022.113153}, number={113153}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Desvillettes, Laurent and Laurençot, Philippe and Trescases, Ariane and Winkler, Michael}, year={2022} }","mla":"Desvillettes, Laurent, et al. “Weak Solutions to Triangular Cross Diffusion Systems Modeling Chemotaxis with Local Sensing.” Nonlinear Analysis, vol. 226, 113153, Elsevier BV, 2022, doi:10.1016/j.na.2022.113153.","short":"L. Desvillettes, P. Laurençot, A. Trescases, M. Winkler, Nonlinear Analysis 226 (2022).","apa":"Desvillettes, L., Laurençot, P., Trescases, A., & Winkler, M. (2022). Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing. Nonlinear Analysis, 226, Article 113153. https://doi.org/10.1016/j.na.2022.113153"}},{"abstract":[{"text":"In a ball $\\Omega \\subset \\mathbb {R}^{n}$ with $n\\ge 2$, the chemotaxis system\r\n\\[ \\left\\{ \\begin{array}{@{}l} u_t = \\nabla \\cdot \\big( D(u)\\nabla u\\big) + \\nabla\\cdot \\big(\\dfrac{u}{v} \\nabla v\\big), \\\\ 0=\\Delta v - uv \\end{array} \\right. \\]is considered along with no-flux boundary conditions for $u$ and with prescribed constant positive Dirichlet boundary data for $v$. It is shown that if $D\\in C^{3}([0,\\infty ))$ is such that $0< D(\\xi ) \\le {K_D} (\\xi +1)^{-\\alpha }$ for all $\\xi >0$ with some ${K_D}>0$ and $\\alpha >0$, then for all initial data from a considerably large set of radial functions on $\\Omega$, the corresponding initial-boundary value problem admits a solution blowing up in finite time.","lang":"eng"}],"status":"public","publication":"Proceedings of the Royal Society of Edinburgh: Section A Mathematics","type":"journal_article","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"53331","user_id":"31496","year":"2022","intvolume":" 153","page":"1150-1166","citation":{"mla":"Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 153, no. 4, Cambridge University Press (CUP), 2022, pp. 1150–66, doi:10.1017/prm.2022.39.","short":"Y. Wang, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153 (2022) 1150–1166.","bibtex":"@article{Wang_Winkler_2022, title={Finite-time blow-up in a repulsive chemotaxis-consumption system}, volume={153}, DOI={10.1017/prm.2022.39}, number={4}, journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, publisher={Cambridge University Press (CUP)}, author={Wang, Yulan and Winkler, Michael}, year={2022}, pages={1150–1166} }","apa":"Wang, Y., & Winkler, M. (2022). Finite-time blow-up in a repulsive chemotaxis-consumption system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 153(4), 1150–1166. https://doi.org/10.1017/prm.2022.39","chicago":"Wang, Yulan, and Michael Winkler. “Finite-Time Blow-up in a Repulsive Chemotaxis-Consumption System.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153, no. 4 (2022): 1150–66. https://doi.org/10.1017/prm.2022.39.","ieee":"Y. Wang and M. Winkler, “Finite-time blow-up in a repulsive chemotaxis-consumption system,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 153, no. 4, pp. 1150–1166, 2022, doi: 10.1017/prm.2022.39.","ama":"Wang Y, Winkler M. Finite-time blow-up in a repulsive chemotaxis-consumption system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2022;153(4):1150-1166. doi:10.1017/prm.2022.39"},"publication_identifier":{"issn":["0308-2105","1473-7124"]},"publication_status":"published","issue":"4","title":"Finite-time blow-up in a repulsive chemotaxis-consumption system","doi":"10.1017/prm.2022.39","date_updated":"2024-04-07T12:44:30Z","publisher":"Cambridge University Press (CUP)","volume":153,"date_created":"2024-04-07T12:44:26Z","author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael"}]},{"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"_id":"53344","user_id":"31496","abstract":[{"lang":"eng","text":" A no-flux initial-boundary value problem for the cross-diffusion system [Formula: see text] is considered in smoothly bounded domains [Formula: see text] with [Formula: see text]. It is shown that whenever [Formula: see text] is positive on [Formula: see text] and such that [Formula: see text] for some [Formula: see text], for all suitably regular positive initial data a global very weak solution, particularly preserving mass in its first component, can be constructed. This extends previous results which either concentrate on non-degenerate analogs, or are restricted to the special case [Formula: see text]. To appropriately cope with the considerably stronger cross-degeneracies thus allowed through [Formula: see text] when [Formula: see text] is large, in its core part the analysis relies on the use of the Moser–Trudinger inequality in controlling the respective diffusion rates [Formula: see text] from below. "}],"status":"public","type":"journal_article","publication":"Bulletin of Mathematical Sciences","title":"Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model","doi":"10.1142/s1664360722500126","publisher":"World Scientific Pub Co Pte Ltd","date_updated":"2024-04-07T12:55:11Z","date_created":"2024-04-07T12:55:07Z","author":[{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"volume":13,"year":"2022","citation":{"mla":"Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction of Global Solutions to a Strongly Degenerate Migration Model.” Bulletin of Mathematical Sciences, vol. 13, no. 02, World Scientific Pub Co Pte Ltd, 2022, doi:10.1142/s1664360722500126.","bibtex":"@article{Winkler_2022, title={Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model}, volume={13}, DOI={10.1142/s1664360722500126}, number={02}, journal={Bulletin of Mathematical Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }","short":"M. Winkler, Bulletin of Mathematical Sciences 13 (2022).","apa":"Winkler, M. (2022). Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. Bulletin of Mathematical Sciences, 13(02). https://doi.org/10.1142/s1664360722500126","chicago":"Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction of Global Solutions to a Strongly Degenerate Migration Model.” Bulletin of Mathematical Sciences 13, no. 02 (2022). https://doi.org/10.1142/s1664360722500126.","ieee":"M. Winkler, “Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model,” Bulletin of Mathematical Sciences, vol. 13, no. 02, 2022, doi: 10.1142/s1664360722500126.","ama":"Winkler M. Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model. Bulletin of Mathematical Sciences. 2022;13(02). doi:10.1142/s1664360722500126"},"intvolume":" 13","publication_status":"published","publication_identifier":{"issn":["1664-3607","1664-3615"]},"issue":"02"},{"intvolume":" 100","citation":{"ama":"Fochmann M, Heinemann-Heile V, Huber H-P, Maiterth R, Sureth-Sloane C. Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation). Vol 100.; 2022. doi:10.2139/ssrn.4210460","chicago":"Fochmann, Martin, Vanessa Heinemann-Heile, Hans-Peter Huber, Ralf Maiterth, and Caren Sureth-Sloane. Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation). Vol. 100. TRR 266 Accounting for Transparency Working Paper Series, 2022. https://doi.org/10.2139/ssrn.4210460.","ieee":"M. Fochmann, V. Heinemann-Heile, H.-P. Huber, R. Maiterth, and C. Sureth-Sloane, Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation), vol. 100. 2022.","apa":"Fochmann, M., Heinemann-Heile, V., Huber, H.-P., Maiterth, R., & Sureth-Sloane, C. (2022). Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation) (Vol. 100). https://doi.org/10.2139/ssrn.4210460","short":"M. Fochmann, V. Heinemann-Heile, H.-P. Huber, R. Maiterth, C. Sureth-Sloane, Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation), 2022.","mla":"Fochmann, Martin, et al. Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation). 2022, doi:10.2139/ssrn.4210460.","bibtex":"@book{Fochmann_Heinemann-Heile_Huber_Maiterth_Sureth-Sloane_2022, series={TRR 266 Accounting for Transparency Working Paper Series}, title={Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)}, volume={100}, DOI={10.2139/ssrn.4210460}, author={Fochmann, Martin and Heinemann-Heile, Vanessa and Huber, Hans-Peter and Maiterth, Ralf and Sureth-Sloane, Caren}, year={2022}, collection={TRR 266 Accounting for Transparency Working Paper Series} }"},"year":"2022","publication_identifier":{"issn":["1556-5068"]},"publication_status":"published","doi":"10.2139/ssrn.4210460","main_file_link":[{"open_access":"1"}],"title":"Zusatzkosten der Besteuerung – Eine Analyse des steuerlichen Verwaltungsaufwands und der subjektiv wahrgenommenen Steuerbelastung (An Empirical Analysis of Firms’ Hidden Cost of Taxation)","volume":100,"date_created":"2023-01-10T10:51:40Z","author":[{"last_name":"Fochmann","full_name":"Fochmann, Martin","first_name":"Martin"},{"first_name":"Vanessa","id":"83380","full_name":"Heinemann-Heile, Vanessa","last_name":"Heinemann-Heile"},{"first_name":"Hans-Peter","full_name":"Huber, Hans-Peter","last_name":"Huber"},{"first_name":"Ralf","full_name":"Maiterth, Ralf","last_name":"Maiterth"},{"first_name":"Caren","id":"530","full_name":"Sureth-Sloane, Caren","last_name":"Sureth-Sloane","orcid":" 0000-0002-8183-5901"}],"date_updated":"2024-04-08T11:33:02Z","oa":"1","status":"public","type":"working_paper","language":[{"iso":"ger"}],"keyword":["General Earth and Planetary Sciences","General Environmental Science"],"department":[{"_id":"187"}],"series_title":"TRR 266 Accounting for Transparency Working Paper Series","user_id":"530","_id":"35788"},{"publication_status":"published","publication_identifier":{"issn":["1556-5068"]},"citation":{"ieee":"S. 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