[{"citation":{"chicago":"Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i> 30(17) (2020): 7593–7618. <a href=\"https://doi.org/10.1002/rnc.5197\">https://doi.org/10.1002/rnc.5197</a>.","short":"C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 30(17) (2020) 7593–7618.","apa":"Hernández Castellanos, C. I., Ober-Blöbaum, S., &#38; Peitz, S. (2020). Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International Journal of Robust and Nonlinear Control</i>, <i>30(17)</i>, 7593–7618. <a href=\"https://doi.org/10.1002/rnc.5197\">https://doi.org/10.1002/rnc.5197</a>","ieee":"C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 30(17), pp. 7593–7618, 2020, doi: <a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>.","ama":"Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. <i>International Journal of Robust and Nonlinear Control</i>. 2020;30(17):7593-7618. doi:<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>","bibtex":"@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty}, volume={30(17)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>}, journal={International Journal of Robust and Nonlinear Control}, author={Hernández Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2020}, pages={7593–7618} }","mla":"Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 30(17), 2020, pp. 7593–618, doi:<a href=\"https://doi.org/10.1002/rnc.5197\">10.1002/rnc.5197</a>."},"publication":"International Journal of Robust and Nonlinear Control","abstract":[{"text":"In real-world problems, uncertainties (e.g., errors in the measurement,\r\nprecision errors) often lead to poor performance of numerical algorithms when\r\nnot explicitly taken into account. This is also the case for control problems,\r\nwhere optimal solutions can degrade in quality or even become infeasible. Thus,\r\nthere is the need to design methods that can handle uncertainty. In this work,\r\nwe consider nonlinear multi-objective optimal control problems with uncertainty\r\non the initial conditions, and in particular their incorporation into a\r\nfeedback loop via model predictive control (MPC). In multi-objective optimal\r\ncontrol, an optimal compromise between multiple conflicting criteria has to be\r\nfound. For such problems, not much has been reported in terms of uncertainties.\r\nTo address this problem class, we design an offline/online framework to compute\r\nan approximation of efficient control strategies. This approach is closely\r\nrelated to explicit MPC for nonlinear systems, where the potentially expensive\r\noptimization problem is solved in an offline phase in order to enable fast\r\nsolutions in the online phase. In order to reduce the numerical cost of the\r\noffline phase, we exploit symmetries in the control problems. Furthermore, in\r\norder to ensure optimality of the solutions, we include an additional online\r\noptimization step, which is considerably cheaper than the original\r\nmulti-objective optimization problem. We test our framework on a car\r\nmaneuvering problem where safety and speed are the objectives. The\r\nmulti-objective framework allows for online adaptations of the desired\r\nobjective. Alternatively, an automatic scalarizing procedure yields very\r\nefficient feedback controls. Our results show that the method is capable of\r\ndesigning driving strategies that deal better with uncertainties in the initial\r\nconditions, which translates into potentially safer and faster driving\r\nstrategies.","lang":"eng"}],"date_created":"2020-03-13T12:45:56Z","department":[{"_id":"101"}],"type":"journal_article","author":[{"last_name":"Hernández Castellanos","first_name":"Carlos Ignacio","full_name":"Hernández Castellanos, Carlos Ignacio"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Peitz, Sebastian","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","id":"47427"}],"year":"2020","title":"Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty","status":"public","date_updated":"2022-01-21T09:55:39Z","language":[{"iso":"eng"}],"_id":"16297","page":"7593-7618","volume":"30(17)","user_id":"15694","doi":"10.1002/rnc.5197"},{"author":[{"full_name":"Hernández Castellanos, C. I. O.","first_name":"C. I. O.","last_name":"Hernández Castellanos"},{"full_name":"Schütze, G.","first_name":"G.","last_name":"Schütze"},{"full_name":"Sun, J.-Q.","first_name":"J.-Q.","last_name":"Sun"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"last_name":"Morales-Luna","first_name":"G.","full_name":"Morales-Luna, G."}],"status":"public","year":"2020","title":"Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping","date_updated":"2022-01-21T09:57:35Z","_id":"29398","language":[{"iso":"eng"}],"volume":"8(11):1959","user_id":"15694","citation":{"mla":"Hernández Castellanos, C. I. O., et al. “Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping.” <i>Mathematics</i>, vol. 8(11):1959, 2020.","ama":"Hernández Castellanos CIO, Schütze G, Sun J-Q, Ober-Blöbaum S, Morales-Luna G. Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping. <i>Mathematics</i>. 2020;8(11):1959.","bibtex":"@article{Hernández Castellanos_Schütze_Sun_Ober-Blöbaum_Morales-Luna_2020, title={Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping}, volume={8(11):1959}, journal={Mathematics}, author={Hernández Castellanos, C. I. O. and Schütze, G. and Sun, J.-Q. and Ober-Blöbaum, Sina and Morales-Luna, G.}, year={2020} }","apa":"Hernández Castellanos, C. I. O., Schütze, G., Sun, J.-Q., Ober-Blöbaum, S., &#38; Morales-Luna, G. (2020). Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping. <i>Mathematics</i>, <i>8(11):1959</i>.","ieee":"C. I. O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, and G. Morales-Luna, “Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping,” <i>Mathematics</i>, vol. 8(11):1959, 2020.","short":"C.I.O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, G. Morales-Luna, Mathematics 8(11):1959 (2020).","chicago":"Hernández Castellanos, C. I. O., G. Schütze, J.-Q. Sun, Sina Ober-Blöbaum, and G. Morales-Luna. “Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping.” <i>Mathematics</i> 8(11):1959 (2020)."},"publication":"Mathematics","date_created":"2022-01-18T11:08:28Z","department":[{"_id":"636"}],"type":"journal_article"},{"author":[{"last_name":"Lishkova","first_name":"Y.","full_name":"Lishkova, Y."},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"full_name":"Cannon, M.","last_name":"Cannon","first_name":"M."},{"full_name":"Leyendecker, S.","first_name":"S.","last_name":"Leyendecker"}],"year":"2020","status":"public","title":"A multirate variational approach to simulation and optimal control for flexible spacecraft","date_updated":"2022-01-21T13:45:40Z","_id":"29422","language":[{"iso":"eng"}],"user_id":"15694","citation":{"chicago":"Lishkova, Y., Sina Ober-Blöbaum, M. Cannon, and S. Leyendecker. “A Multirate Variational Approach to Simulation and Optimal Control for Flexible Spacecraft.” In <i>Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe</i>, 2020.","short":"Y. Lishkova, S. Ober-Blöbaum, M. Cannon, S. Leyendecker, in: Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe, 2020.","ieee":"Y. Lishkova, S. Ober-Blöbaum, M. Cannon, and S. Leyendecker, “A multirate variational approach to simulation and optimal control for flexible spacecraft,” 2020.","apa":"Lishkova, Y., Ober-Blöbaum, S., Cannon, M., &#38; Leyendecker, S. (2020). A multirate variational approach to simulation and optimal control for flexible spacecraft. <i>Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe</i>.","bibtex":"@inproceedings{Lishkova_Ober-Blöbaum_Cannon_Leyendecker_2020, title={A multirate variational approach to simulation and optimal control for flexible spacecraft}, booktitle={Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe}, author={Lishkova, Y. and Ober-Blöbaum, Sina and Cannon, M. and Leyendecker, S.}, year={2020} }","ama":"Lishkova Y, Ober-Blöbaum S, Cannon M, Leyendecker S. A multirate variational approach to simulation and optimal control for flexible spacecraft. In: <i>Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe</i>. ; 2020.","mla":"Lishkova, Y., et al. “A Multirate Variational Approach to Simulation and Optimal Control for Flexible Spacecraft.” <i>Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe</i>, 2020."},"publication":"Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe","date_created":"2022-01-18T14:37:53Z","department":[{"_id":"636"}],"type":"conference"},{"publication":"24th International Symposium on Mathematical Theory of Networks and Systems","citation":{"apa":"Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., &#38; Worthmann, K. (2020). A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>.","ieee":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems,” 2020.","chicago":"Faulwasser, T., K. Flaßkamp, Sina Ober-Blöbaum, and K.  Worthmann. “A Dissipativity Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical Systems.” In <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>, 2020.","short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: 24th International Symposium on Mathematical Theory of Networks and Systems, 2020.","mla":"Faulwasser, T., et al. “A Dissipativity Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical Systems.” <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>, 2020.","ama":"Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. In: <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>. ; 2020.","bibtex":"@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2020, title={A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems}, booktitle={24th International Symposium on Mathematical Theory of Networks and Systems}, author={Faulwasser, T. and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann, K. }, year={2020} }"},"date_created":"2022-01-18T14:42:07Z","type":"conference","department":[{"_id":"636"}],"year":"2020","title":"A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems","status":"public","author":[{"full_name":"Faulwasser, T.","first_name":"T.","last_name":"Faulwasser"},{"first_name":"K.","last_name":"Flaßkamp","full_name":"Flaßkamp, K."},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"last_name":"Worthmann","first_name":"K. ","full_name":"Worthmann, K. "}],"date_updated":"2022-01-21T13:46:57Z","_id":"29423","language":[{"iso":"eng"}],"user_id":"15694"},{"date_created":"2022-01-18T14:45:22Z","department":[{"_id":"636"}],"type":"conference","citation":{"bibtex":"@inproceedings{Cresson_Jiménez_Ober-Blöbaum_2020, title={Modelling of the convection-diffusion equation through fractional restricted calculus of variations}, booktitle={24th International Symposium on Mathematical Theory of Networks and Systems}, author={Cresson, J.  and Jiménez, F. and Ober-Blöbaum, Sina}, year={2020} }","ama":"Cresson J, Jiménez F, Ober-Blöbaum S. Modelling of the convection-diffusion equation through fractional restricted calculus of variations. In: <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>. ; 2020.","short":"J. Cresson, F. Jiménez, S. Ober-Blöbaum, in: 24th International Symposium on Mathematical Theory of Networks and Systems, 2020.","chicago":"Cresson, J. , F. Jiménez, and Sina Ober-Blöbaum. “Modelling of the Convection-Diffusion Equation through Fractional Restricted Calculus of Variations.” In <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>, 2020.","ieee":"J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Modelling of the convection-diffusion equation through fractional restricted calculus of variations,” 2020.","apa":"Cresson, J., Jiménez, F., &#38; Ober-Blöbaum, S. (2020). Modelling of the convection-diffusion equation through fractional restricted calculus of variations. <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>.","mla":"Cresson, J., et al. “Modelling of the Convection-Diffusion Equation through Fractional Restricted Calculus of Variations.” <i>24th International Symposium on Mathematical Theory of Networks and Systems</i>, 2020."},"publication":"24th International Symposium on Mathematical Theory of Networks and Systems","language":[{"iso":"eng"}],"_id":"29424","user_id":"15694","author":[{"full_name":"Cresson, J. ","last_name":"Cresson","first_name":"J. "},{"last_name":"Jiménez","first_name":"F.","full_name":"Jiménez, F."},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"}],"year":"2020","status":"public","title":"Modelling of the convection-diffusion equation through fractional restricted calculus of variations","date_updated":"2022-01-21T13:47:49Z"},{"status":"public","_id":"29545","publisher":"Springer Science and Business Media LLC","page":"295-314","volume":213,"user_id":"87909","citation":{"mla":"Jean, Frédéric, et al. “On Weyl’s Type Theorems and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” <i>Geometriae Dedicata</i>, vol. 213, no. 1, Springer Science and Business Media LLC, 2020, pp. 295–314, doi:<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>.","ama":"Jean F, Maslovskaya S, Zelenko I. On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry. <i>Geometriae Dedicata</i>. 2020;213(1):295-314. doi:<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>","bibtex":"@article{Jean_Maslovskaya_Zelenko_2020, title={On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry}, volume={213}, DOI={<a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>}, number={1}, journal={Geometriae Dedicata}, publisher={Springer Science and Business Media LLC}, author={Jean, Frédéric and Maslovskaya, Sofya and Zelenko, Igor}, year={2020}, pages={295–314} }","apa":"Jean, F., Maslovskaya, S., &#38; Zelenko, I. (2020). On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry. <i>Geometriae Dedicata</i>, <i>213</i>(1), 295–314. <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">https://doi.org/10.1007/s10711-020-00581-z</a>","ieee":"F. Jean, S. Maslovskaya, and I. Zelenko, “On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry,” <i>Geometriae Dedicata</i>, vol. 213, no. 1, pp. 295–314, 2020, doi: <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">10.1007/s10711-020-00581-z</a>.","short":"F. Jean, S. Maslovskaya, I. Zelenko, Geometriae Dedicata 213 (2020) 295–314.","chicago":"Jean, Frédéric, Sofya Maslovskaya, and Igor Zelenko. “On Weyl’s Type Theorems and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” <i>Geometriae Dedicata</i> 213, no. 1 (2020): 295–314. <a href=\"https://doi.org/10.1007/s10711-020-00581-z\">https://doi.org/10.1007/s10711-020-00581-z</a>."},"author":[{"full_name":"Jean, Frédéric","last_name":"Jean","first_name":"Frédéric"},{"id":"87909","first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya"},{"full_name":"Zelenko, Igor","last_name":"Zelenko","first_name":"Igor"}],"publication_identifier":{"issn":["0046-5755","1572-9168"]},"year":"2020","title":"On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry","intvolume":"       213","date_updated":"2022-01-26T13:19:39Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.1007/s10711-020-00581-z","publication":"Geometriae Dedicata","issue":"1","date_created":"2022-01-26T13:19:18Z","department":[{"_id":"636"}],"keyword":["Geometry and Topology"],"type":"journal_article"},{"date_updated":"2022-01-26T13:39:01Z","year":"2020","title":"The turnpike property in maximization of microbial metabolite production","status":"public","author":[{"full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya","id":"87909"},{"last_name":"Caillau","first_name":"Jean-Baptiste","full_name":"Caillau, Jean-Baptiste"},{"first_name":"Walid","last_name":"Djema","full_name":"Djema, Walid"},{"last_name":"Giraldi","first_name":"Laetitia","full_name":"Giraldi, Laetitia"},{"full_name":"Jean-Luc, Jean-Luc","first_name":"Jean-Luc","last_name":"Jean-Luc"},{"full_name":"Pomet, Jean-Baptiste","last_name":"Pomet","first_name":"Jean-Baptiste"}],"conference":{"name":"IFAC 2020 - 21rst IFAC World Congress"},"user_id":"87909","main_file_link":[{"open_access":"1","url":"https://hal.archives-ouvertes.fr/hal-02916081/document"}],"language":[{"iso":"eng"}],"_id":"29546","extern":"1","quality_controlled":"1","citation":{"apa":"Maslovskaya, S., Caillau, J.-B., Djema, W., Giraldi, L., Jean-Luc, J.-L., &#38; Pomet, J.-B. (2020). <i>The turnpike property in maximization of microbial metabolite production</i>. IFAC 2020 - 21rst IFAC World Congress.","mla":"Maslovskaya, Sofya, et al. <i>The Turnpike Property in Maximization of Microbial Metabolite Production</i>. 2020.","ieee":"S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, and J.-B. Pomet, “The turnpike property in maximization of microbial metabolite production,” presented at the IFAC 2020 - 21rst IFAC World Congress, 2020.","ama":"Maslovskaya S, Caillau J-B, Djema W, Giraldi L, Jean-Luc J-L, Pomet J-B. The turnpike property in maximization of microbial metabolite production. In: ; 2020.","short":"S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, J.-B. Pomet, in: 2020.","chicago":"Maslovskaya, Sofya, Jean-Baptiste Caillau, Walid Djema, Laetitia Giraldi, Jean-Luc Jean-Luc, and Jean-Baptiste Pomet. “The Turnpike Property in Maximization of Microbial Metabolite Production,” 2020.","bibtex":"@inproceedings{Maslovskaya_Caillau_Djema_Giraldi_Jean-Luc_Pomet_2020, title={The turnpike property in maximization of microbial metabolite production}, author={Maslovskaya, Sofya and Caillau, Jean-Baptiste and Djema, Walid and Giraldi, Laetitia and Jean-Luc, Jean-Luc and Pomet, Jean-Baptiste}, year={2020} }"},"type":"conference_abstract","department":[{"_id":"636"}],"oa":"1","date_created":"2022-01-26T13:26:36Z"},{"department":[{"_id":"636"}],"type":"book_chapter","date_created":"2022-01-18T12:58:18Z","place":"Cham","citation":{"chicago":"Flaßkamp, K., Sina Ober-Blöbaum, and S.  Peitz. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” In <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 209–37. Cham: Springer International Publishing, 2020.","short":"K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer International Publishing, Cham, 2020, pp. 209–237.","apa":"Flaßkamp, K., Ober-Blöbaum, S., &#38; Peitz, S. (2020). Symmetry in optimal control: A multiobjective model predictive control approach. In O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, &#38; K. Padberg-Gehle (Eds.), <i>Advances in Dynamics, Optimization and Computation</i> (pp. 209–237). Springer International Publishing.","ieee":"K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in optimal control: A multiobjective model predictive control approach,” in <i>Advances in Dynamics, Optimization and Computation</i>, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 209–237.","ama":"Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in optimal control: A multiobjective model predictive control approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum S, Padberg-Gehle K, eds. <i>Advances in Dynamics, Optimization and Computation</i>. Springer International Publishing; 2020:209-237.","bibtex":"@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry in optimal control: A multiobjective model predictive control approach}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer International Publishing}, author={Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. }, editor={Junge, Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2020}, pages={209–237} }","mla":"Flaßkamp, K., et al. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge et al., Springer International Publishing, 2020, pp. 209–37."},"publication":"Advances in Dynamics, Optimization and Computation","editor":[{"full_name":"Junge, Oliver","first_name":"Oliver","last_name":"Junge"},{"full_name":"Schütze, Oliver","first_name":"Oliver","last_name":"Schütze"},{"first_name":"Gary","last_name":"Froyland","full_name":"Froyland, Gary"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Padberg-Gehle, Kathrin","first_name":"Kathrin","last_name":"Padberg-Gehle"}],"user_id":"15694","_id":"29413","language":[{"iso":"eng"}],"publisher":"Springer International Publishing","page":"209-237","date_updated":"2023-11-08T08:15:14Z","author":[{"last_name":"Flaßkamp","first_name":"K.","full_name":"Flaßkamp, K."},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"full_name":"Peitz, S. ","last_name":"Peitz","first_name":"S. "}],"status":"public","year":"2020","title":"Symmetry in optimal control: A multiobjective model predictive control approach"},{"citation":{"ieee":"R. Gerlach and A. Ziessler, “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems,” in <i>Advances in Dynamics, Optimization and Computation</i>, vol. 304, O. Junge, O. Schütze, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 66–85.","apa":"Gerlach, R., &#38; Ziessler, A. (2020). The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In O. Junge, O. Schütze, S. Ober-Blöbaum, &#38; K. Padberg-Gehle (Eds.), <i>Advances in Dynamics, Optimization and Computation</i> (Vol. 304, pp. 66–85). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">https://doi.org/10.1007/978-3-030-51264-4_3</a>","short":"R. Gerlach, A. Ziessler, in: O. Junge, O. Schütze, S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation, Springer International Publishing, Cham, 2020, pp. 66–85.","chicago":"Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” In <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge, Oliver Schütze, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 304:66–85. Studies in Systems, Decision and Control. Cham: Springer International Publishing, 2020. <a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">https://doi.org/10.1007/978-3-030-51264-4_3</a>.","mla":"Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” <i>Advances in Dynamics, Optimization and Computation</i>, edited by Oliver Junge et al., vol. 304, Springer International Publishing, 2020, pp. 66–85, doi:<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>.","bibtex":"@inbook{Gerlach_Ziessler_2020, place={Cham}, series={Studies in Systems, Decision and Control}, title={The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems}, volume={304}, DOI={<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>}, booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer International Publishing}, author={Gerlach, Raphael and Ziessler, Adrian}, editor={Junge, Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2020}, pages={66–85}, collection={Studies in Systems, Decision and Control} }","ama":"Gerlach R, Ziessler A. The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In: Junge O, Schütze O, Ober-Blöbaum S, Padberg-Gehle K, eds. <i>Advances in Dynamics, Optimization and Computation</i>. Vol 304. Studies in Systems, Decision and Control. Springer International Publishing; 2020:66-85. doi:<a href=\"https://doi.org/10.1007/978-3-030-51264-4_3\">10.1007/978-3-030-51264-4_3</a>"},"place":"Cham","status":"public","user_id":"32655","editor":[{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"},{"last_name":"Schütze","first_name":"Oliver","full_name":"Schütze, Oliver"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Kathrin","last_name":"Padberg-Gehle","full_name":"Padberg-Gehle, Kathrin"}],"volume":304,"page":"66-85","_id":"17994","publisher":"Springer International Publishing","abstract":[{"text":"In this work we review the novel framework for the computation of finite dimensional invariant sets of infinite dimensional dynamical systems developed in [6] and [36]. By utilizing results on embedding techniques for infinite dimensional systems we extend a classical subdivision scheme [8] as well as a continuation algorithm [7] for the computation of attractors and invariant manifolds of finite dimensional systems to the infinite dimensional case. We show how to implement this approach for the analysis of delay differential equations and partial differential equations and illustrate the feasibility of our implementation by computing the attractor of the Mackey-Glass equation and the unstable manifold of the one-dimensional Kuramoto-Sivashinsky equation.","lang":"eng"}],"publication":"Advances in Dynamics, Optimization and Computation","type":"book_chapter","department":[{"_id":"101"}],"date_created":"2020-08-14T15:02:22Z","date_updated":"2023-11-17T13:13:25Z","publication_status":"published","intvolume":"       304","title":"The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems","year":"2020","publication_identifier":{"issn":["2198-4182","2198-4190"],"isbn":["9783030512637","9783030512644"]},"author":[{"id":"32655","last_name":"Gerlach","first_name":"Raphael","full_name":"Gerlach, Raphael"},{"last_name":"Ziessler","first_name":"Adrian","full_name":"Ziessler, Adrian"}],"doi":"10.1007/978-3-030-51264-4_3","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-030-51264-4_3"}],"language":[{"iso":"eng"}],"series_title":"Studies in Systems, Decision and Control"},{"citation":{"ieee":"M. Dellnitz, B. Gebken, R. Gerlach, and S. Klus, “On the equivariance properties of self-adjoint matrices,” <i>Dynamical Systems</i>, vol. 35, no. 2, pp. 197–215, 2020, doi: <a href=\"https://doi.org/10.1080/14689367.2019.1661355\">10.1080/14689367.2019.1661355</a>.","apa":"Dellnitz, M., Gebken, B., Gerlach, R., &#38; Klus, S. (2020). On the equivariance properties of self-adjoint matrices. <i>Dynamical Systems</i>, <i>35</i>(2), 197–215. <a href=\"https://doi.org/10.1080/14689367.2019.1661355\">https://doi.org/10.1080/14689367.2019.1661355</a>","short":"M. Dellnitz, B. Gebken, R. Gerlach, S. Klus, Dynamical Systems 35 (2020) 197–215.","chicago":"Dellnitz, Michael, Bennet Gebken, Raphael Gerlach, and Stefan Klus. “On the Equivariance Properties of Self-Adjoint Matrices.” <i>Dynamical Systems</i> 35, no. 2 (2020): 197–215. <a href=\"https://doi.org/10.1080/14689367.2019.1661355\">https://doi.org/10.1080/14689367.2019.1661355</a>.","mla":"Dellnitz, Michael, et al. “On the Equivariance Properties of Self-Adjoint Matrices.” <i>Dynamical Systems</i>, vol. 35, no. 2, 2020, pp. 197–215, doi:<a href=\"https://doi.org/10.1080/14689367.2019.1661355\">10.1080/14689367.2019.1661355</a>.","bibtex":"@article{Dellnitz_Gebken_Gerlach_Klus_2020, title={On the equivariance properties of self-adjoint matrices}, volume={35}, DOI={<a href=\"https://doi.org/10.1080/14689367.2019.1661355\">10.1080/14689367.2019.1661355</a>}, number={2}, journal={Dynamical Systems}, author={Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}, year={2020}, pages={197–215} }","ama":"Dellnitz M, Gebken B, Gerlach R, Klus S. On the equivariance properties of self-adjoint matrices. <i>Dynamical Systems</i>. 2020;35(2):197-215. doi:<a href=\"https://doi.org/10.1080/14689367.2019.1661355\">10.1080/14689367.2019.1661355</a>"},"status":"public","user_id":"32655","volume":35,"page":"197-215","_id":"16712","abstract":[{"lang":"eng","text":"We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi) where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions."}],"publication":"Dynamical Systems","issue":"2","type":"journal_article","department":[{"_id":"101"}],"date_created":"2020-04-16T14:07:25Z","publication_status":"published","date_updated":"2023-11-17T13:12:59Z","intvolume":"        35","year":"2020","title":"On the equivariance properties of self-adjoint matrices","author":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"last_name":"Gebken","first_name":"Bennet","full_name":"Gebken, Bennet","id":"32643"},{"full_name":"Gerlach, Raphael","first_name":"Raphael","last_name":"Gerlach","id":"32655"},{"full_name":"Klus, Stefan","last_name":"Klus","first_name":"Stefan"}],"publication_identifier":{"issn":["1468-9367","1468-9375"]},"doi":"10.1080/14689367.2019.1661355","main_file_link":[{"url":"https://doi.org/10.1080/14689367.2019.1661355"}],"language":[{"iso":"eng"}]},{"status":"public","page":"638-728","publisher":"Oxford University Press (OUP)","_id":"45954","user_id":"100441","volume":41,"citation":{"mla":"Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal of Numerical Analysis</i>, vol. 41, no. 1, Oxford University Press (OUP), 2020, pp. 638–728, doi:<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>.","ama":"Hipp D, Kovács B. Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical Analysis</i>. 2020;41(1):638-728. doi:<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>","bibtex":"@article{Hipp_Kovács_2020, title={Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}, volume={41}, DOI={<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Hipp, David and Kovács, Balázs}, year={2020}, pages={638–728} }","apa":"Hipp, D., &#38; Kovács, B. (2020). Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical Analysis</i>, <i>41</i>(1), 638–728. <a href=\"https://doi.org/10.1093/imanum/drz073\">https://doi.org/10.1093/imanum/drz073</a>","ieee":"D. Hipp and B. Kovács, “Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates,” <i>IMA Journal of Numerical Analysis</i>, vol. 41, no. 1, pp. 638–728, 2020, doi: <a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>.","chicago":"Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal of Numerical Analysis</i> 41, no. 1 (2020): 638–728. <a href=\"https://doi.org/10.1093/imanum/drz073\">https://doi.org/10.1093/imanum/drz073</a>.","short":"D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 638–728."},"title":"Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates","year":"2020","author":[{"full_name":"Hipp, David","last_name":"Hipp","first_name":"David"},{"first_name":"Balázs","last_name":"Kovács","full_name":"Kovács, Balázs"}],"publication_identifier":{"issn":["0272-4979","1464-3642"]},"date_updated":"2024-04-03T09:14:14Z","publication_status":"published","intvolume":"        41","language":[{"iso":"eng"}],"doi":"10.1093/imanum/drz073","publication":"IMA Journal of Numerical Analysis","issue":"1","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>"}],"date_created":"2023-07-10T11:42:43Z","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"department":[{"_id":"841"}]},{"date_created":"2023-07-10T11:42:31Z","department":[{"_id":"841"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"publication":"IMA Journal of Numerical Analysis","issue":"1","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>$L^2$ norm error estimates of semi- and full discretizations of wave equations with dynamic boundary conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied. The analysis rests on an abstract formulation and error estimates, via energy techniques, within this abstract setting. Four prototypical linear wave equations with dynamic boundary conditions are analysed, which fit into the abstract framework. For problems with velocity terms or with acoustic boundary conditions we prove surprising results: for such problems the spatial convergence order is shown to be less than 2. These can also be observed in the presented numerical experiments.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"doi":"10.1093/imanum/drz073","publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"first_name":"David","last_name":"Hipp","full_name":"Hipp, David"},{"full_name":"Kovács, Balázs","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","id":"100441"}],"year":"2020","title":"Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates","intvolume":"        41","publication_status":"published","date_updated":"2024-04-03T09:20:44Z","citation":{"chicago":"Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal of Numerical Analysis</i> 41, no. 1 (2020): 638–728. <a href=\"https://doi.org/10.1093/imanum/drz073\">https://doi.org/10.1093/imanum/drz073</a>.","short":"D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 638–728.","apa":"Hipp, D., &#38; Kovács, B. (2020). Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical Analysis</i>, <i>41</i>(1), 638–728. <a href=\"https://doi.org/10.1093/imanum/drz073\">https://doi.org/10.1093/imanum/drz073</a>","ieee":"D. Hipp and B. Kovács, “Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates,” <i>IMA Journal of Numerical Analysis</i>, vol. 41, no. 1, pp. 638–728, 2020, doi: <a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>.","ama":"Hipp D, Kovács B. Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical Analysis</i>. 2020;41(1):638-728. doi:<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>","bibtex":"@article{Hipp_Kovács_2020, title={Finite element error analysis of wave equations with dynamic boundary conditions: <i>L</i>2 estimates}, volume={41}, DOI={<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Hipp, David and Kovács, Balázs}, year={2020}, pages={638–728} }","mla":"Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal of Numerical Analysis</i>, vol. 41, no. 1, Oxford University Press (OUP), 2020, pp. 638–728, doi:<a href=\"https://doi.org/10.1093/imanum/drz073\">10.1093/imanum/drz073</a>."},"_id":"45953","publisher":"Oxford University Press (OUP)","page":"638-728","volume":41,"user_id":"100441","status":"public"},{"publication":"Mathematics of Computation","issue":"329","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"department":[{"_id":"841"}],"date_created":"2023-07-10T11:42:57Z","publication_status":"published","date_updated":"2024-04-03T09:20:36Z","intvolume":"        90","year":"2020","title":"Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation","author":[{"full_name":"Akrivis, Georgios","last_name":"Akrivis","first_name":"Georgios"},{"full_name":"Feischl, Michael","last_name":"Feischl","first_name":"Michael"},{"id":"100441","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs"},{"full_name":"Lubich, Christian","last_name":"Lubich","first_name":"Christian"}],"publication_identifier":{"issn":["0025-5718","1088-6842"]},"doi":"10.1090/mcom/3597","language":[{"iso":"eng"}],"citation":{"mla":"Akrivis, Georgios, et al. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” <i>Mathematics of Computation</i>, vol. 90, no. 329, American Mathematical Society (AMS), 2020, pp. 995–1038, doi:<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>.","ama":"Akrivis G, Feischl M, Kovács B, Lubich C. Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. <i>Mathematics of Computation</i>. 2020;90(329):995-1038. doi:<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>","bibtex":"@article{Akrivis_Feischl_Kovács_Lubich_2020, title={Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}, volume={90}, DOI={<a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>}, number={329}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and Lubich, Christian}, year={2020}, pages={995–1038} }","apa":"Akrivis, G., Feischl, M., Kovács, B., &#38; Lubich, C. (2020). Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. <i>Mathematics of Computation</i>, <i>90</i>(329), 995–1038. <a href=\"https://doi.org/10.1090/mcom/3597\">https://doi.org/10.1090/mcom/3597</a>","ieee":"G. Akrivis, M. Feischl, B. Kovács, and C. Lubich, “Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation,” <i>Mathematics of Computation</i>, vol. 90, no. 329, pp. 995–1038, 2020, doi: <a href=\"https://doi.org/10.1090/mcom/3597\">10.1090/mcom/3597</a>.","chicago":"Akrivis, Georgios, Michael Feischl, Balázs Kovács, and Christian Lubich. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” <i>Mathematics of Computation</i> 90, no. 329 (2020): 995–1038. <a href=\"https://doi.org/10.1090/mcom/3597\">https://doi.org/10.1090/mcom/3597</a>.","short":"G. Akrivis, M. Feischl, B. Kovács, C. Lubich, Mathematics of Computation 90 (2020) 995–1038."},"status":"public","user_id":"100441","volume":90,"page":"995-1038","_id":"45955","publisher":"American Mathematical Society (AMS)"},{"issue":"4","publication":"Interfaces and Free Boundaries","date_created":"2023-07-10T11:42:14Z","department":[{"_id":"841"}],"keyword":["Applied Mathematics"],"type":"journal_article","author":[{"full_name":"Kovács, Balázs","first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","id":"100441"},{"first_name":"Buyang","last_name":"Li","full_name":"Li, Buyang"},{"last_name":"Lubich","first_name":"Christian","full_name":"Lubich, Christian"}],"publication_identifier":{"issn":["1463-9963"]},"title":"A convergent algorithm for forced mean curvature flow driven by diffusion on the surface","year":"2020","intvolume":"        22","date_updated":"2024-04-03T09:21:02Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.4171/ifb/446","citation":{"chicago":"Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Algorithm for Forced Mean Curvature Flow Driven by Diffusion on the Surface.” <i>Interfaces and Free Boundaries</i> 22, no. 4 (2020): 443–64. <a href=\"https://doi.org/10.4171/ifb/446\">https://doi.org/10.4171/ifb/446</a>.","short":"B. Kovács, B. Li, C. Lubich, Interfaces and Free Boundaries 22 (2020) 443–464.","ieee":"B. Kovács, B. Li, and C. Lubich, “A convergent algorithm for forced mean curvature flow driven by diffusion on the surface,” <i>Interfaces and Free Boundaries</i>, vol. 22, no. 4, pp. 443–464, 2020, doi: <a href=\"https://doi.org/10.4171/ifb/446\">10.4171/ifb/446</a>.","apa":"Kovács, B., Li, B., &#38; Lubich, C. (2020). A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. <i>Interfaces and Free Boundaries</i>, <i>22</i>(4), 443–464. <a href=\"https://doi.org/10.4171/ifb/446\">https://doi.org/10.4171/ifb/446</a>","bibtex":"@article{Kovács_Li_Lubich_2020, title={A convergent algorithm for forced mean curvature flow driven by diffusion on the surface}, volume={22}, DOI={<a href=\"https://doi.org/10.4171/ifb/446\">10.4171/ifb/446</a>}, number={4}, journal={Interfaces and Free Boundaries}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2020}, pages={443–464} }","ama":"Kovács B, Li B, Lubich C. A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. <i>Interfaces and Free Boundaries</i>. 2020;22(4):443-464. doi:<a href=\"https://doi.org/10.4171/ifb/446\">10.4171/ifb/446</a>","mla":"Kovács, Balázs, et al. “A Convergent Algorithm for Forced Mean Curvature Flow Driven by Diffusion on the Surface.” <i>Interfaces and Free Boundaries</i>, vol. 22, no. 4, European Mathematical Society - EMS - Publishing House GmbH, 2020, pp. 443–64, doi:<a href=\"https://doi.org/10.4171/ifb/446\">10.4171/ifb/446</a>."},"status":"public","publisher":"European Mathematical Society - EMS - Publishing House GmbH","_id":"45952","page":"443-464","volume":22,"user_id":"100441"},{"title":"On the distribution of αp modulo one in imaginary quadratic number fields with class number one","year":"2020","status":"public","author":[{"first_name":"St.","last_name":"Baier","full_name":"Baier, St."},{"id":"106108","full_name":"Technau, Marc","first_name":"Marc","orcid":"0000-0001-9650-2459","last_name":"Technau"}],"date_updated":"2024-07-24T07:23:57Z","intvolume":"        32","page":"719–760","language":[{"iso":"eng"}],"_id":"55288","doi":"10.5802/jtnb.1141","user_id":"106108","volume":32,"publication":"J. Théor. Nombres Bordx.","issue":"2","citation":{"apa":"Baier, St., &#38; Technau, M. (2020). On the distribution of αp modulo one in imaginary quadratic number fields with class number one. <i>J. Théor. Nombres Bordx.</i>, <i>32</i>(2), 719–760. <a href=\"https://doi.org/10.5802/jtnb.1141\">https://doi.org/10.5802/jtnb.1141</a>","ieee":"St. Baier and M. Technau, “On the distribution of αp modulo one in imaginary quadratic number fields with class number one,” <i>J. Théor. Nombres Bordx.</i>, vol. 32, no. 2, pp. 719–760, 2020, doi: <a href=\"https://doi.org/10.5802/jtnb.1141\">10.5802/jtnb.1141</a>.","chicago":"Baier, St., and Marc Technau. “On the Distribution of Αp modulo One in Imaginary Quadratic Number Fields with Class Number One.” <i>J. Théor. Nombres Bordx.</i> 32, no. 2 (2020): 719–760. <a href=\"https://doi.org/10.5802/jtnb.1141\">https://doi.org/10.5802/jtnb.1141</a>.","short":"St. Baier, M. Technau, J. Théor. Nombres Bordx. 32 (2020) 719–760.","mla":"Baier, St., and Marc Technau. “On the Distribution of Αp modulo One in Imaginary Quadratic Number Fields with Class Number One.” <i>J. Théor. Nombres Bordx.</i>, vol. 32, no. 2, 2020, pp. 719–760, doi:<a href=\"https://doi.org/10.5802/jtnb.1141\">10.5802/jtnb.1141</a>.","ama":"Baier St, Technau M. On the distribution of αp modulo one in imaginary quadratic number fields with class number one. <i>J Théor Nombres Bordx</i>. 2020;32(2):719–760. doi:<a href=\"https://doi.org/10.5802/jtnb.1141\">10.5802/jtnb.1141</a>","bibtex":"@article{Baier_Technau_2020, title={On the distribution of αp modulo one in imaginary quadratic number fields with class number one}, volume={32}, DOI={<a href=\"https://doi.org/10.5802/jtnb.1141\">10.5802/jtnb.1141</a>}, number={2}, journal={J. Théor. Nombres Bordx.}, author={Baier, St. and Technau, Marc}, year={2020}, pages={719–760} }"},"date_created":"2024-07-16T11:09:02Z","type":"journal_article","department":[{"_id":"102"}]},{"volume":208,"user_id":"106108","doi":"10.1016/j.jnt.2019.07.022","language":[{"iso":"eng"}],"_id":"55286","page":"148–167","intvolume":"       208","date_updated":"2024-07-24T07:24:11Z","author":[{"orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc","full_name":"Technau, Marc","id":"106108"}],"status":"public","title":"Modular hyperbolas and Beatty sequences","year":"2020","department":[{"_id":"102"}],"type":"journal_article","date_created":"2024-07-16T11:09:02Z","extern":"1","citation":{"short":"M. Technau, J. Number Theory 208 (2020) 148–167.","chicago":"Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” <i>J. Number Theory</i> 208 (2020): 148–167. <a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">https://doi.org/10.1016/j.jnt.2019.07.022</a>.","ieee":"M. Technau, “Modular hyperbolas and Beatty sequences,” <i>J. Number Theory</i>, vol. 208, pp. 148–167, 2020, doi: <a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">10.1016/j.jnt.2019.07.022</a>.","apa":"Technau, M. (2020). Modular hyperbolas and Beatty sequences. <i>J. Number Theory</i>, <i>208</i>, 148–167. <a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">https://doi.org/10.1016/j.jnt.2019.07.022</a>","bibtex":"@article{Technau_2020, title={Modular hyperbolas and Beatty sequences}, volume={208}, DOI={<a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">10.1016/j.jnt.2019.07.022</a>}, journal={J. Number Theory}, author={Technau, Marc}, year={2020}, pages={148–167} }","ama":"Technau M. Modular hyperbolas and Beatty sequences. <i>J Number Theory</i>. 2020;208:148–167. doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">10.1016/j.jnt.2019.07.022</a>","mla":"Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” <i>J. Number Theory</i>, vol. 208, 2020, pp. 148–167, doi:<a href=\"https://doi.org/10.1016/j.jnt.2019.07.022\">10.1016/j.jnt.2019.07.022</a>."},"publication":"J. Number Theory"},{"date_updated":"2024-07-24T07:25:54Z","intvolume":"        63","status":"public","title":"Kloosterman sums with twice-differentiable functions","year":"2020","author":[{"first_name":"I. E.","last_name":"Shparlinski","full_name":"Shparlinski, I. E."},{"full_name":"Technau, Marc","first_name":"Marc","last_name":"Technau","orcid":"0000-0001-9650-2459","id":"106108"}],"user_id":"106108","doi":"10.7169/facm/1845","volume":63,"page":"113–124","language":[{"iso":"eng"}],"_id":"55287","extern":"1","publication":"Funct. Approximatio, Comment. Math.","issue":"1","citation":{"apa":"Shparlinski, I. E., &#38; Technau, M. (2020). Kloosterman sums with twice-differentiable functions. <i>Funct. Approximatio, Comment. Math.</i>, <i>63</i>(1), 113–124. <a href=\"https://doi.org/10.7169/facm/1845\">https://doi.org/10.7169/facm/1845</a>","ieee":"I. E. Shparlinski and M. Technau, “Kloosterman sums with twice-differentiable functions,” <i>Funct. Approximatio, Comment. Math.</i>, vol. 63, no. 1, pp. 113–124, 2020, doi: <a href=\"https://doi.org/10.7169/facm/1845\">10.7169/facm/1845</a>.","chicago":"Shparlinski, I. E., and Marc Technau. “Kloosterman Sums with Twice-Differentiable Functions.” <i>Funct. Approximatio, Comment. Math.</i> 63, no. 1 (2020): 113–124. <a href=\"https://doi.org/10.7169/facm/1845\">https://doi.org/10.7169/facm/1845</a>.","short":"I.E. Shparlinski, M. Technau, Funct. Approximatio, Comment. Math. 63 (2020) 113–124.","mla":"Shparlinski, I. E., and Marc Technau. “Kloosterman Sums with Twice-Differentiable Functions.” <i>Funct. Approximatio, Comment. Math.</i>, vol. 63, no. 1, 2020, pp. 113–124, doi:<a href=\"https://doi.org/10.7169/facm/1845\">10.7169/facm/1845</a>.","ama":"Shparlinski IE, Technau M. Kloosterman sums with twice-differentiable functions. <i>Funct Approximatio, Comment Math</i>. 2020;63(1):113–124. doi:<a href=\"https://doi.org/10.7169/facm/1845\">10.7169/facm/1845</a>","bibtex":"@article{Shparlinski_Technau_2020, title={Kloosterman sums with twice-differentiable functions}, volume={63}, DOI={<a href=\"https://doi.org/10.7169/facm/1845\">10.7169/facm/1845</a>}, number={1}, journal={Funct. Approximatio, Comment. Math.}, author={Shparlinski, I. E. and Technau, Marc}, year={2020}, pages={113–124} }"},"type":"journal_article","department":[{"_id":"102"}],"date_created":"2024-07-16T11:09:02Z"},{"date_created":"2024-07-16T11:09:02Z","department":[{"_id":"102"}],"type":"journal_article","citation":{"bibtex":"@article{Barth_Beck_Dose_Glaßer_Michler_Technau_2020, title={Emptiness problems for integer circuits}, volume={824–825}, DOI={<a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">10.1016/j.tcs.2020.03.023</a>}, journal={Theoretical Computer Science}, author={Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}, year={2020}, pages={11–35} }","ama":"Barth D, Beck M, Dose T, Glaßer Ch, Michler L, Technau M. Emptiness problems for integer circuits. <i>Theoretical Computer Science</i>. 2020;824-825:11–35. doi:<a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">10.1016/j.tcs.2020.03.023</a>","mla":"Barth, D., et al. “Emptiness Problems for Integer Circuits.” <i>Theoretical Computer Science</i>, vol. 824–825, 2020, pp. 11–35, doi:<a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">10.1016/j.tcs.2020.03.023</a>.","chicago":"Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau. “Emptiness Problems for Integer Circuits.” <i>Theoretical Computer Science</i> 824–825 (2020): 11–35. <a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">https://doi.org/10.1016/j.tcs.2020.03.023</a>.","short":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, Theoretical Computer Science 824–825 (2020) 11–35.","ieee":"D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, “Emptiness problems for integer circuits,” <i>Theoretical Computer Science</i>, vol. 824–825, pp. 11–35, 2020, doi: <a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">10.1016/j.tcs.2020.03.023</a>.","apa":"Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M. (2020). Emptiness problems for integer circuits. <i>Theoretical Computer Science</i>, <i>824–825</i>, 11–35. <a href=\"https://doi.org/10.1016/j.tcs.2020.03.023\">https://doi.org/10.1016/j.tcs.2020.03.023</a>"},"publication":"Theoretical Computer Science","extern":"1","language":[{"iso":"eng"}],"_id":"55283","page":"11–35","volume":"824-825","doi":"10.1016/j.tcs.2020.03.023","user_id":"106108","author":[{"full_name":"Barth, D.","first_name":"D.","last_name":"Barth"},{"first_name":"M.","last_name":"Beck","full_name":"Beck, M."},{"full_name":"Dose, T.","first_name":"T.","last_name":"Dose"},{"last_name":"Glaßer","first_name":"Ch.","full_name":"Glaßer, Ch."},{"full_name":"Michler, L.","last_name":"Michler","first_name":"L."},{"id":"106108","full_name":"Technau, Marc","orcid":"0000-0001-9650-2459","last_name":"Technau","first_name":"Marc"}],"year":"2020","title":"Emptiness problems for integer circuits","status":"public","date_updated":"2024-07-24T07:25:29Z"},{"publication":"Acta Arithmetica","issue":"3","abstract":[{"text":"Let D<0 be a fundamental discriminant and denote by E(D) the exponent of the ideal class group Cl(D) of K=ℚ(√D). Under the assumption that no Siegel zeros exist we compute all such D with E(D) dividing 8. We compute all D with |D| ≤ 3.1⋅10²⁰ such that E(D) ≤ 8.","lang":"eng"}],"date_created":"2022-12-22T10:51:13Z","department":[{"_id":"102"}],"type":"journal_article","keyword":["Algebra and Number Theory"],"author":[{"full_name":"Elsenhans, Andreas-Stephan","last_name":"Elsenhans","first_name":"Andreas-Stephan"},{"id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen","last_name":"Klüners"},{"first_name":"Florin","last_name":"Nicolae","full_name":"Nicolae, Florin"}],"publication_identifier":{"issn":["0065-1036","1730-6264"]},"title":"Imaginary quadratic number fields with class groups of small exponent","year":"2020","intvolume":"       193","date_updated":"2023-03-06T10:19:53Z","publication_status":"published","language":[{"iso":"eng"}],"doi":"10.4064/aa180220-20-3","citation":{"bibtex":"@article{Elsenhans_Klüners_Nicolae_2020, title={Imaginary quadratic number fields with class groups of small exponent}, volume={193}, DOI={<a href=\"https://doi.org/10.4064/aa180220-20-3\">10.4064/aa180220-20-3</a>}, number={3}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen and Nicolae, Florin}, year={2020}, pages={217–233} }","ama":"Elsenhans A-S, Klüners J, Nicolae F. Imaginary quadratic number fields with class groups of small exponent. <i>Acta Arithmetica</i>. 2020;193(3):217-233. doi:<a href=\"https://doi.org/10.4064/aa180220-20-3\">10.4064/aa180220-20-3</a>","mla":"Elsenhans, Andreas-Stephan, et al. “Imaginary Quadratic Number Fields with Class Groups of Small Exponent.” <i>Acta Arithmetica</i>, vol. 193, no. 3, Institute of Mathematics, Polish Academy of Sciences, 2020, pp. 217–33, doi:<a href=\"https://doi.org/10.4064/aa180220-20-3\">10.4064/aa180220-20-3</a>.","short":"A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233.","chicago":"Elsenhans, Andreas-Stephan, Jürgen Klüners, and Florin Nicolae. “Imaginary Quadratic Number Fields with Class Groups of Small Exponent.” <i>Acta Arithmetica</i> 193, no. 3 (2020): 217–33. <a href=\"https://doi.org/10.4064/aa180220-20-3\">https://doi.org/10.4064/aa180220-20-3</a>.","ieee":"A.-S. Elsenhans, J. Klüners, and F. Nicolae, “Imaginary quadratic number fields with class groups of small exponent,” <i>Acta Arithmetica</i>, vol. 193, no. 3, pp. 217–233, 2020, doi: <a href=\"https://doi.org/10.4064/aa180220-20-3\">10.4064/aa180220-20-3</a>.","apa":"Elsenhans, A.-S., Klüners, J., &#38; Nicolae, F. (2020). Imaginary quadratic number fields with class groups of small exponent. <i>Acta Arithmetica</i>, <i>193</i>(3), 217–233. <a href=\"https://doi.org/10.4064/aa180220-20-3\">https://doi.org/10.4064/aa180220-20-3</a>"},"external_id":{"arxiv":["1803.02056 "]},"status":"public","publisher":"Institute of Mathematics, Polish Academy of Sciences","_id":"34842","page":"217-233","volume":193,"user_id":"93826"},{"abstract":[{"lang":"eng","text":"In this work we present a set-oriented path following method for the computation of relative global\r\nattractors of parameter-dependent dynamical systems. We start with an initial approximation of the\r\nrelative global attractor for a fixed parameter λ0 computed by a set-oriented subdivision method.\r\nBy using previously obtained approximations of the parameter-dependent relative global attractor\r\nwe can track it with respect to a one-dimensional parameter λ > λ0 without restarting the whole\r\nsubdivision procedure. We illustrate the feasibility of the set-oriented path following method by\r\nexploring the dynamics in low-dimensional models for shear flows during the transition to turbulence\r\nand of large-scale atmospheric regime changes .\r\n"}],"publication":"SIAM Journal on Applied Dynamical Systems","citation":{"short":"R. Gerlach, A. Ziessler, B. Eckhardt, M. Dellnitz, SIAM Journal on Applied Dynamical Systems (2020) 705–723.","chicago":"Gerlach, Raphael, Adrian Ziessler, Bruno Eckhardt, and Michael Dellnitz. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2020, 705–23. <a href=\"https://doi.org/10.1137/19m1247139\">https://doi.org/10.1137/19m1247139</a>.","ieee":"R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors,” <i>SIAM Journal on Applied Dynamical Systems</i>, pp. 705–723, 2020, doi: <a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>.","apa":"Gerlach, R., Ziessler, A., Eckhardt, B., &#38; Dellnitz, M. (2020). A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. <i>SIAM Journal on Applied Dynamical Systems</i>, 705–723. <a href=\"https://doi.org/10.1137/19m1247139\">https://doi.org/10.1137/19m1247139</a>","bibtex":"@article{Gerlach_Ziessler_Eckhardt_Dellnitz_2020, title={A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}, DOI={<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>}, journal={SIAM Journal on Applied Dynamical Systems}, author={Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}, year={2020}, pages={705–723} }","ama":"Gerlach R, Ziessler A, Eckhardt B, Dellnitz M. A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. <i>SIAM Journal on Applied Dynamical Systems</i>. Published online 2020:705-723. doi:<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>","mla":"Gerlach, Raphael, et al. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2020, pp. 705–23, doi:<a href=\"https://doi.org/10.1137/19m1247139\">10.1137/19m1247139</a>."},"type":"journal_article","department":[{"_id":"101"}],"date_created":"2020-04-16T14:05:41Z","publication_status":"published","date_updated":"2024-10-01T13:37:43Z","status":"public","year":"2020","title":"A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors","author":[{"id":"32655","first_name":"Raphael","last_name":"Gerlach","full_name":"Gerlach, Raphael"},{"full_name":"Ziessler, Adrian","first_name":"Adrian","last_name":"Ziessler"},{"full_name":"Eckhardt, Bruno","first_name":"Bruno","last_name":"Eckhardt"},{"last_name":"Dellnitz","first_name":"Michael","full_name":"Dellnitz, Michael"}],"publication_identifier":{"issn":["1536-0040"]},"user_id":"32655","doi":"10.1137/19m1247139","main_file_link":[{"url":"https://epubs.siam.org/doi/epdf/10.1137/19M1247139"}],"page":"705-723","_id":"16710","language":[{"iso":"eng"}]}]