--- _id: '16297' abstract: - lang: eng 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." author: - first_name: Carlos Ignacio full_name: Hernández Castellanos, Carlos Ignacio last_name: Hernández Castellanos - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: https://orcid.org/0000-0002-3389-793X citation: ama: Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. International Journal of Robust and Nonlinear Control. 2020;30(17):7593-7618. doi:10.1002/rnc.5197 apa: Hernández Castellanos, C. I., Ober-Blöbaum, S., & Peitz, S. (2020). Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty. International Journal of Robust and Nonlinear Control, 30(17), 7593–7618. https://doi.org/10.1002/rnc.5197 bibtex: '@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty}, volume={30(17)}, DOI={10.1002/rnc.5197}, 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} }' chicago: 'Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” International Journal of Robust and Nonlinear Control 30(17) (2020): 7593–7618. https://doi.org/10.1002/rnc.5197.' ieee: 'C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective Model Predictive Control for Nonlinear Systems  Under Uncertainty,” International Journal of Robust and Nonlinear Control, vol. 30(17), pp. 7593–7618, 2020, doi: 10.1002/rnc.5197.' mla: Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems  Under Uncertainty.” International Journal of Robust and Nonlinear Control, vol. 30(17), 2020, pp. 7593–618, doi:10.1002/rnc.5197. short: C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 30(17) (2020) 7593–7618. date_created: 2020-03-13T12:45:56Z date_updated: 2022-01-21T09:55:39Z department: - _id: '101' doi: 10.1002/rnc.5197 language: - iso: eng page: 7593-7618 publication: International Journal of Robust and Nonlinear Control status: public title: Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty type: journal_article user_id: '15694' volume: 30(17) year: '2020' ... --- _id: '29398' author: - first_name: C. I. O. full_name: Hernández Castellanos, C. I. O. last_name: Hernández Castellanos - first_name: G. full_name: Schütze, G. last_name: Schütze - first_name: J.-Q. full_name: Sun, J.-Q. last_name: Sun - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: G. full_name: Morales-Luna, G. last_name: Morales-Luna citation: 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. Mathematics. 2020;8(11):1959. apa: Hernández Castellanos, C. I. O., Schütze, G., Sun, J.-Q., Ober-Blöbaum, S., & Morales-Luna, G. (2020). Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping. Mathematics, 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} }' 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.” Mathematics 8(11):1959 (2020). 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,” Mathematics, vol. 8(11):1959, 2020. mla: Hernández Castellanos, C. I. O., et al. “Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping.” Mathematics, 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). date_created: 2022-01-18T11:08:28Z date_updated: 2022-01-21T09:57:35Z department: - _id: '636' language: - iso: eng publication: Mathematics status: public title: Numerical computation of lightly multi-objective robust optimal solutions by means of generalized cell mapping type: journal_article user_id: '15694' volume: 8(11):1959 year: '2020' ... --- _id: '29422' author: - first_name: Y. full_name: Lishkova, Y. last_name: Lishkova - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: M. full_name: Cannon, M. last_name: Cannon - first_name: S. full_name: Leyendecker, S. last_name: Leyendecker citation: ama: 'Lishkova Y, Ober-Blöbaum S, Cannon M, Leyendecker S. A multirate variational approach to simulation and optimal control for flexible spacecraft. In: Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe. ; 2020.' apa: Lishkova, Y., Ober-Blöbaum, S., Cannon, M., & Leyendecker, S. (2020). A multirate variational approach to simulation and optimal control for flexible spacecraft. Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe. 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} }' chicago: Lishkova, Y., Sina Ober-Blöbaum, M. Cannon, and S. Leyendecker. “A Multirate Variational Approach to Simulation and Optimal Control for Flexible Spacecraft.” 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. mla: Lishkova, Y., et al. “A Multirate Variational Approach to Simulation and Optimal Control for Flexible Spacecraft.” Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe, 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.' date_created: 2022-01-18T14:37:53Z date_updated: 2022-01-21T13:45:40Z department: - _id: '636' language: - iso: eng publication: Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe status: public title: A multirate variational approach to simulation and optimal control for flexible spacecraft type: conference user_id: '15694' year: '2020' ... --- _id: '29423' author: - first_name: T. full_name: Faulwasser, T. last_name: Faulwasser - first_name: K. full_name: Flaßkamp, K. last_name: Flaßkamp - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: 'K. ' full_name: 'Worthmann, K. ' last_name: Worthmann citation: ama: 'Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. In: 24th International Symposium on Mathematical Theory of Networks and Systems. ; 2020.' apa: Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., & Worthmann, K. (2020). A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. 24th International Symposium on Mathematical Theory of Networks and Systems. 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} }' 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 24th International Symposium on Mathematical Theory of Networks and Systems, 2020. 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. mla: Faulwasser, T., et al. “A Dissipativity Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical Systems.” 24th International Symposium on Mathematical Theory of Networks and Systems, 2020. short: 'T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: 24th International Symposium on Mathematical Theory of Networks and Systems, 2020.' date_created: 2022-01-18T14:42:07Z date_updated: 2022-01-21T13:46:57Z department: - _id: '636' language: - iso: eng publication: 24th International Symposium on Mathematical Theory of Networks and Systems status: public title: A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems type: conference user_id: '15694' year: '2020' ... --- _id: '29424' author: - first_name: 'J. ' full_name: 'Cresson, J. ' last_name: Cresson - first_name: F. full_name: Jiménez, F. last_name: Jiménez - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum citation: ama: 'Cresson J, Jiménez F, Ober-Blöbaum S. Modelling of the convection-diffusion equation through fractional restricted calculus of variations. In: 24th International Symposium on Mathematical Theory of Networks and Systems. ; 2020.' apa: Cresson, J., Jiménez, F., & Ober-Blöbaum, S. (2020). Modelling of the convection-diffusion equation through fractional restricted calculus of variations. 24th International Symposium on Mathematical Theory of Networks and Systems. 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} }' chicago: Cresson, J. , F. Jiménez, and Sina Ober-Blöbaum. “Modelling of the Convection-Diffusion Equation through Fractional Restricted Calculus of Variations.” In 24th International Symposium on Mathematical Theory of Networks and Systems, 2020. ieee: J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Modelling of the convection-diffusion equation through fractional restricted calculus of variations,” 2020. mla: Cresson, J., et al. “Modelling of the Convection-Diffusion Equation through Fractional Restricted Calculus of Variations.” 24th International Symposium on Mathematical Theory of Networks and Systems, 2020. short: 'J. Cresson, F. Jiménez, S. Ober-Blöbaum, in: 24th International Symposium on Mathematical Theory of Networks and Systems, 2020.' date_created: 2022-01-18T14:45:22Z date_updated: 2022-01-21T13:47:49Z department: - _id: '636' language: - iso: eng publication: 24th International Symposium on Mathematical Theory of Networks and Systems status: public title: Modelling of the convection-diffusion equation through fractional restricted calculus of variations type: conference user_id: '15694' year: '2020' ... --- _id: '29545' author: - first_name: Frédéric full_name: Jean, Frédéric last_name: Jean - first_name: Sofya full_name: Maslovskaya, Sofya id: '87909' last_name: Maslovskaya - first_name: Igor full_name: Zelenko, Igor last_name: Zelenko citation: ama: Jean F, Maslovskaya S, Zelenko I. On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry. Geometriae Dedicata. 2020;213(1):295-314. doi:10.1007/s10711-020-00581-z apa: Jean, F., Maslovskaya, S., & Zelenko, I. (2020). On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry. Geometriae Dedicata, 213(1), 295–314. https://doi.org/10.1007/s10711-020-00581-z bibtex: '@article{Jean_Maslovskaya_Zelenko_2020, title={On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry}, volume={213}, DOI={10.1007/s10711-020-00581-z}, 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} }' chicago: 'Jean, Frédéric, Sofya Maslovskaya, and Igor Zelenko. “On Weyl’s Type Theorems and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” Geometriae Dedicata 213, no. 1 (2020): 295–314. https://doi.org/10.1007/s10711-020-00581-z.' ieee: 'F. Jean, S. Maslovskaya, and I. Zelenko, “On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry,” Geometriae Dedicata, vol. 213, no. 1, pp. 295–314, 2020, doi: 10.1007/s10711-020-00581-z.' mla: Jean, Frédéric, et al. “On Weyl’s Type Theorems and Genericity of Projective Rigidity in Sub-Riemannian Geometry.” Geometriae Dedicata, vol. 213, no. 1, Springer Science and Business Media LLC, 2020, pp. 295–314, doi:10.1007/s10711-020-00581-z. short: F. Jean, S. Maslovskaya, I. Zelenko, Geometriae Dedicata 213 (2020) 295–314. date_created: 2022-01-26T13:19:18Z date_updated: 2022-01-26T13:19:39Z department: - _id: '636' doi: 10.1007/s10711-020-00581-z intvolume: ' 213' issue: '1' keyword: - Geometry and Topology language: - iso: eng page: 295-314 publication: Geometriae Dedicata publication_identifier: issn: - 0046-5755 - 1572-9168 publication_status: published publisher: Springer Science and Business Media LLC status: public title: On Weyl’s type theorems and genericity of projective rigidity in sub-Riemannian geometry type: journal_article user_id: '87909' volume: 213 year: '2020' ... --- _id: '29546' author: - first_name: Sofya full_name: Maslovskaya, Sofya id: '87909' last_name: Maslovskaya - first_name: Jean-Baptiste full_name: Caillau, Jean-Baptiste last_name: Caillau - first_name: Walid full_name: Djema, Walid last_name: Djema - first_name: Laetitia full_name: Giraldi, Laetitia last_name: Giraldi - first_name: Jean-Luc full_name: Jean-Luc, Jean-Luc last_name: Jean-Luc - first_name: Jean-Baptiste full_name: Pomet, Jean-Baptiste last_name: Pomet citation: 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.' apa: Maslovskaya, S., Caillau, J.-B., Djema, W., Giraldi, L., Jean-Luc, J.-L., & Pomet, J.-B. (2020). The turnpike property in maximization of microbial metabolite production. IFAC 2020 - 21rst IFAC World Congress. 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} }' 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. 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. mla: Maslovskaya, Sofya, et al. The Turnpike Property in Maximization of Microbial Metabolite Production. 2020. short: 'S. Maslovskaya, J.-B. Caillau, W. Djema, L. Giraldi, J.-L. Jean-Luc, J.-B. Pomet, in: 2020.' conference: name: IFAC 2020 - 21rst IFAC World Congress date_created: 2022-01-26T13:26:36Z date_updated: 2022-01-26T13:39:01Z department: - _id: '636' extern: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://hal.archives-ouvertes.fr/hal-02916081/document oa: '1' quality_controlled: '1' status: public title: The turnpike property in maximization of microbial metabolite production type: conference_abstract user_id: '87909' year: '2020' ... --- _id: '29413' author: - first_name: K. full_name: Flaßkamp, K. last_name: Flaßkamp - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: 'S. ' full_name: 'Peitz, S. ' last_name: Peitz citation: 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. Advances in Dynamics, Optimization and Computation. Springer International Publishing; 2020:209-237.' apa: 'Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in optimal control: A multiobjective model predictive control approach. In O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation (pp. 209–237). Springer International Publishing.' 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} }' chicago: 'Flaßkamp, K., Sina Ober-Blöbaum, and S. Peitz. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” In Advances in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 209–37. Cham: Springer International Publishing, 2020.' ieee: 'K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in optimal control: A multiobjective model predictive control approach,” in Advances in Dynamics, Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 209–237.' mla: 'Flaßkamp, K., et al. “Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach.” Advances in Dynamics, Optimization and Computation, edited by Oliver Junge et al., Springer International Publishing, 2020, pp. 209–37.' 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.' date_created: 2022-01-18T12:58:18Z date_updated: 2023-11-08T08:15:14Z department: - _id: '636' editor: - first_name: Oliver full_name: Junge, Oliver last_name: Junge - first_name: Oliver full_name: Schütze, Oliver last_name: Schütze - first_name: Gary full_name: Froyland, Gary last_name: Froyland - first_name: Sina full_name: Ober-Blöbaum, Sina last_name: Ober-Blöbaum - first_name: Kathrin full_name: Padberg-Gehle, Kathrin last_name: Padberg-Gehle language: - iso: eng page: 209-237 place: Cham publication: Advances in Dynamics, Optimization and Computation publisher: Springer International Publishing status: public title: 'Symmetry in optimal control: A multiobjective model predictive control approach' type: book_chapter user_id: '15694' year: '2020' ... --- _id: '17994' abstract: - lang: eng 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. author: - first_name: Raphael full_name: Gerlach, Raphael id: '32655' last_name: Gerlach - first_name: Adrian full_name: Ziessler, Adrian last_name: Ziessler citation: 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. Advances in Dynamics, Optimization and Computation. Vol 304. Studies in Systems, Decision and Control. Springer International Publishing; 2020:66-85. doi:10.1007/978-3-030-51264-4_3' apa: Gerlach, R., & Ziessler, A. (2020). The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems. In O. Junge, O. Schütze, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation (Vol. 304, pp. 66–85). Springer International Publishing. https://doi.org/10.1007/978-3-030-51264-4_3 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={10.1007/978-3-030-51264-4_3}, 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} }' chicago: 'Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” In Advances in Dynamics, Optimization and Computation, 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. https://doi.org/10.1007/978-3-030-51264-4_3.' ieee: 'R. Gerlach and A. Ziessler, “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems,” in Advances in Dynamics, Optimization and Computation, vol. 304, O. Junge, O. Schütze, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp. 66–85.' mla: Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems.” Advances in Dynamics, Optimization and Computation, edited by Oliver Junge et al., vol. 304, Springer International Publishing, 2020, pp. 66–85, doi:10.1007/978-3-030-51264-4_3. 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.' date_created: 2020-08-14T15:02:22Z date_updated: 2023-11-17T13:13:25Z department: - _id: '101' doi: 10.1007/978-3-030-51264-4_3 editor: - first_name: Oliver full_name: Junge, Oliver last_name: Junge - first_name: Oliver full_name: Schütze, Oliver last_name: Schütze - first_name: Sina full_name: Ober-Blöbaum, Sina last_name: Ober-Blöbaum - first_name: Kathrin full_name: Padberg-Gehle, Kathrin last_name: Padberg-Gehle intvolume: ' 304' language: - iso: eng main_file_link: - url: https://link.springer.com/chapter/10.1007/978-3-030-51264-4_3 page: 66-85 place: Cham publication: Advances in Dynamics, Optimization and Computation publication_identifier: isbn: - '9783030512637' - '9783030512644' issn: - 2198-4182 - 2198-4190 publication_status: published publisher: Springer International Publishing series_title: Studies in Systems, Decision and Control status: public title: The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems type: book_chapter user_id: '32655' volume: 304 year: '2020' ... --- _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. author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken - first_name: Raphael full_name: Gerlach, Raphael id: '32655' last_name: Gerlach - first_name: Stefan full_name: Klus, Stefan last_name: Klus citation: ama: Dellnitz M, Gebken B, Gerlach R, Klus S. On the equivariance properties of self-adjoint matrices. Dynamical Systems. 2020;35(2):197-215. doi:10.1080/14689367.2019.1661355 apa: Dellnitz, M., Gebken, B., Gerlach, R., & Klus, S. (2020). On the equivariance properties of self-adjoint matrices. Dynamical Systems, 35(2), 197–215. https://doi.org/10.1080/14689367.2019.1661355 bibtex: '@article{Dellnitz_Gebken_Gerlach_Klus_2020, title={On the equivariance properties of self-adjoint matrices}, volume={35}, DOI={10.1080/14689367.2019.1661355}, number={2}, journal={Dynamical Systems}, author={Dellnitz, Michael and Gebken, Bennet and Gerlach, Raphael and Klus, Stefan}, year={2020}, pages={197–215} }' chicago: 'Dellnitz, Michael, Bennet Gebken, Raphael Gerlach, and Stefan Klus. “On the Equivariance Properties of Self-Adjoint Matrices.” Dynamical Systems 35, no. 2 (2020): 197–215. https://doi.org/10.1080/14689367.2019.1661355.' ieee: 'M. Dellnitz, B. Gebken, R. Gerlach, and S. Klus, “On the equivariance properties of self-adjoint matrices,” Dynamical Systems, vol. 35, no. 2, pp. 197–215, 2020, doi: 10.1080/14689367.2019.1661355.' mla: Dellnitz, Michael, et al. “On the Equivariance Properties of Self-Adjoint Matrices.” Dynamical Systems, vol. 35, no. 2, 2020, pp. 197–215, doi:10.1080/14689367.2019.1661355. short: M. Dellnitz, B. Gebken, R. Gerlach, S. Klus, Dynamical Systems 35 (2020) 197–215. date_created: 2020-04-16T14:07:25Z date_updated: 2023-11-17T13:12:59Z department: - _id: '101' doi: 10.1080/14689367.2019.1661355 intvolume: ' 35' issue: '2' language: - iso: eng main_file_link: - url: https://doi.org/10.1080/14689367.2019.1661355 page: 197-215 publication: Dynamical Systems publication_identifier: issn: - 1468-9367 - 1468-9375 publication_status: published status: public title: On the equivariance properties of self-adjoint matrices type: journal_article user_id: '32655' volume: 35 year: '2020' ... --- _id: '45954' abstract: - lang: eng text: "Abstract\r\n $L^2$ 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." author: - first_name: David full_name: Hipp, David last_name: Hipp - first_name: Balázs full_name: Kovács, Balázs last_name: Kovács citation: ama: 'Hipp D, Kovács B. Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates. IMA Journal of Numerical Analysis. 2020;41(1):638-728. doi:10.1093/imanum/drz073' apa: 'Hipp, D., & Kovács, B. (2020). Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates. IMA Journal of Numerical Analysis, 41(1), 638–728. https://doi.org/10.1093/imanum/drz073' bibtex: '@article{Hipp_Kovács_2020, title={Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates}, volume={41}, DOI={10.1093/imanum/drz073}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Hipp, David and Kovács, Balázs}, year={2020}, pages={638–728} }' chicago: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: L2 Estimates.” IMA Journal of Numerical Analysis 41, no. 1 (2020): 638–728. https://doi.org/10.1093/imanum/drz073.' ieee: 'D. Hipp and B. Kovács, “Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates,” IMA Journal of Numerical Analysis, vol. 41, no. 1, pp. 638–728, 2020, doi: 10.1093/imanum/drz073.' mla: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: L2 Estimates.” IMA Journal of Numerical Analysis, vol. 41, no. 1, Oxford University Press (OUP), 2020, pp. 638–728, doi:10.1093/imanum/drz073.' short: D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 638–728. date_created: 2023-07-10T11:42:43Z date_updated: 2024-04-03T09:14:14Z department: - _id: '841' doi: 10.1093/imanum/drz073 intvolume: ' 41' issue: '1' keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng page: 638-728 publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: 'Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates' type: journal_article user_id: '100441' volume: 41 year: '2020' ... --- _id: '45953' abstract: - lang: eng text: "Abstract\r\n $L^2$ 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." author: - first_name: David full_name: Hipp, David last_name: Hipp - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 citation: ama: 'Hipp D, Kovács B. Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates. IMA Journal of Numerical Analysis. 2020;41(1):638-728. doi:10.1093/imanum/drz073' apa: 'Hipp, D., & Kovács, B. (2020). Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates. IMA Journal of Numerical Analysis, 41(1), 638–728. https://doi.org/10.1093/imanum/drz073' bibtex: '@article{Hipp_Kovács_2020, title={Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates}, volume={41}, DOI={10.1093/imanum/drz073}, number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Hipp, David and Kovács, Balázs}, year={2020}, pages={638–728} }' chicago: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: L2 Estimates.” IMA Journal of Numerical Analysis 41, no. 1 (2020): 638–728. https://doi.org/10.1093/imanum/drz073.' ieee: 'D. Hipp and B. Kovács, “Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates,” IMA Journal of Numerical Analysis, vol. 41, no. 1, pp. 638–728, 2020, doi: 10.1093/imanum/drz073.' mla: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations with Dynamic Boundary Conditions: L2 Estimates.” IMA Journal of Numerical Analysis, vol. 41, no. 1, Oxford University Press (OUP), 2020, pp. 638–728, doi:10.1093/imanum/drz073.' short: D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 638–728. date_created: 2023-07-10T11:42:31Z date_updated: 2024-04-03T09:20:44Z department: - _id: '841' doi: 10.1093/imanum/drz073 intvolume: ' 41' issue: '1' keyword: - Applied Mathematics - Computational Mathematics - General Mathematics language: - iso: eng page: 638-728 publication: IMA Journal of Numerical Analysis publication_identifier: issn: - 0272-4979 - 1464-3642 publication_status: published publisher: Oxford University Press (OUP) status: public title: 'Finite element error analysis of wave equations with dynamic boundary conditions: L2 estimates' type: journal_article user_id: '100441' volume: 41 year: '2020' ... --- _id: '45955' author: - first_name: Georgios full_name: Akrivis, Georgios last_name: Akrivis - first_name: Michael full_name: Feischl, Michael last_name: Feischl - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Christian full_name: Lubich, Christian last_name: Lubich citation: ama: Akrivis G, Feischl M, Kovács B, Lubich C. Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. Mathematics of Computation. 2020;90(329):995-1038. doi:10.1090/mcom/3597 apa: Akrivis, G., Feischl, M., Kovács, B., & Lubich, C. (2020). Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation. Mathematics of Computation, 90(329), 995–1038. https://doi.org/10.1090/mcom/3597 bibtex: '@article{Akrivis_Feischl_Kovács_Lubich_2020, title={Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation}, volume={90}, DOI={10.1090/mcom/3597}, 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} }' chicago: 'Akrivis, Georgios, Michael Feischl, Balázs Kovács, and Christian Lubich. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” Mathematics of Computation 90, no. 329 (2020): 995–1038. https://doi.org/10.1090/mcom/3597.' ieee: 'G. Akrivis, M. Feischl, B. Kovács, and C. Lubich, “Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation,” Mathematics of Computation, vol. 90, no. 329, pp. 995–1038, 2020, doi: 10.1090/mcom/3597.' mla: Akrivis, Georgios, et al. “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert Equation.” Mathematics of Computation, vol. 90, no. 329, American Mathematical Society (AMS), 2020, pp. 995–1038, doi:10.1090/mcom/3597. short: G. Akrivis, M. Feischl, B. Kovács, C. Lubich, Mathematics of Computation 90 (2020) 995–1038. date_created: 2023-07-10T11:42:57Z date_updated: 2024-04-03T09:20:36Z department: - _id: '841' doi: 10.1090/mcom/3597 intvolume: ' 90' issue: '329' keyword: - Applied Mathematics - Computational Mathematics - Algebra and Number Theory language: - iso: eng page: 995-1038 publication: Mathematics of Computation publication_identifier: issn: - 0025-5718 - 1088-6842 publication_status: published publisher: American Mathematical Society (AMS) status: public title: Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation type: journal_article user_id: '100441' volume: 90 year: '2020' ... --- _id: '45952' author: - first_name: Balázs full_name: Kovács, Balázs id: '100441' last_name: Kovács orcid: 0000-0001-9872-3474 - first_name: Buyang full_name: Li, Buyang last_name: Li - first_name: Christian full_name: Lubich, Christian last_name: Lubich citation: ama: Kovács B, Li B, Lubich C. A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. Interfaces and Free Boundaries. 2020;22(4):443-464. doi:10.4171/ifb/446 apa: Kovács, B., Li, B., & Lubich, C. (2020). A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. Interfaces and Free Boundaries, 22(4), 443–464. https://doi.org/10.4171/ifb/446 bibtex: '@article{Kovács_Li_Lubich_2020, title={A convergent algorithm for forced mean curvature flow driven by diffusion on the surface}, volume={22}, DOI={10.4171/ifb/446}, 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} }' chicago: 'Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Algorithm for Forced Mean Curvature Flow Driven by Diffusion on the Surface.” Interfaces and Free Boundaries 22, no. 4 (2020): 443–64. https://doi.org/10.4171/ifb/446.' ieee: 'B. Kovács, B. Li, and C. Lubich, “A convergent algorithm for forced mean curvature flow driven by diffusion on the surface,” Interfaces and Free Boundaries, vol. 22, no. 4, pp. 443–464, 2020, doi: 10.4171/ifb/446.' mla: Kovács, Balázs, et al. “A Convergent Algorithm for Forced Mean Curvature Flow Driven by Diffusion on the Surface.” Interfaces and Free Boundaries, vol. 22, no. 4, European Mathematical Society - EMS - Publishing House GmbH, 2020, pp. 443–64, doi:10.4171/ifb/446. short: B. Kovács, B. Li, C. Lubich, Interfaces and Free Boundaries 22 (2020) 443–464. date_created: 2023-07-10T11:42:14Z date_updated: 2024-04-03T09:21:02Z department: - _id: '841' doi: 10.4171/ifb/446 intvolume: ' 22' issue: '4' keyword: - Applied Mathematics language: - iso: eng page: 443-464 publication: Interfaces and Free Boundaries publication_identifier: issn: - 1463-9963 publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: A convergent algorithm for forced mean curvature flow driven by diffusion on the surface type: journal_article user_id: '100441' volume: 22 year: '2020' ... --- _id: '55288' author: - first_name: St. full_name: Baier, St. last_name: Baier - first_name: Marc full_name: Technau, Marc id: '106108' last_name: Technau orcid: 0000-0001-9650-2459 citation: ama: Baier St, Technau M. On the distribution of αp modulo one in imaginary quadratic number fields with class number one. J Théor Nombres Bordx. 2020;32(2):719–760. doi:10.5802/jtnb.1141 apa: Baier, St., & Technau, M. (2020). On the distribution of αp modulo one in imaginary quadratic number fields with class number one. J. Théor. Nombres Bordx., 32(2), 719–760. https://doi.org/10.5802/jtnb.1141 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={10.5802/jtnb.1141}, number={2}, journal={J. Théor. Nombres Bordx.}, author={Baier, St. and Technau, Marc}, year={2020}, pages={719–760} }' chicago: 'Baier, St., and Marc Technau. “On the Distribution of Αp modulo One in Imaginary Quadratic Number Fields with Class Number One.” J. Théor. Nombres Bordx. 32, no. 2 (2020): 719–760. https://doi.org/10.5802/jtnb.1141.' ieee: 'St. Baier and M. Technau, “On the distribution of αp modulo one in imaginary quadratic number fields with class number one,” J. Théor. Nombres Bordx., vol. 32, no. 2, pp. 719–760, 2020, doi: 10.5802/jtnb.1141.' mla: Baier, St., and Marc Technau. “On the Distribution of Αp modulo One in Imaginary Quadratic Number Fields with Class Number One.” J. Théor. Nombres Bordx., vol. 32, no. 2, 2020, pp. 719–760, doi:10.5802/jtnb.1141. short: St. Baier, M. Technau, J. Théor. Nombres Bordx. 32 (2020) 719–760. date_created: 2024-07-16T11:09:02Z date_updated: 2024-07-24T07:23:57Z department: - _id: '102' doi: 10.5802/jtnb.1141 intvolume: ' 32' issue: '2' language: - iso: eng page: 719–760 publication: J. Théor. Nombres Bordx. status: public title: On the distribution of αp modulo one in imaginary quadratic number fields with class number one type: journal_article user_id: '106108' volume: 32 year: '2020' ... --- _id: '55286' author: - first_name: Marc full_name: Technau, Marc id: '106108' last_name: Technau orcid: 0000-0001-9650-2459 citation: ama: Technau M. Modular hyperbolas and Beatty sequences. J Number Theory. 2020;208:148–167. doi:10.1016/j.jnt.2019.07.022 apa: Technau, M. (2020). Modular hyperbolas and Beatty sequences. J. Number Theory, 208, 148–167. https://doi.org/10.1016/j.jnt.2019.07.022 bibtex: '@article{Technau_2020, title={Modular hyperbolas and Beatty sequences}, volume={208}, DOI={10.1016/j.jnt.2019.07.022}, journal={J. Number Theory}, author={Technau, Marc}, year={2020}, pages={148–167} }' chicago: 'Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” J. Number Theory 208 (2020): 148–167. https://doi.org/10.1016/j.jnt.2019.07.022.' ieee: 'M. Technau, “Modular hyperbolas and Beatty sequences,” J. Number Theory, vol. 208, pp. 148–167, 2020, doi: 10.1016/j.jnt.2019.07.022.' mla: Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” J. Number Theory, vol. 208, 2020, pp. 148–167, doi:10.1016/j.jnt.2019.07.022. short: M. Technau, J. Number Theory 208 (2020) 148–167. date_created: 2024-07-16T11:09:02Z date_updated: 2024-07-24T07:24:11Z department: - _id: '102' doi: 10.1016/j.jnt.2019.07.022 extern: '1' intvolume: ' 208' language: - iso: eng page: 148–167 publication: J. Number Theory status: public title: Modular hyperbolas and Beatty sequences type: journal_article user_id: '106108' volume: 208 year: '2020' ... --- _id: '55287' author: - first_name: I. E. full_name: Shparlinski, I. E. last_name: Shparlinski - first_name: Marc full_name: Technau, Marc id: '106108' last_name: Technau orcid: 0000-0001-9650-2459 citation: ama: Shparlinski IE, Technau M. Kloosterman sums with twice-differentiable functions. Funct Approximatio, Comment Math. 2020;63(1):113–124. doi:10.7169/facm/1845 apa: Shparlinski, I. E., & Technau, M. (2020). Kloosterman sums with twice-differentiable functions. Funct. Approximatio, Comment. Math., 63(1), 113–124. https://doi.org/10.7169/facm/1845 bibtex: '@article{Shparlinski_Technau_2020, title={Kloosterman sums with twice-differentiable functions}, volume={63}, DOI={10.7169/facm/1845}, number={1}, journal={Funct. Approximatio, Comment. Math.}, author={Shparlinski, I. E. and Technau, Marc}, year={2020}, pages={113–124} }' chicago: 'Shparlinski, I. E., and Marc Technau. “Kloosterman Sums with Twice-Differentiable Functions.” Funct. Approximatio, Comment. Math. 63, no. 1 (2020): 113–124. https://doi.org/10.7169/facm/1845.' ieee: 'I. E. Shparlinski and M. Technau, “Kloosterman sums with twice-differentiable functions,” Funct. Approximatio, Comment. Math., vol. 63, no. 1, pp. 113–124, 2020, doi: 10.7169/facm/1845.' mla: Shparlinski, I. E., and Marc Technau. “Kloosterman Sums with Twice-Differentiable Functions.” Funct. Approximatio, Comment. Math., vol. 63, no. 1, 2020, pp. 113–124, doi:10.7169/facm/1845. short: I.E. Shparlinski, M. Technau, Funct. Approximatio, Comment. Math. 63 (2020) 113–124. date_created: 2024-07-16T11:09:02Z date_updated: 2024-07-24T07:25:54Z department: - _id: '102' doi: 10.7169/facm/1845 extern: '1' intvolume: ' 63' issue: '1' language: - iso: eng page: 113–124 publication: Funct. Approximatio, Comment. Math. status: public title: Kloosterman sums with twice-differentiable functions type: journal_article user_id: '106108' volume: 63 year: '2020' ... --- _id: '55283' author: - first_name: D. full_name: Barth, D. last_name: Barth - first_name: M. full_name: Beck, M. last_name: Beck - first_name: T. full_name: Dose, T. last_name: Dose - first_name: Ch. full_name: Glaßer, Ch. last_name: Glaßer - first_name: L. full_name: Michler, L. last_name: Michler - first_name: Marc full_name: Technau, Marc id: '106108' last_name: Technau orcid: 0000-0001-9650-2459 citation: ama: Barth D, Beck M, Dose T, Glaßer Ch, Michler L, Technau M. Emptiness problems for integer circuits. Theoretical Computer Science. 2020;824-825:11–35. doi:10.1016/j.tcs.2020.03.023 apa: Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., & Technau, M. (2020). Emptiness problems for integer circuits. Theoretical Computer Science, 824–825, 11–35. https://doi.org/10.1016/j.tcs.2020.03.023 bibtex: '@article{Barth_Beck_Dose_Glaßer_Michler_Technau_2020, title={Emptiness problems for integer circuits}, volume={824–825}, DOI={10.1016/j.tcs.2020.03.023}, 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} }' chicago: 'Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau. “Emptiness Problems for Integer Circuits.” Theoretical Computer Science 824–825 (2020): 11–35. https://doi.org/10.1016/j.tcs.2020.03.023.' ieee: 'D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, “Emptiness problems for integer circuits,” Theoretical Computer Science, vol. 824–825, pp. 11–35, 2020, doi: 10.1016/j.tcs.2020.03.023.' mla: Barth, D., et al. “Emptiness Problems for Integer Circuits.” Theoretical Computer Science, vol. 824–825, 2020, pp. 11–35, doi:10.1016/j.tcs.2020.03.023. short: D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, Theoretical Computer Science 824–825 (2020) 11–35. date_created: 2024-07-16T11:09:02Z date_updated: 2024-07-24T07:25:29Z department: - _id: '102' doi: 10.1016/j.tcs.2020.03.023 extern: '1' language: - iso: eng page: 11–35 publication: Theoretical Computer Science status: public title: Emptiness problems for integer circuits type: journal_article user_id: '106108' volume: 824-825 year: '2020' ... --- _id: '34842' abstract: - lang: eng 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. author: - first_name: Andreas-Stephan full_name: Elsenhans, Andreas-Stephan last_name: Elsenhans - first_name: Jürgen full_name: Klüners, Jürgen id: '21202' last_name: Klüners - first_name: Florin full_name: Nicolae, Florin last_name: Nicolae citation: ama: Elsenhans A-S, Klüners J, Nicolae F. Imaginary quadratic number fields with class groups of small exponent. Acta Arithmetica. 2020;193(3):217-233. doi:10.4064/aa180220-20-3 apa: Elsenhans, A.-S., Klüners, J., & Nicolae, F. (2020). Imaginary quadratic number fields with class groups of small exponent. Acta Arithmetica, 193(3), 217–233. https://doi.org/10.4064/aa180220-20-3 bibtex: '@article{Elsenhans_Klüners_Nicolae_2020, title={Imaginary quadratic number fields with class groups of small exponent}, volume={193}, DOI={10.4064/aa180220-20-3}, 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} }' chicago: 'Elsenhans, Andreas-Stephan, Jürgen Klüners, and Florin Nicolae. “Imaginary Quadratic Number Fields with Class Groups of Small Exponent.” Acta Arithmetica 193, no. 3 (2020): 217–33. https://doi.org/10.4064/aa180220-20-3.' ieee: 'A.-S. Elsenhans, J. Klüners, and F. Nicolae, “Imaginary quadratic number fields with class groups of small exponent,” Acta Arithmetica, vol. 193, no. 3, pp. 217–233, 2020, doi: 10.4064/aa180220-20-3.' mla: Elsenhans, Andreas-Stephan, et al. “Imaginary Quadratic Number Fields with Class Groups of Small Exponent.” Acta Arithmetica, vol. 193, no. 3, Institute of Mathematics, Polish Academy of Sciences, 2020, pp. 217–33, doi:10.4064/aa180220-20-3. short: A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233. date_created: 2022-12-22T10:51:13Z date_updated: 2023-03-06T10:19:53Z department: - _id: '102' doi: 10.4064/aa180220-20-3 external_id: arxiv: - '1803.02056 ' intvolume: ' 193' issue: '3' keyword: - Algebra and Number Theory language: - iso: eng page: 217-233 publication: Acta Arithmetica publication_identifier: issn: - 0065-1036 - 1730-6264 publication_status: published publisher: Institute of Mathematics, Polish Academy of Sciences status: public title: Imaginary quadratic number fields with class groups of small exponent type: journal_article user_id: '93826' volume: 193 year: '2020' ... --- _id: '16710' 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" author: - first_name: Raphael full_name: Gerlach, Raphael id: '32655' last_name: Gerlach - first_name: Adrian full_name: Ziessler, Adrian last_name: Ziessler - first_name: Bruno full_name: Eckhardt, Bruno last_name: Eckhardt - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz citation: ama: Gerlach R, Ziessler A, Eckhardt B, Dellnitz M. A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. SIAM Journal on Applied Dynamical Systems. Published online 2020:705-723. doi:10.1137/19m1247139 apa: Gerlach, R., Ziessler, A., Eckhardt, B., & Dellnitz, M. (2020). A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors. SIAM Journal on Applied Dynamical Systems, 705–723. https://doi.org/10.1137/19m1247139 bibtex: '@article{Gerlach_Ziessler_Eckhardt_Dellnitz_2020, title={A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors}, DOI={10.1137/19m1247139}, journal={SIAM Journal on Applied Dynamical Systems}, author={Gerlach, Raphael and Ziessler, Adrian and Eckhardt, Bruno and Dellnitz, Michael}, year={2020}, pages={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.” SIAM Journal on Applied Dynamical Systems, 2020, 705–23. https://doi.org/10.1137/19m1247139. ieee: 'R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors,” SIAM Journal on Applied Dynamical Systems, pp. 705–723, 2020, doi: 10.1137/19m1247139.' mla: Gerlach, Raphael, et al. “A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors.” SIAM Journal on Applied Dynamical Systems, 2020, pp. 705–23, doi:10.1137/19m1247139. short: R. Gerlach, A. Ziessler, B. Eckhardt, M. Dellnitz, SIAM Journal on Applied Dynamical Systems (2020) 705–723. date_created: 2020-04-16T14:05:41Z date_updated: 2024-10-01T13:37:43Z department: - _id: '101' doi: 10.1137/19m1247139 language: - iso: eng main_file_link: - url: https://epubs.siam.org/doi/epdf/10.1137/19M1247139 page: 705-723 publication: SIAM Journal on Applied Dynamical Systems publication_identifier: issn: - 1536-0040 publication_status: published status: public title: A Set-Oriented Path Following Method for the Approximation of Parameter Dependent Attractors type: journal_article user_id: '32655' year: '2020' ...