[{"language":[{"iso":"eng"}],"_id":"16867","user_id":"47427","department":[{"_id":"101"}],"abstract":[{"lang":"eng","text":"In this article, we present an efficient descent method for locally Lipschitz\r\ncontinuous multiobjective optimization problems (MOPs). The method is realized\r\nby combining a theoretical result regarding the computation of descent\r\ndirections for nonsmooth MOPs with a practical method to approximate the\r\nsubdifferentials of the objective functions. We show convergence to points\r\nwhich satisfy a necessary condition for Pareto optimality. Using a set of test\r\nproblems, we compare our method to the multiobjective proximal bundle method by\r\nM\\\"akel\\\"a. The results indicate that our method is competitive while being\r\neasier to implement. While the number of objective function evaluations is\r\nlarger, the overall number of subgradient evaluations is lower. Finally, we\r\nshow that our method can be combined with a subdivision algorithm to compute\r\nentire Pareto sets of nonsmooth MOPs."}],"status":"public","type":"journal_article","publication":"Journal of Optimization Theory and Applications","title":"An efficient descent method for locally Lipschitz multiobjective optimization problems","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf"}],"doi":"10.1007/s10957-020-01803-w","oa":"1","date_updated":"2022-01-06T06:52:57Z","author":[{"full_name":"Gebken, Bennet","id":"32643","last_name":"Gebken","first_name":"Bennet"},{"full_name":"Peitz, Sebastian","id":"47427","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"}],"date_created":"2020-04-27T09:11:22Z","volume":188,"year":"2021","citation":{"ama":"Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective optimization problems. <i>Journal of Optimization Theory and Applications</i>. 2021;188:696-723. doi:<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>","ieee":"B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz multiobjective optimization problems,” <i>Journal of Optimization Theory and Applications</i>, vol. 188, pp. 696–723, 2021.","chicago":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” <i>Journal of Optimization Theory and Applications</i> 188 (2021): 696–723. <a href=\"https://doi.org/10.1007/s10957-020-01803-w\">https://doi.org/10.1007/s10957-020-01803-w</a>.","mla":"Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” <i>Journal of Optimization Theory and Applications</i>, vol. 188, 2021, pp. 696–723, doi:<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>.","short":"B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188 (2021) 696–723.","bibtex":"@article{Gebken_Peitz_2021, title={An efficient descent method for locally Lipschitz multiobjective optimization problems}, volume={188}, DOI={<a href=\"https://doi.org/10.1007/s10957-020-01803-w\">10.1007/s10957-020-01803-w</a>}, journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={696–723} }","apa":"Gebken, B., &#38; Peitz, S. (2021). An efficient descent method for locally Lipschitz multiobjective optimization problems. <i>Journal of Optimization Theory and Applications</i>, <i>188</i>, 696–723. <a href=\"https://doi.org/10.1007/s10957-020-01803-w\">https://doi.org/10.1007/s10957-020-01803-w</a>"},"intvolume":"       188","page":"696-723","publication_status":"published"},{"title":"Inverse multiobjective optimization: Inferring decision criteria from data","main_file_link":[{"open_access":"1","url":"https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf"}],"doi":"10.1007/s10898-020-00983-z","publisher":"Springer","oa":"1","date_updated":"2022-01-06T06:52:48Z","date_created":"2020-03-13T12:45:05Z","author":[{"first_name":"Bennet","full_name":"Gebken, Bennet","id":"32643","last_name":"Gebken"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz"}],"volume":80,"year":"2021","citation":{"chicago":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” <i>Journal of Global Optimization</i> 80 (2021): 3–29. <a href=\"https://doi.org/10.1007/s10898-020-00983-z\">https://doi.org/10.1007/s10898-020-00983-z</a>.","ieee":"B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision criteria from data,” <i>Journal of Global Optimization</i>, vol. 80, pp. 3–29, 2021.","ama":"Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision criteria from data. <i>Journal of Global Optimization</i>. 2021;80:3-29. doi:<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>","bibtex":"@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization: Inferring decision criteria from data}, volume={80}, DOI={<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>}, journal={Journal of Global Optimization}, publisher={Springer}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021}, pages={3–29} }","mla":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” <i>Journal of Global Optimization</i>, vol. 80, Springer, 2021, pp. 3–29, doi:<a href=\"https://doi.org/10.1007/s10898-020-00983-z\">10.1007/s10898-020-00983-z</a>.","short":"B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29.","apa":"Gebken, B., &#38; Peitz, S. (2021). Inverse multiobjective optimization: Inferring decision criteria from data. <i>Journal of Global Optimization</i>, <i>80</i>, 3–29. <a href=\"https://doi.org/10.1007/s10898-020-00983-z\">https://doi.org/10.1007/s10898-020-00983-z</a>"},"intvolume":"        80","page":"3-29","language":[{"iso":"eng"}],"_id":"16295","user_id":"47427","department":[{"_id":"101"}],"abstract":[{"text":"It is a challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists. This task can be understood as the inverse problem of multiobjective optimization, where the goal is to find the objective function vector of a given Pareto set. To this end, we present a method to construct the objective function vector of an unconstrained multiobjective optimization problem (MOP) such that the Pareto critical set contains a given set of data points with prescribed KKT multipliers. If such an MOP can not be found, then the method instead produces an MOP whose Pareto critical set is at least close to the data points. The key idea is to consider the objective function vector in the multiobjective KKT conditions as variable and then search for the objectives that minimize the Euclidean norm of the resulting system of equations. By expressing the objectives in a finite-dimensional basis, we transform this problem into a homogeneous, linear system of equations that can be solved efficiently. Potential applications of this approach include the identification of objectives (both from clean and noisy data) and the construction of surrogate models for expensive MOPs.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Journal of Global Optimization"},{"status":"public","abstract":[{"lang":"ger","text":"Ein zentraler Aspekt bei der Untersuchung dynamischer Systeme ist die Analyse ihrer invarianten Mengen wie des globalen Attraktors und (in)stabiler Mannigfaltigkeiten. Insbesondere wenn das zugrunde liegende System von einem Parameter abhängt, ist es entscheidend, sie im Bezug auf diesen Parameter effizient zu verfolgen. Für die Berechnung invarianter Mengen stützen wir uns für ihre Approximation auf numerische Algorithmen. Typischerweise können diese Methoden jedoch nur auf endlich-dimensionale dynamische Systeme angewendet werden. In dieser Arbeit präsentieren wir daher einen numerischen Rahmen für die globale dynamische Analyse unendlich-dimensionaler Systeme. Wir werden Einbettungstechniken verwenden, um das core dynamical system (CDS) zu definieren, welches ein dynamisch äquivalentes endlich-dimensionales System ist.Das CDS wird dann verwendet, um eingebettete invariante Mengen, also eins-zu-eins Bilder, mittels Mengen-orientierten numerischen Methoden zu approximieren. Bei der Konstruktion des CDS ist es entscheidend, eine geeignete Beobachtungsabbildung auszuwählen und die geeignete inverse Abbildung zu entwerfen. Dazu werden wir geeignete numerische Implementierungen des CDS für DDEs und PDEs vorstellen. Für eine nachfolgende geometrische Analyse der eingebetteten invarianten Menge betrachten wir eine Lerntechnik namens diffusion maps, die ihre intrinsische Geometrie enthüllt sowie ihre Dimension schätzt. Schließlich wenden wir unsere entwickelten numerischen Methoden an einigen bekannten unendlich-dimensionale dynamischen Systeme an, wie die Mackey-Glass-Gleichung, die Kuramoto-Sivashinsky-Gleichung und die Navier-Stokes-Gleichung."},{"lang":"eng","text":"One central aspect in the study of dynamical systems is the analysis of its invariant sets such as the global attractor and (un)stable manifolds. In particular, when the underlying system depends on a parameter it is crucial to efficiently track those set with respect to this parameter. For the computation of invariant sets we rely on numerical algorithms for their approximation but typically those tools can only be applied to finite-dimensional dynamical systems. Thus, in thesis we present a numerical framework for the global dynamical analysis of infinite-dimensional systems. We will use embedding techniques for the definition of the core dynamical system (CDS) which is a dynamically equivalent finite-dimensional system. The CDS is then used for the approximation of related embedded invariant sets, i.e, one-to-one images, by set-oriented numerical methods. For the construction of the CDS it is crucial to choose an appropriate observation map and to design its corresponding inverse. Therefore, we will present suitable numerical realizations of the CDS for DDEs and PDEs. For a subsequent geometric analysis of the embedded invariant set we will consider a manifold learning technique called diffusion maps which reveals its intrinsic geometry and estimates its dimension. Finally, we apply our develop numerical tools on some well-known infinite-dimensional dynamical systems such as the Mackey-Glass equation, the Kuramoto-Sivashinsky equation and the Navier-Stokes equation."}],"type":"dissertation","language":[{"iso":"eng"}],"department":[{"_id":"101"}],"user_id":"32643","_id":"32057","citation":{"short":"R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems, 2021.","mla":"Gerlach, Raphael. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. 2021, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>.","bibtex":"@book{Gerlach_2021, title={The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>}, author={Gerlach, Raphael}, year={2021} }","apa":"Gerlach, R. (2021). <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1278\">https://doi.org/10.17619/UNIPB/1-1278</a>","ieee":"R. Gerlach, <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>. 2021.","chicago":"Gerlach, Raphael. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>, 2021. <a href=\"https://doi.org/10.17619/UNIPB/1-1278\">https://doi.org/10.17619/UNIPB/1-1278</a>.","ama":"Gerlach R. <i>The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems</i>.; 2021. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1278\">10.17619/UNIPB/1-1278</a>"},"year":"2021","doi":"10.17619/UNIPB/1-1278","main_file_link":[{"open_access":"1","url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/6214949"}],"title":"The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems","date_created":"2022-06-20T09:54:24Z","supervisor":[{"first_name":"Michael","full_name":"Dellnitz , Michael","last_name":"Dellnitz "},{"first_name":"Péter","last_name":"Koltai","full_name":"Koltai, Péter"}],"author":[{"first_name":"Raphael","id":"32655","full_name":"Gerlach, Raphael","last_name":"Gerlach"}],"date_updated":"2022-06-20T13:40:30Z","oa":"1"},{"publication":"Journal of Symplectic Geometry","type":"journal_article","status":"public","department":[{"_id":"548"}],"user_id":"70575","_id":"32016","language":[{"iso":"eng"}],"article_type":"original","issue":"6","publication_identifier":{"unknown":["1540-2347","1527-5256"]},"publication_status":"published","intvolume":"        19","page":"1281 - 1337","citation":{"mla":"Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” <i>Journal of Symplectic Geometry</i>, vol. 19, no. 6, 2021, pp. 1281–337, doi:<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>.","bibtex":"@article{Delarue_Ramacher_2021, title={Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions}, volume={19}, DOI={<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>}, number={6}, journal={Journal of Symplectic Geometry}, author={Delarue, Benjamin and Ramacher, Pablo}, year={2021}, pages={1281–1337} }","short":"B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337.","apa":"Delarue, B., &#38; Ramacher, P. (2021). Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. <i>Journal of Symplectic Geometry</i>, <i>19</i>(6), 1281–1337. <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">https://doi.org/10.4310/JSG.2021.v19.n6.a1</a>","ama":"Delarue B, Ramacher P. Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. <i>Journal of Symplectic Geometry</i>. 2021;19(6):1281-1337. doi:<a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>","ieee":"B. Delarue and P. Ramacher, “Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions,” <i>Journal of Symplectic Geometry</i>, vol. 19, no. 6, pp. 1281–1337, 2021, doi: <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">10.4310/JSG.2021.v19.n6.a1</a>.","chicago":"Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” <i>Journal of Symplectic Geometry</i> 19, no. 6 (2021): 1281–1337. <a href=\"https://doi.org/10.4310/JSG.2021.v19.n6.a1\">https://doi.org/10.4310/JSG.2021.v19.n6.a1</a>."},"year":"2021","volume":19,"date_created":"2022-06-20T08:46:56Z","author":[{"first_name":"Benjamin","last_name":"Delarue","id":"70575","full_name":"Delarue, Benjamin"},{"first_name":"Pablo","last_name":"Ramacher","full_name":"Ramacher, Pablo"}],"date_updated":"2022-06-21T11:54:50Z","doi":"10.4310/JSG.2021.v19.n6.a1","title":"Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions"},{"doi":"10.1016/j.jctb.2021.11.001","title":"Nowhere-zero 3-flows in toroidal graphs","author":[{"first_name":"Jiaao","last_name":"Li","full_name":"Li, Jiaao"},{"id":"92748","full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai"},{"full_name":"Miao, Zhengke","last_name":"Miao","first_name":"Zhengke"},{"full_name":"Shi, Yongtang","last_name":"Shi","first_name":"Yongtang"},{"first_name":"Weifan","full_name":"Wang, Weifan","last_name":"Wang"},{"last_name":"Zhang","full_name":"Zhang, Cun-Quan","first_name":"Cun-Quan"}],"date_created":"2022-11-09T08:43:55Z","volume":153,"publisher":"Elsevier BV","date_updated":"2022-11-09T08:44:37Z","citation":{"bibtex":"@article{Li_Ma_Miao_Shi_Wang_Zhang_2021, title={Nowhere-zero 3-flows in toroidal graphs}, volume={153}, DOI={<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>}, journal={Journal of Combinatorial Theory, Series B}, publisher={Elsevier BV}, author={Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang, Weifan and Zhang, Cun-Quan}, year={2021}, pages={61–80} }","short":"J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, C.-Q. Zhang, Journal of Combinatorial Theory, Series B 153 (2021) 61–80.","mla":"Li, Jiaao, et al. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial Theory, Series B</i>, vol. 153, Elsevier BV, 2021, pp. 61–80, doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>.","ama":"Li J, Ma Y, Miao Z, Shi Y, Wang W, Zhang C-Q. Nowhere-zero 3-flows in toroidal graphs. <i>Journal of Combinatorial Theory, Series B</i>. 2021;153:61-80. doi:<a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>","apa":"Li, J., Ma, Y., Miao, Z., Shi, Y., Wang, W., &#38; Zhang, C.-Q. (2021). Nowhere-zero 3-flows in toroidal graphs. <i>Journal of Combinatorial Theory, Series B</i>, <i>153</i>, 61–80. <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">https://doi.org/10.1016/j.jctb.2021.11.001</a>","chicago":"Li, Jiaao, Yulai Ma, Zhengke Miao, Yongtang Shi, Weifan Wang, and Cun-Quan Zhang. “Nowhere-Zero 3-Flows in Toroidal Graphs.” <i>Journal of Combinatorial Theory, Series B</i> 153 (2021): 61–80. <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">https://doi.org/10.1016/j.jctb.2021.11.001</a>.","ieee":"J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, and C.-Q. Zhang, “Nowhere-zero 3-flows in toroidal graphs,” <i>Journal of Combinatorial Theory, Series B</i>, vol. 153, pp. 61–80, 2021, doi: <a href=\"https://doi.org/10.1016/j.jctb.2021.11.001\">10.1016/j.jctb.2021.11.001</a>."},"intvolume":"       153","page":"61-80","year":"2021","publication_status":"published","publication_identifier":{"issn":["0095-8956"]},"language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"user_id":"15540","department":[{"_id":"542"}],"_id":"34042","status":"public","type":"journal_article","publication":"Journal of Combinatorial Theory, Series B"},{"language":[{"iso":"eng"}],"keyword":["Contraction group","Torsion group","Extension","Cocycle","Section","Equivariant cohomology","Abelian group","Nilpotent group","Isomorphism types"],"abstract":[{"lang":"eng","text":"A locally compact contraction group is a pair (G,α), where G is a locally compact group and α:G→G an automorphism such that αn(x)→e pointwise as n→∞. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2-cocycles to construct uncountably many pairwise non-isomorphic totally disconnected, locally compact contraction groups (G,α) which are central extensions0→Fp((t))→G→Fp((t))→0 of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups."}],"publication":"Journal of Algebra","title":"Decompositions of locally compact contraction groups, series and extensions","date_created":"2022-12-21T18:43:08Z","year":"2021","quality_controlled":"1","article_type":"original","user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34786","status":"public","type":"journal_article","doi":"https://doi.org/10.1016/j.jalgebra.2020.11.007","author":[{"id":"178","full_name":"Glöckner, Helge","last_name":"Glöckner","first_name":"Helge"},{"first_name":"George A.","last_name":"Willis","full_name":"Willis, George A."}],"volume":570,"date_updated":"2022-12-21T18:58:44Z","citation":{"mla":"Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction Groups, Series and Extensions.” <i>Journal of Algebra</i>, vol. 570, 2021, pp. 164–214, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.","short":"H. Glöckner, G.A. Willis, Journal of Algebra 570 (2021) 164–214.","bibtex":"@article{Glöckner_Willis_2021, title={Decompositions of locally compact contraction groups, series and extensions}, volume={570}, DOI={<a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>}, journal={Journal of Algebra}, author={Glöckner, Helge and Willis, George A.}, year={2021}, pages={164–214} }","apa":"Glöckner, H., &#38; Willis, G. A. (2021). Decompositions of locally compact contraction groups, series and extensions. <i>Journal of Algebra</i>, <i>570</i>, 164–214. <a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>","ama":"Glöckner H, Willis GA. Decompositions of locally compact contraction groups, series and extensions. <i>Journal of Algebra</i>. 2021;570:164-214. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>","chicago":"Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction Groups, Series and Extensions.” <i>Journal of Algebra</i> 570 (2021): 164–214. <a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>.","ieee":"H. Glöckner and G. A. Willis, “Decompositions of locally compact contraction groups, series and extensions,” <i>Journal of Algebra</i>, vol. 570, pp. 164–214, 2021, doi: <a href=\"https://doi.org/10.1016/j.jalgebra.2020.11.007\">https://doi.org/10.1016/j.jalgebra.2020.11.007</a>."},"page":"164-214","intvolume":"       570","publication_identifier":{"issn":["0021-8693"]}},{"citation":{"apa":"Glöckner, H. (2021). Direct limits of regular Lie groups. <i>Mathematische Nachrichten</i>, <i>294</i>(1), 74–81. <a href=\"https://doi.org/10.1002/mana.201900073\">https://doi.org/10.1002/mana.201900073</a>","mla":"Glöckner, Helge. “Direct Limits of Regular Lie Groups.” <i>Mathematische Nachrichten</i>, vol. 294, no. 1, 2021, pp. 74–81, doi:<a href=\"https://doi.org/10.1002/mana.201900073\">10.1002/mana.201900073</a>.","bibtex":"@article{Glöckner_2021, title={Direct limits of regular Lie groups}, volume={294}, DOI={<a href=\"https://doi.org/10.1002/mana.201900073\">10.1002/mana.201900073</a>}, number={1}, journal={Mathematische Nachrichten}, author={Glöckner, Helge}, year={2021}, pages={74–81} }","short":"H. Glöckner, Mathematische Nachrichten 294 (2021) 74–81.","ama":"Glöckner H. Direct limits of regular Lie groups. <i>Mathematische Nachrichten</i>. 2021;294(1):74–81. doi:<a href=\"https://doi.org/10.1002/mana.201900073\">10.1002/mana.201900073</a>","chicago":"Glöckner, Helge. “Direct Limits of Regular Lie Groups.” <i>Mathematische Nachrichten</i> 294, no. 1 (2021): 74–81. <a href=\"https://doi.org/10.1002/mana.201900073\">https://doi.org/10.1002/mana.201900073</a>.","ieee":"H. Glöckner, “Direct limits of regular Lie groups,” <i>Mathematische Nachrichten</i>, vol. 294, no. 1, pp. 74–81, 2021, doi: <a href=\"https://doi.org/10.1002/mana.201900073\">10.1002/mana.201900073</a>."},"page":"74–81","intvolume":"       294","year":"2021","issue":"1","quality_controlled":"1","publication_identifier":{"issn":["0025-584X"]},"doi":"10.1002/mana.201900073","title":"Direct limits of regular Lie groups","author":[{"full_name":"Glöckner, Helge","id":"178","last_name":"Glöckner","first_name":"Helge"}],"date_created":"2022-12-21T19:57:32Z","volume":294,"date_updated":"2022-12-21T20:00:29Z","status":"public","type":"journal_article","publication":"Mathematische Nachrichten","language":[{"iso":"eng"}],"article_type":"original","user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34795"},{"citation":{"chicago":"Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms of Lie Groups over  Local Fields.” <i>ArXiv:2101.02981</i>, 2021.","ieee":"H. Glöckner, “Contraction groups and the big cell for endomorphisms of Lie groups over  local fields,” <i>arXiv:2101.02981</i>. 2021.","ama":"Glöckner H. Contraction groups and the big cell for endomorphisms of Lie groups over  local fields. <i>arXiv:210102981</i>. Published online 2021.","apa":"Glöckner, H. (2021). Contraction groups and the big cell for endomorphisms of Lie groups over  local fields. In <i>arXiv:2101.02981</i>.","short":"H. Glöckner, ArXiv:2101.02981 (2021).","bibtex":"@article{Glöckner_2021, title={Contraction groups and the big cell for endomorphisms of Lie groups over  local fields}, journal={arXiv:2101.02981}, author={Glöckner, Helge}, year={2021} }","mla":"Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms of Lie Groups over  Local Fields.” <i>ArXiv:2101.02981</i>, 2021."},"year":"2021","author":[{"full_name":"Glöckner, Helge","id":"178","last_name":"Glöckner","first_name":"Helge"}],"date_created":"2022-12-22T07:47:35Z","date_updated":"2022-12-22T07:48:29Z","title":"Contraction groups and the big cell for endomorphisms of Lie groups over  local fields","type":"preprint","publication":"arXiv:2101.02981","status":"public","abstract":[{"text":"Let $G$ be a Lie group over a totally disconnected local field and $\\alpha$\r\nbe an analytic endomorphism of $G$. The contraction group of $\\alpha$ ist the\r\nset of all $x\\in G$ such that $\\alpha^n(x)\\to e$ as $n\\to\\infty$. Call sequence\r\n$(x_{-n})_{n\\geq 0}$ in $G$ an $\\alpha$-regressive trajectory for $x\\in G$ if\r\n$\\alpha(x_{-n})=x_{-n+1}$ for all $n\\geq 1$ and $x_0=x$. The anti-contraction\r\ngroup of $\\alpha$ is the set of all $x\\in G$ admitting an $\\alpha$-regressive\r\ntrajectory $(x_{-n})_{n\\geq 0}$ such that $x_{-n}\\to e$ as $n\\to\\infty$. The\r\nLevi subgroup is the set of all $x\\in G$ whose $\\alpha$-orbit is relatively\r\ncompact, and such that $x$ admits an $\\alpha$-regressive trajectory\r\n$(x_{-n})_{n\\geq 0}$ such that $\\{x_{-n}\\colon n\\geq 0\\}$ is relatively\r\ncompact. The big cell associated to $\\alpha$ is the set $\\Omega$ of all all\r\nproducts $xyz$ with $x$ in the contraction group, $y$ in the Levi subgroup and\r\n$z$ in the anti-contraction group. Let $\\pi$ be the mapping from the cartesian\r\nproduct of the contraction group, Levi subgroup and anti-contraction group to\r\n$\\Omega$ which maps $(x,y,z)$ to $xyz$. We show: $\\Omega$ is open in $G$ and\r\n$\\pi$ is \\'{e}tale for suitable immersed Lie subgroup structures on the three\r\nsubgroups just mentioned. Moreover, we study group-theoretic properties of\r\ncontraction groups and anti-contraction groups.","lang":"eng"}],"user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"34806","external_id":{"arxiv":["2101.02981"]},"language":[{"iso":"eng"}]},{"citation":{"apa":"Ober-Blöbaum, S., &#38; Vermeeren, M. (2021). Superconvergence of galerkin variational integrators. In IFAC-PapersOnLine (Ed.), <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)</i> (pp. 327–333).","mla":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp. 327–33.","short":"S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.","bibtex":"@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum, Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333} }","ieee":"S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational integrators,” in <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, 2021, vol. 54(19), pp. 327–333.","chicago":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” In <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.","ama":"Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators. In: IFAC-PapersOnLine, ed. <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>. Vol 54(19). ; 2021:327-333."},"page":"327-333","corporate_editor":["IFAC-PapersOnLine"],"year":"2021","date_created":"2022-01-18T14:27:56Z","author":[{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"last_name":"Vermeeren","full_name":"Vermeeren, M.","first_name":"M."}],"volume":"54(19)","date_updated":"2022-01-21T13:36:53Z","title":"Superconvergence of galerkin variational integrators","type":"conference","publication":"7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC","status":"public","user_id":"15694","department":[{"_id":"636"}],"_id":"29421","language":[{"iso":"eng"}]},{"abstract":[{"text":"Model predictive control is a prominent approach to construct a feedback\r\ncontrol loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge in MPC is to solve model-based optimal control problems in a very\r\nshort amount of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit formulation where the underlying optimization problems are\r\nsolved a priori in an offline phase. In this article, we present an extension\r\nof this concept in two significant ways. We consider nonlinear problems and -\r\nmore importantly - problems with multiple conflicting objective functions. In\r\nthe offline phase, we build a library of Pareto optimal solutions from which we\r\nthen obtain a valid compromise solution in the online phase according to a\r\ndecision maker's preference. Since the standard multi-parametric programming\r\napproach is no longer valid in this situation, we instead use interpolation\r\nbetween different entries of the library. To reduce the number of problems that\r\nhave to be solved in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the corresponding multiobjective optimal control problem. The\r\nresults are verified using two different examples from autonomous driving.","lang":"eng"}],"status":"public","type":"journal_article","publication":"International Journal of Robust and Nonlinear Control","language":[{"iso":"eng"}],"project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"16294","user_id":"15694","department":[{"_id":"101"}],"year":"2021","citation":{"apa":"Ober-Blöbaum, S., &#38; Peitz, S. (2021). Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>, <i>31(2)</i>, 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>","short":"S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear Control 31(2) (2021) 380–403.","bibtex":"@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model predictive control for nonlinear systems  with symmetries}, volume={31(2)}, DOI={<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>}, journal={International Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2021}, pages={380–403} }","mla":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), 2021, pp. 380–403, doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","ama":"Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for nonlinear systems  with symmetries. <i>International Journal of Robust and Nonlinear Control</i>. 2021;31(2):380-403. doi:<a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>","ieee":"S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control for nonlinear systems  with symmetries,” <i>International Journal of Robust and Nonlinear Control</i>, vol. 31(2), pp. 380–403, 2021, doi: <a href=\"https://doi.org/10.1002/rnc.5281\">10.1002/rnc.5281</a>.","chicago":"Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive Control for Nonlinear Systems  with Symmetries.” <i>International Journal of Robust and Nonlinear Control</i> 31(2) (2021): 380–403. <a href=\"https://doi.org/10.1002/rnc.5281\">https://doi.org/10.1002/rnc.5281</a>."},"page":"380-403","title":"Explicit multiobjective model predictive control for nonlinear systems  with symmetries","main_file_link":[{"url":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281","open_access":"1"}],"doi":"10.1002/rnc.5281","date_updated":"2022-01-24T13:27:50Z","oa":"1","author":[{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X"}],"date_created":"2020-03-13T12:44:36Z","volume":"31(2)"},{"publication":"Automatica","type":"journal_article","status":"public","_id":"29543","department":[{"_id":"636"}],"user_id":"87909","keyword":["Electrical and Electronic Engineering","Control and Systems Engineering"],"article_number":"109804","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0005-1098"]},"publication_status":"published","year":"2021","intvolume":"       132","citation":{"short":"W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).","bibtex":"@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features in optimal selection of species represented by quota models}, volume={132}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>}, number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema, Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021} }","mla":"Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i>, vol. 132, 109804, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>.","apa":"Djema, W., Giraldi, L., Maslovskaya, S., &#38; Bernard, O. (2021). Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>, <i>132</i>, Article 109804. <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>","ieee":"W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features in optimal selection of species represented by quota models,” <i>Automatica</i>, vol. 132, Art. no. 109804, 2021, doi: <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>.","chicago":"Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i> 132 (2021). <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>.","ama":"Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>. 2021;132. doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>"},"date_updated":"2022-01-26T13:15:33Z","publisher":"Elsevier BV","volume":132,"date_created":"2022-01-26T13:13:06Z","author":[{"first_name":"Walid","last_name":"Djema","full_name":"Djema, Walid"},{"last_name":"Giraldi","full_name":"Giraldi, Laetitia","first_name":"Laetitia"},{"last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909","first_name":"Sofya"},{"first_name":"Olivier","full_name":"Bernard, Olivier","last_name":"Bernard"}],"title":"Turnpike features in optimal selection of species represented by quota models","doi":"10.1016/j.automatica.2021.109804"},{"type":"preprint","abstract":[{"lang":"eng","text":"We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane."}],"status":"public","_id":"31058","external_id":{"arxiv":["2109.05907"]},"department":[{"_id":"10"},{"_id":"548"}],"user_id":"50168","language":[{"iso":"eng"}],"year":"2021","citation":{"chicago":"Schütte, Philipp, Tobias Weich, and Benjamin Delarue. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” 2021.","ieee":"P. Schütte, T. Weich, and B. Delarue, “Resonances and weighted zeta functions for obstacle scattering via smooth models.” 2021.","ama":"Schütte P, Weich T, Delarue B. Resonances and weighted zeta functions for obstacle scattering via smooth models. Published online 2021.","apa":"Schütte, P., Weich, T., &#38; Delarue, B. (2021). <i>Resonances and weighted zeta functions for obstacle scattering via smooth models</i>.","mla":"Schütte, Philipp, et al. <i>Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models</i>. 2021.","bibtex":"@article{Schütte_Weich_Delarue_2021, title={Resonances and weighted zeta functions for obstacle scattering via smooth models}, author={Schütte, Philipp and Weich, Tobias and Delarue, Benjamin}, year={2021} }","short":"P. Schütte, T. Weich, B. Delarue, (2021)."},"date_updated":"2022-05-17T12:05:52Z","date_created":"2022-05-04T12:25:58Z","author":[{"first_name":"Philipp","full_name":"Schütte, Philipp","id":"50168","last_name":"Schütte"},{"full_name":"Weich, Tobias","id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias"},{"last_name":"Delarue","full_name":"Delarue, Benjamin","first_name":"Benjamin"}],"title":"Resonances and weighted zeta functions for obstacle scattering via smooth models"},{"type":"review","publication":"Mathematische Semesterberichte","status":"public","user_id":"32202","department":[{"_id":"97"}],"_id":"31385","language":[{"iso":"ger"}],"publication_status":"published","citation":{"ieee":"M. Hoffmann, “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie,” <i>Mathematische Semesterberichte</i>, vol. 68. pp. 295–297, 2021, doi: <a href=\"https://doi.org/10.1007/s00591-021-00299-3\">10.1007/s00591-021-00299-3</a>.","chicago":"Hoffmann, Max. “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie.” <i>Mathematische Semesterberichte</i>, 2021. <a href=\"https://doi.org/10.1007/s00591-021-00299-3\">https://doi.org/10.1007/s00591-021-00299-3</a>.","ama":"Hoffmann M. Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie. <i>Mathematische Semesterberichte</i>. 2021;68:295–297. doi:<a href=\"https://doi.org/10.1007/s00591-021-00299-3\">10.1007/s00591-021-00299-3</a>","bibtex":"@article{Hoffmann_2021, title={Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie}, volume={68}, DOI={<a href=\"https://doi.org/10.1007/s00591-021-00299-3\">10.1007/s00591-021-00299-3</a>}, journal={Mathematische Semesterberichte}, author={Hoffmann, Max}, year={2021}, pages={295–297} }","short":"M. Hoffmann, Mathematische Semesterberichte 68 (2021) 295–297.","mla":"Hoffmann, Max. “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie.” <i>Mathematische Semesterberichte</i>, vol. 68, 2021, pp. 295–297, doi:<a href=\"https://doi.org/10.1007/s00591-021-00299-3\">10.1007/s00591-021-00299-3</a>.","apa":"Hoffmann, M. (2021). Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie. In <i>Mathematische Semesterberichte</i> (Vol. 68, pp. 295–297). <a href=\"https://doi.org/10.1007/s00591-021-00299-3\">https://doi.org/10.1007/s00591-021-00299-3</a>"},"intvolume":"        68","page":"295–297","year":"2021","author":[{"first_name":"Max","id":"32202","full_name":"Hoffmann, Max","last_name":"Hoffmann"}],"date_created":"2022-05-22T15:20:46Z","volume":68,"date_updated":"2022-05-22T15:58:33Z","oa":"1","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/s00591-021-00299-3"}],"doi":"10.1007/s00591-021-00299-3","title":"Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie"},{"editor":[{"first_name":"Rolf","full_name":"Biehler, Rolf","last_name":"Biehler"},{"full_name":"Eichler, Andreas","last_name":"Eichler","first_name":"Andreas"},{"full_name":"Hochmuth, Reinhard","last_name":"Hochmuth","first_name":"Reinhard"},{"first_name":"Stefanie","full_name":"Rach, Stefanie","last_name":"Rach"},{"first_name":"Niclas","last_name":"Schaper","full_name":"Schaper, Niclas"}],"status":"public","publication":" Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert","type":"book_chapter","language":[{"iso":"ger"}],"_id":"31364","department":[{"_id":"97"}],"user_id":"32202","year":"2021","place":"Berlin, Heidelberg","page":"179–204","citation":{"apa":"Hoffmann, M. (2021). Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn. In R. Biehler, A. Eichler, R. Hochmuth, S. Rach, &#38; N. Schaper (Eds.), <i> Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert</i> (pp. 179–204). Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-662-62854-6_9\">https://doi.org/10.1007/978-3-662-62854-6_9</a>","short":"M. Hoffmann, in: R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper (Eds.),  Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert, Springer Berlin Heidelberg, Berlin, Heidelberg, 2021, pp. 179–204.","mla":"Hoffmann, Max. “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn.” <i> Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert</i>, edited by Rolf Biehler et al., Springer Berlin Heidelberg, 2021, pp. 179–204, doi:<a href=\"https://doi.org/10.1007/978-3-662-62854-6_9\">10.1007/978-3-662-62854-6_9</a>.","bibtex":"@inbook{Hoffmann_2021, place={Berlin, Heidelberg}, title={Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-62854-6_9\">10.1007/978-3-662-62854-6_9</a>}, booktitle={ Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert}, publisher={Springer Berlin Heidelberg}, author={Hoffmann, Max}, editor={Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}, year={2021}, pages={179–204} }","ieee":"M. Hoffmann, “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn,” in <i> Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert</i>, R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2021, pp. 179–204.","chicago":"Hoffmann, Max. “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn.” In <i> Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert</i>, edited by Rolf Biehler, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and Niclas Schaper, 179–204. Berlin, Heidelberg: Springer Berlin Heidelberg, 2021. <a href=\"https://doi.org/10.1007/978-3-662-62854-6_9\">https://doi.org/10.1007/978-3-662-62854-6_9</a>.","ama":"Hoffmann M. Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn. In: Biehler R, Eichler A, Hochmuth R, Rach S, Schaper N, eds. <i> Lehrinnovationen in der Hochschulmathematik.  praxisrelevant – didaktisch fundiert – forschungsbasiert</i>. Springer Berlin Heidelberg; 2021:179–204. doi:<a href=\"https://doi.org/10.1007/978-3-662-62854-6_9\">10.1007/978-3-662-62854-6_9</a>"},"quality_controlled":"1","publication_identifier":{"isbn":["9783662628539","9783662628546"],"issn":["2197-8751","2197-876X"]},"publication_status":"published","title":"Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn","doi":"10.1007/978-3-662-62854-6_9","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/978-3-662-62854-6_9"}],"date_updated":"2022-05-24T13:18:09Z","publisher":"Springer Berlin Heidelberg","author":[{"full_name":"Hoffmann, Max","id":"32202","last_name":"Hoffmann","first_name":"Max"}],"date_created":"2022-05-22T13:56:39Z"},{"publisher":"Oxford University Press (OUP)","date_created":"2022-05-17T12:00:36Z","title":"Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces","issue":"11","year":"2021","external_id":{"arxiv":["1710.04625"]},"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"publication":"International Mathematics Research Notices","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>For a compact Riemannian locally symmetric space $\\mathcal M$ of rank 1 and an associated vector bundle $\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\\sigma )$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$ over $\\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau }$ and $\\mathbf W_{\\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory and Lie theory.</jats:p>","lang":"eng"}],"date_updated":"2022-05-25T06:42:01Z","volume":2021,"author":[{"first_name":"Benjamin","full_name":"Küster, Benjamin","last_name":"Küster"},{"last_name":"Weich","full_name":"Weich, Tobias","first_name":"Tobias"}],"doi":"10.1093/imrn/rnz068","publication_identifier":{"issn":["1073-7928","1687-0247"]},"publication_status":"published","intvolume":"      2021","page":"8225-8296","citation":{"apa":"Küster, B., &#38; Weich, T. (2021). Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>, <i>2021</i>(11), 8225–8296. <a href=\"https://doi.org/10.1093/imrn/rnz068\">https://doi.org/10.1093/imrn/rnz068</a>","bibtex":"@article{Küster_Weich_2021, title={Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>}, number={11}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2021}, pages={8225–8296} }","mla":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research Notices</i>, vol. 2021, no. 11, Oxford University Press (OUP), 2021, pp. 8225–96, doi:<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>.","short":"B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021) 8225–8296.","ama":"Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>. 2021;2021(11):8225-8296. doi:<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>","ieee":"B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces,” <i>International Mathematics Research Notices</i>, vol. 2021, no. 11, pp. 8225–8296, 2021, doi: <a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>.","chicago":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research Notices</i> 2021, no. 11 (2021): 8225–96. <a href=\"https://doi.org/10.1093/imrn/rnz068\">https://doi.org/10.1093/imrn/rnz068</a>."},"_id":"31261","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","type":"journal_article","status":"public"},{"_id":"31576","user_id":"85821","department":[{"_id":"98"},{"_id":"543"}],"language":[{"iso":"ger"}],"type":"journal_article","publication":"Zeitschrift für Grundschulforschung (ZfG)","status":"public","publisher":"Springer","date_updated":"2022-06-02T08:04:19Z","author":[{"full_name":"Häsel-Weide, Uta","id":"60267","last_name":"Häsel-Weide","first_name":"Uta"},{"last_name":"Nührenbürger","full_name":"Nührenbürger, Marcus","first_name":"Marcus"}],"date_created":"2022-06-02T08:04:02Z","title":"Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.","publication_status":"published","issue":"14","related_material":{"link":[{"url":"https://link.springer.com/content/pdf/10.1007/s42278-020-00097-1.pdf","relation":"contains"}]},"year":"2021","citation":{"apa":"Häsel-Weide, U., &#38; Nührenbürger, M. (2021). Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. <i>Zeitschrift für Grundschulforschung (ZfG)</i>, <i>14</i>, 49–65.","short":"U. Häsel-Weide, M. Nührenbürger, Zeitschrift für Grundschulforschung (ZfG) (2021) 49–65.","mla":"Häsel-Weide, Uta, and Marcus Nührenbürger. “Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.” <i>Zeitschrift für Grundschulforschung (ZfG)</i>, no. 14, Springer, 2021, pp. 49–65.","bibtex":"@article{Häsel-Weide_Nührenbürger_2021, title={Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.}, number={14}, journal={Zeitschrift für Grundschulforschung (ZfG)}, publisher={Springer}, author={Häsel-Weide, Uta and Nührenbürger, Marcus}, year={2021}, pages={49–65} }","chicago":"Häsel-Weide, Uta, and Marcus Nührenbürger. “Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.” <i>Zeitschrift für Grundschulforschung (ZfG)</i>, no. 14 (2021): 49–65.","ieee":"U. Häsel-Weide and M. Nührenbürger, “Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.,” <i>Zeitschrift für Grundschulforschung (ZfG)</i>, no. 14, pp. 49–65, 2021.","ama":"Häsel-Weide U, Nührenbürger M. Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. <i>Zeitschrift für Grundschulforschung (ZfG)</i>. 2021;(14):49-65."},"page":"49-65"},{"publication_status":"published","publication_identifier":{"issn":[" 2701-9012"]},"issue":"2","related_material":{"link":[{"url":"https://zmfp.de/fileadmin/user_upload/veroeffentlichungen/ZMFP_2021_Ha__sel-Weide_Scho__ttler_Dezimalsystem_ISSN.pdf","relation":"contains"}]},"year":"2021","citation":{"apa":"Häsel-Weide, U., &#38; Schöttler, C. (2021). Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen. <i>Zeitschrift für Mathematikdidaktik in Forschung &#38; Praxis (ZMFP)</i>, <i>2</i>.","short":"U. Häsel-Weide, C. Schöttler, Zeitschrift für Mathematikdidaktik in Forschung &#38; Praxis (ZMFP) (2021).","bibtex":"@article{Häsel-Weide_Schöttler_2021, title={Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen}, number={2}, journal={Zeitschrift für Mathematikdidaktik in Forschung &#38; Praxis (ZMFP)}, author={Häsel-Weide, Uta and Schöttler, Christian}, year={2021} }","mla":"Häsel-Weide, Uta, and Christian Schöttler. “Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen.” <i>Zeitschrift für Mathematikdidaktik in Forschung &#38; Praxis (ZMFP)</i>, no. 2, 2021.","chicago":"Häsel-Weide, Uta, and Christian Schöttler. “Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen.” <i>Zeitschrift für Mathematikdidaktik in Forschung &#38; Praxis (ZMFP)</i>, no. 2 (2021).","ieee":"U. Häsel-Weide and C. Schöttler, “Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen,” <i>Zeitschrift für Mathematikdidaktik in Forschung &#38; Praxis (ZMFP)</i>, no. 2, 2021.","ama":"Häsel-Weide U, Schöttler C. Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen. <i>Zeitschrift für Mathematikdidaktik in Forschung &#38; Praxis (ZMFP)</i>. 2021;(2)."},"date_updated":"2022-06-02T09:05:00Z","date_created":"2022-06-02T08:09:31Z","author":[{"last_name":"Häsel-Weide","id":"60267","full_name":"Häsel-Weide, Uta","first_name":"Uta"},{"last_name":"Schöttler","full_name":"Schöttler, Christian","first_name":"Christian"}],"title":"Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen","type":"journal_article","publication":"Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP)","status":"public","_id":"31577","user_id":"85821","department":[{"_id":"98"},{"_id":"543"}],"language":[{"iso":"ger"}]},{"_id":"32810","department":[{"_id":"542"}],"user_id":"15540","keyword":["Discrete Mathematics and Combinatorics"],"article_number":"103451","language":[{"iso":"eng"}],"publication":"European Journal of Combinatorics","type":"journal_article","status":"public","publisher":"Elsevier BV","date_updated":"2022-08-15T09:35:32Z","volume":100,"date_created":"2022-08-15T09:35:02Z","author":[{"full_name":"Li, Jiaao","last_name":"Li","first_name":"Jiaao"},{"id":"92748","full_name":"Ma, Yulai","last_name":"Ma","first_name":"Yulai"},{"first_name":"Yongtang","full_name":"Shi, Yongtang","last_name":"Shi"},{"full_name":"Wang, Weifan","last_name":"Wang","first_name":"Weifan"},{"first_name":"Yezhou","full_name":"Wu, Yezhou","last_name":"Wu"}],"title":"On 3-flow-critical graphs","doi":"10.1016/j.ejc.2021.103451","publication_identifier":{"issn":["0195-6698"]},"publication_status":"published","year":"2021","intvolume":"       100","citation":{"apa":"Li, J., Ma, Y., Shi, Y., Wang, W., &#38; Wu, Y. (2021). On 3-flow-critical graphs. <i>European Journal of Combinatorics</i>, <i>100</i>, Article 103451. <a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">https://doi.org/10.1016/j.ejc.2021.103451</a>","short":"J. Li, Y. Ma, Y. Shi, W. Wang, Y. Wu, European Journal of Combinatorics 100 (2021).","bibtex":"@article{Li_Ma_Shi_Wang_Wu_2021, title={On 3-flow-critical graphs}, volume={100}, DOI={<a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">10.1016/j.ejc.2021.103451</a>}, number={103451}, journal={European Journal of Combinatorics}, publisher={Elsevier BV}, author={Li, Jiaao and Ma, Yulai and Shi, Yongtang and Wang, Weifan and Wu, Yezhou}, year={2021} }","mla":"Li, Jiaao, et al. “On 3-Flow-Critical Graphs.” <i>European Journal of Combinatorics</i>, vol. 100, 103451, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">10.1016/j.ejc.2021.103451</a>.","chicago":"Li, Jiaao, Yulai Ma, Yongtang Shi, Weifan Wang, and Yezhou Wu. “On 3-Flow-Critical Graphs.” <i>European Journal of Combinatorics</i> 100 (2021). <a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">https://doi.org/10.1016/j.ejc.2021.103451</a>.","ieee":"J. Li, Y. Ma, Y. Shi, W. Wang, and Y. Wu, “On 3-flow-critical graphs,” <i>European Journal of Combinatorics</i>, vol. 100, Art. no. 103451, 2021, doi: <a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">10.1016/j.ejc.2021.103451</a>.","ama":"Li J, Ma Y, Shi Y, Wang W, Wu Y. On 3-flow-critical graphs. <i>European Journal of Combinatorics</i>. 2021;100. doi:<a href=\"https://doi.org/10.1016/j.ejc.2021.103451\">10.1016/j.ejc.2021.103451</a>"}},{"user_id":"85821","department":[{"_id":"96"}],"_id":"33278","status":"public","type":"journal_article","main_file_link":[{"url":"https://link.springer.com/article/10.1007/s00023-021-01121-5","open_access":"1"}],"author":[{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"first_name":"Tobias","full_name":"Weich, Tobias","last_name":"Weich"},{"full_name":"Wolf, Lasse","last_name":"Wolf","first_name":"Lasse"}],"volume":23,"oa":"1","date_updated":"2022-09-08T06:06:13Z","citation":{"apa":"Kolb, M., Weich, T., &#38; Wolf, L. (2021). Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. <i>Annales Henri Poincaré </i>, <i>23</i>(4), 1283–1296.","short":"M. Kolb, T. Weich, L. Wolf, Annales Henri Poincaré  23 (2021) 1283–1296.","bibtex":"@article{Kolb_Weich_Wolf_2021, title={Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature}, volume={23}, number={4}, journal={Annales Henri Poincaré }, publisher={Springer Science + Business Media}, author={Kolb, Martin and Weich, Tobias and Wolf, Lasse}, year={2021}, pages={1283–1296} }","mla":"Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature.” <i>Annales Henri Poincaré </i>, vol. 23, no. 4, Springer Science + Business Media, 2021, pp. 1283–96.","ama":"Kolb M, Weich T, Wolf L. Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature. <i>Annales Henri Poincaré </i>. 2021;23(4):1283-1296.","ieee":"M. Kolb, T. Weich, and L. Wolf, “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature,” <i>Annales Henri Poincaré </i>, vol. 23, no. 4, pp. 1283–1296, 2021.","chicago":"Kolb, Martin, Tobias Weich, and Lasse Wolf. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature.” <i>Annales Henri Poincaré </i> 23, no. 4 (2021): 1283–96."},"intvolume":"        23","page":"1283-1296","related_material":{"link":[{"url":"https://link.springer.com/article/10.1007/s00023-021-01121-5","relation":"contains"}]},"publication_status":"published","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is an orientable compact constantly curved surface, we show that in the limit of infinitely large perturbation the L2-spectrum of the infinitesimal generator of a time-rescaled version of the process converges to the Laplace spectrum of the base manifold."}],"publication":"Annales Henri Poincaré ","title":"Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature","date_created":"2022-09-07T07:05:33Z","publisher":"Springer Science + Business Media","year":"2021","issue":"4"},{"date_created":"2022-09-26T06:53:59Z","author":[{"first_name":"Thomas","last_name":"Richthammer","id":"62054","full_name":"Richthammer, Thomas"},{"full_name":"Fiedler, Michael","last_name":"Fiedler","first_name":"Michael"}],"volume":132,"date_updated":"2022-09-26T06:54:06Z","publisher":"Elsevier","doi":"https://doi.org/10.1016/j.spa.2020.10.003","title":"A lower bound on the displacement of particles in 2D Gibbsian particle systems","publication_status":"published","citation":{"ama":"Richthammer T, Fiedler M. A lower bound on the displacement of particles in 2D Gibbsian particle systems. <i>Stochastic Processes and their Applications</i>. 2021;132:1-32. doi:<a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>","ieee":"T. Richthammer and M. Fiedler, “A lower bound on the displacement of particles in 2D Gibbsian particle systems,” <i>Stochastic Processes and their Applications</i>, vol. 132, pp. 1–32, 2021, doi: <a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>.","chicago":"Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement of Particles in 2D Gibbsian Particle Systems.” <i>Stochastic Processes and Their Applications</i> 132 (2021): 1–32. <a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>.","mla":"Richthammer, Thomas, and Michael Fiedler. “A Lower Bound on the Displacement of Particles in 2D Gibbsian Particle Systems.” <i>Stochastic Processes and Their Applications</i>, vol. 132, Elsevier, 2021, pp. 1–32, doi:<a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>.","short":"T. Richthammer, M. Fiedler, Stochastic Processes and Their Applications 132 (2021) 1–32.","bibtex":"@article{Richthammer_Fiedler_2021, title={A lower bound on the displacement of particles in 2D Gibbsian particle systems}, volume={132}, DOI={<a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>}, journal={Stochastic Processes and their Applications}, publisher={Elsevier}, author={Richthammer, Thomas and Fiedler, Michael}, year={2021}, pages={1–32} }","apa":"Richthammer, T., &#38; Fiedler, M. (2021). A lower bound on the displacement of particles in 2D Gibbsian particle systems. <i>Stochastic Processes and Their Applications</i>, <i>132</i>, 1–32. <a href=\"https://doi.org/10.1016/j.spa.2020.10.003\">https://doi.org/10.1016/j.spa.2020.10.003</a>"},"intvolume":"       132","page":"1-32","year":"2021","user_id":"85821","department":[{"_id":"96"}],"_id":"33481","language":[{"iso":"eng"}],"type":"journal_article","publication":"Stochastic Processes and their Applications","status":"public","abstract":[{"text":"While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we investigate to which extent particles within a box of size may fluctuate from their ideal lattice position. We show that particles near the center of the box typically show a displacement at least of order . Thus we extend recent results on the hard disk model to particle systems with fairly arbitrary particle spins and interaction. Our result applies to models such as rather general continuum Potts type models, e.g. with Widom–Rowlinson or Lenard-Jones-type interaction.","lang":"eng"}]}]