---
_id: '21820'
abstract:
- lang: eng
text: The reduction of high-dimensional systems to effective models on a
smaller set of variables is an essential task in many areas of science. For stochastic
dynamics governed by diffusion processes, a general procedure to find effective
equations is the conditioning approach. In this paper, we are interested in the
spectrum of the generator of the resulting effective dynamics, and how it compares
to the spectrum of the full generator. We prove a new relative error bound in
terms of the eigenfunction approximation error for reversible systems. We also
present numerical examples indicating that, if Kramers–Moyal (KM) type approximations
are used to compute the spectrum of the reduced generator, it seems largely insensitive
to the time window used for the KM estimators. We analyze the implications of
these observations for systems driven by underdamped Langevin dynamics, and show
how meaningful effective dynamics can be defined in this setting.
article_number: '134'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Lorenzo
full_name: Boninsegna, Lorenzo
last_name: Boninsegna
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective
Dynamics from Conditional Expectations. Entropy. 2021. doi:10.3390/e23020134
apa: Nüske, F., Koltai, P., Boninsegna, L., & Clementi, C. (2021). Spectral
Properties of Effective Dynamics from Conditional Expectations. Entropy.
https://doi.org/10.3390/e23020134
bibtex: '@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties
of Effective Dynamics from Conditional Expectations}, DOI={10.3390/e23020134},
number={134}, journal={Entropy}, author={Nüske, Feliks and Koltai, Péter and Boninsegna,
Lorenzo and Clementi, Cecilia}, year={2021} }'
chicago: Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi.
“Spectral Properties of Effective Dynamics from Conditional Expectations.” Entropy,
2021. https://doi.org/10.3390/e23020134.
ieee: F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties
of Effective Dynamics from Conditional Expectations,” Entropy, 2021.
mla: Nüske, Feliks, et al. “Spectral Properties of Effective Dynamics from Conditional
Expectations.” Entropy, 134, 2021, doi:10.3390/e23020134.
short: F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).
date_created: 2021-04-28T18:07:56Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e23020134
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/23/2/134
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Spectral Properties of Effective Dynamics from Conditional Expectations
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '16867'
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."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective
optimization problems. Journal of Optimization Theory and Applications.
2021;188:696-723. doi:10.1007/s10957-020-01803-w
apa: Gebken, B., & Peitz, S. (2021). An efficient descent method for locally
Lipschitz multiobjective optimization problems. Journal of Optimization Theory
and Applications, 188, 696–723. https://doi.org/10.1007/s10957-020-01803-w
bibtex: '@article{Gebken_Peitz_2021, title={An efficient descent method for locally
Lipschitz multiobjective optimization problems}, volume={188}, DOI={10.1007/s10957-020-01803-w},
journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet
and Peitz, Sebastian}, year={2021}, pages={696–723} }'
chicago: 'Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for
Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization
Theory and Applications 188 (2021): 696–723. https://doi.org/10.1007/s10957-020-01803-w.'
ieee: B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz
multiobjective optimization problems,” Journal of Optimization Theory and Applications,
vol. 188, pp. 696–723, 2021.
mla: Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally
Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory
and Applications, vol. 188, 2021, pp. 696–723, doi:10.1007/s10957-020-01803-w.
short: B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188
(2021) 696–723.
date_created: 2020-04-27T09:11:22Z
date_updated: 2022-01-06T06:52:57Z
department:
- _id: '101'
doi: 10.1007/s10957-020-01803-w
intvolume: ' 188'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf
oa: '1'
page: 696-723
publication: Journal of Optimization Theory and Applications
publication_status: published
status: public
title: An efficient descent method for locally Lipschitz multiobjective optimization
problems
type: journal_article
user_id: '47427'
volume: 188
year: '2021'
...
---
_id: '16295'
abstract:
- lang: eng
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.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: 'Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision
criteria from data. Journal of Global Optimization. 2021;80:3-29. doi:10.1007/s10898-020-00983-z'
apa: 'Gebken, B., & Peitz, S. (2021). Inverse multiobjective optimization: Inferring
decision criteria from data. Journal of Global Optimization, 80,
3–29. https://doi.org/10.1007/s10898-020-00983-z'
bibtex: '@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization:
Inferring decision criteria from data}, volume={80}, DOI={10.1007/s10898-020-00983-z},
journal={Journal of Global Optimization}, publisher={Springer}, author={Gebken,
Bennet and Peitz, Sebastian}, year={2021}, pages={3–29} }'
chicago: 'Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization:
Inferring Decision Criteria from Data.” Journal of Global Optimization
80 (2021): 3–29. https://doi.org/10.1007/s10898-020-00983-z.'
ieee: 'B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision
criteria from data,” Journal of Global Optimization, vol. 80, pp. 3–29,
2021.'
mla: 'Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization:
Inferring Decision Criteria from Data.” Journal of Global Optimization,
vol. 80, Springer, 2021, pp. 3–29, doi:10.1007/s10898-020-00983-z.'
short: B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29.
date_created: 2020-03-13T12:45:05Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/s10898-020-00983-z
intvolume: ' 80'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf
oa: '1'
page: 3-29
publication: Journal of Global Optimization
publisher: Springer
status: public
title: 'Inverse multiobjective optimization: Inferring decision criteria from data'
type: journal_article
user_id: '47427'
volume: 80
year: '2021'
...
---
_id: '32057'
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.
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
citation:
ama: Gerlach R. The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems.; 2021. doi:10.17619/UNIPB/1-1278
apa: Gerlach, R. (2021). The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems. https://doi.org/10.17619/UNIPB/1-1278
bibtex: '@book{Gerlach_2021, title={The Computation and Analysis of Invariant Sets
of Infinite-Dimensional Systems}, DOI={10.17619/UNIPB/1-1278},
author={Gerlach, Raphael}, year={2021} }'
chicago: Gerlach, Raphael. The Computation and Analysis of Invariant Sets of
Infinite-Dimensional Systems, 2021. https://doi.org/10.17619/UNIPB/1-1278.
ieee: R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems. 2021.
mla: Gerlach, Raphael. The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems. 2021, doi:10.17619/UNIPB/1-1278.
short: R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems, 2021.
date_created: 2022-06-20T09:54:24Z
date_updated: 2022-06-20T13:40:30Z
department:
- _id: '101'
doi: 10.17619/UNIPB/1-1278
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/download/pdf/6214949
oa: '1'
status: public
supervisor:
- first_name: Michael
full_name: Dellnitz , Michael
last_name: 'Dellnitz '
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
title: The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems
type: dissertation
user_id: '32643'
year: '2021'
...
---
_id: '32016'
article_type: original
author:
- first_name: Benjamin
full_name: Delarue, Benjamin
id: '70575'
last_name: Delarue
- first_name: Pablo
full_name: Ramacher, Pablo
last_name: Ramacher
citation:
ama: Delarue B, Ramacher P. Asymptotic expansion of generalized Witten integrals
for Hamiltonian circle actions. Journal of Symplectic Geometry. 2021;19(6):1281-1337.
doi:10.4310/JSG.2021.v19.n6.a1
apa: Delarue, B., & Ramacher, P. (2021). Asymptotic expansion of generalized
Witten integrals for Hamiltonian circle actions. Journal of Symplectic Geometry,
19(6), 1281–1337. https://doi.org/10.4310/JSG.2021.v19.n6.a1
bibtex: '@article{Delarue_Ramacher_2021, title={Asymptotic expansion of generalized
Witten integrals for Hamiltonian circle actions}, volume={19}, DOI={10.4310/JSG.2021.v19.n6.a1},
number={6}, journal={Journal of Symplectic Geometry}, author={Delarue, Benjamin
and Ramacher, Pablo}, year={2021}, pages={1281–1337} }'
chicago: 'Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized
Witten Integrals for Hamiltonian Circle Actions.” Journal of Symplectic Geometry
19, no. 6 (2021): 1281–1337. https://doi.org/10.4310/JSG.2021.v19.n6.a1.'
ieee: 'B. Delarue and P. Ramacher, “Asymptotic expansion of generalized Witten integrals
for Hamiltonian circle actions,” Journal of Symplectic Geometry, vol. 19,
no. 6, pp. 1281–1337, 2021, doi: 10.4310/JSG.2021.v19.n6.a1.'
mla: Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized
Witten Integrals for Hamiltonian Circle Actions.” Journal of Symplectic Geometry,
vol. 19, no. 6, 2021, pp. 1281–337, doi:10.4310/JSG.2021.v19.n6.a1.
short: B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337.
date_created: 2022-06-20T08:46:56Z
date_updated: 2022-06-21T11:54:50Z
department:
- _id: '548'
doi: 10.4310/JSG.2021.v19.n6.a1
intvolume: ' 19'
issue: '6'
language:
- iso: eng
page: 1281 - 1337
publication: Journal of Symplectic Geometry
publication_identifier:
unknown:
- 1540-2347
- 1527-5256
publication_status: published
status: public
title: Asymptotic expansion of generalized Witten integrals for Hamiltonian circle
actions
type: journal_article
user_id: '70575'
volume: 19
year: '2021'
...
---
_id: '34042'
author:
- first_name: Jiaao
full_name: Li, Jiaao
last_name: Li
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
last_name: Ma
- first_name: Zhengke
full_name: Miao, Zhengke
last_name: Miao
- first_name: Yongtang
full_name: Shi, Yongtang
last_name: Shi
- first_name: Weifan
full_name: Wang, Weifan
last_name: Wang
- first_name: Cun-Quan
full_name: Zhang, Cun-Quan
last_name: Zhang
citation:
ama: Li J, Ma Y, Miao Z, Shi Y, Wang W, Zhang C-Q. Nowhere-zero 3-flows in toroidal
graphs. Journal of Combinatorial Theory, Series B. 2021;153:61-80. doi:10.1016/j.jctb.2021.11.001
apa: Li, J., Ma, Y., Miao, Z., Shi, Y., Wang, W., & Zhang, C.-Q. (2021). Nowhere-zero
3-flows in toroidal graphs. Journal of Combinatorial Theory, Series B,
153, 61–80. https://doi.org/10.1016/j.jctb.2021.11.001
bibtex: '@article{Li_Ma_Miao_Shi_Wang_Zhang_2021, title={Nowhere-zero 3-flows in
toroidal graphs}, volume={153}, DOI={10.1016/j.jctb.2021.11.001},
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} }'
chicago: 'Li, Jiaao, Yulai Ma, Zhengke Miao, Yongtang Shi, Weifan Wang, and Cun-Quan
Zhang. “Nowhere-Zero 3-Flows in Toroidal Graphs.” Journal of Combinatorial
Theory, Series B 153 (2021): 61–80. https://doi.org/10.1016/j.jctb.2021.11.001.'
ieee: 'J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, and C.-Q. Zhang, “Nowhere-zero 3-flows
in toroidal graphs,” Journal of Combinatorial Theory, Series B, vol. 153,
pp. 61–80, 2021, doi: 10.1016/j.jctb.2021.11.001.'
mla: Li, Jiaao, et al. “Nowhere-Zero 3-Flows in Toroidal Graphs.” Journal of
Combinatorial Theory, Series B, vol. 153, Elsevier BV, 2021, pp. 61–80, doi:10.1016/j.jctb.2021.11.001.
short: J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, C.-Q. Zhang, Journal of Combinatorial
Theory, Series B 153 (2021) 61–80.
date_created: 2022-11-09T08:43:55Z
date_updated: 2022-11-09T08:44:37Z
department:
- _id: '542'
doi: 10.1016/j.jctb.2021.11.001
intvolume: ' 153'
keyword:
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
language:
- iso: eng
page: 61-80
publication: Journal of Combinatorial Theory, Series B
publication_identifier:
issn:
- 0095-8956
publication_status: published
publisher: Elsevier BV
status: public
title: Nowhere-zero 3-flows in toroidal graphs
type: journal_article
user_id: '15540'
volume: 153
year: '2021'
...
---
_id: '34786'
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.
article_type: original
author:
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
- first_name: George A.
full_name: Willis, George A.
last_name: Willis
citation:
ama: Glöckner H, Willis GA. Decompositions of locally compact contraction groups,
series and extensions. Journal of Algebra. 2021;570:164-214. doi:https://doi.org/10.1016/j.jalgebra.2020.11.007
apa: Glöckner, H., & Willis, G. A. (2021). Decompositions of locally compact
contraction groups, series and extensions. Journal of Algebra, 570,
164–214. https://doi.org/10.1016/j.jalgebra.2020.11.007
bibtex: '@article{Glöckner_Willis_2021, title={Decompositions of locally compact
contraction groups, series and extensions}, volume={570}, DOI={https://doi.org/10.1016/j.jalgebra.2020.11.007},
journal={Journal of Algebra}, author={Glöckner, Helge and Willis, George A.},
year={2021}, pages={164–214} }'
chicago: 'Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact
Contraction Groups, Series and Extensions.” Journal of Algebra 570 (2021):
164–214. https://doi.org/10.1016/j.jalgebra.2020.11.007.'
ieee: 'H. Glöckner and G. A. Willis, “Decompositions of locally compact contraction
groups, series and extensions,” Journal of Algebra, vol. 570, pp. 164–214,
2021, doi: https://doi.org/10.1016/j.jalgebra.2020.11.007.'
mla: Glöckner, Helge, and George A. Willis. “Decompositions of Locally Compact Contraction
Groups, Series and Extensions.” Journal of Algebra, vol. 570, 2021, pp.
164–214, doi:https://doi.org/10.1016/j.jalgebra.2020.11.007.
short: H. Glöckner, G.A. Willis, Journal of Algebra 570 (2021) 164–214.
date_created: 2022-12-21T18:43:08Z
date_updated: 2022-12-21T18:58:44Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: https://doi.org/10.1016/j.jalgebra.2020.11.007
intvolume: ' 570'
keyword:
- Contraction group
- Torsion group
- Extension
- Cocycle
- Section
- Equivariant cohomology
- Abelian group
- Nilpotent group
- Isomorphism types
language:
- iso: eng
page: 164-214
publication: Journal of Algebra
publication_identifier:
issn:
- 0021-8693
quality_controlled: '1'
status: public
title: Decompositions of locally compact contraction groups, series and extensions
type: journal_article
user_id: '178'
volume: 570
year: '2021'
...
---
_id: '34795'
article_type: original
author:
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
citation:
ama: Glöckner H. Direct limits of regular Lie groups. Mathematische Nachrichten.
2021;294(1):74–81. doi:10.1002/mana.201900073
apa: Glöckner, H. (2021). Direct limits of regular Lie groups. Mathematische
Nachrichten, 294(1), 74–81. https://doi.org/10.1002/mana.201900073
bibtex: '@article{Glöckner_2021, title={Direct limits of regular Lie groups}, volume={294},
DOI={10.1002/mana.201900073},
number={1}, journal={Mathematische Nachrichten}, author={Glöckner, Helge}, year={2021},
pages={74–81} }'
chicago: 'Glöckner, Helge. “Direct Limits of Regular Lie Groups.” Mathematische
Nachrichten 294, no. 1 (2021): 74–81. https://doi.org/10.1002/mana.201900073.'
ieee: 'H. Glöckner, “Direct limits of regular Lie groups,” Mathematische Nachrichten,
vol. 294, no. 1, pp. 74–81, 2021, doi: 10.1002/mana.201900073.'
mla: Glöckner, Helge. “Direct Limits of Regular Lie Groups.” Mathematische Nachrichten,
vol. 294, no. 1, 2021, pp. 74–81, doi:10.1002/mana.201900073.
short: H. Glöckner, Mathematische Nachrichten 294 (2021) 74–81.
date_created: 2022-12-21T19:57:32Z
date_updated: 2022-12-21T20:00:29Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1002/mana.201900073
intvolume: ' 294'
issue: '1'
language:
- iso: eng
page: 74–81
publication: Mathematische Nachrichten
publication_identifier:
issn:
- 0025-584X
quality_controlled: '1'
status: public
title: Direct limits of regular Lie groups
type: journal_article
user_id: '178'
volume: 294
year: '2021'
...
---
_id: '34806'
abstract:
- lang: eng
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."
author:
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
citation:
ama: Glöckner H. Contraction groups and the big cell for endomorphisms of Lie groups
over local fields. arXiv:210102981. Published online 2021.
apa: Glöckner, H. (2021). Contraction groups and the big cell for endomorphisms
of Lie groups over local fields. In arXiv:2101.02981.
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} }'
chicago: Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms
of Lie Groups over Local Fields.” ArXiv:2101.02981, 2021.
ieee: H. Glöckner, “Contraction groups and the big cell for endomorphisms of Lie
groups over local fields,” arXiv:2101.02981. 2021.
mla: Glöckner, Helge. “Contraction Groups and the Big Cell for Endomorphisms of
Lie Groups over Local Fields.” ArXiv:2101.02981, 2021.
short: H. Glöckner, ArXiv:2101.02981 (2021).
date_created: 2022-12-22T07:47:35Z
date_updated: 2022-12-22T07:48:29Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
arxiv:
- '2101.02981'
language:
- iso: eng
publication: arXiv:2101.02981
status: public
title: Contraction groups and the big cell for endomorphisms of Lie groups over local
fields
type: preprint
user_id: '178'
year: '2021'
...
---
_id: '29421'
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: M.
full_name: Vermeeren, M.
last_name: Vermeeren
citation:
ama: 'Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators.
In: IFAC-PapersOnLine, ed. 7th IIFAC Workshop on Lagrangian and Hamiltonian
Methods for Nonlinear Control LHMNC. Vol 54(19). ; 2021:327-333.'
apa: 'Ober-Blöbaum, S., & Vermeeren, M. (2021). Superconvergence of galerkin
variational integrators. In IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on
Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)
(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}
}'
chicago: Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational
Integrators.” In 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.
ieee: S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational
integrators,” in 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, 2021, vol. 54(19), pp. 327–333.
mla: Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational
Integrators.” 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, 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.'
corporate_editor:
- IFAC-PapersOnLine
date_created: 2022-01-18T14:27:56Z
date_updated: 2022-01-21T13:36:53Z
department:
- _id: '636'
language:
- iso: eng
page: 327-333
publication: 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear
Control LHMNC
status: public
title: Superconvergence of galerkin variational integrators
type: conference
user_id: '15694'
volume: 54(19)
year: '2021'
...
---
_id: '16294'
abstract:
- lang: eng
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."
author:
- 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: Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for
nonlinear systems with symmetries. International Journal of Robust and Nonlinear
Control. 2021;31(2):380-403. doi:10.1002/rnc.5281
apa: Ober-Blöbaum, S., & Peitz, S. (2021). Explicit multiobjective model predictive
control for nonlinear systems with symmetries. International Journal of Robust
and Nonlinear Control, 31(2), 380–403. https://doi.org/10.1002/rnc.5281
bibtex: '@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model
predictive control for nonlinear systems with symmetries}, volume={31(2)}, DOI={10.1002/rnc.5281}, journal={International
Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz,
Sebastian}, year={2021}, pages={380–403} }'
chicago: 'Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model
Predictive Control for Nonlinear Systems with Symmetries.” International Journal
of Robust and Nonlinear Control 31(2) (2021): 380–403. https://doi.org/10.1002/rnc.5281.'
ieee: 'S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control
for nonlinear systems with symmetries,” International Journal of Robust and
Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi: 10.1002/rnc.5281.'
mla: Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive
Control for Nonlinear Systems with Symmetries.” International Journal of Robust
and Nonlinear Control, vol. 31(2), 2021, pp. 380–403, doi:10.1002/rnc.5281.
short: S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear
Control 31(2) (2021) 380–403.
date_created: 2020-03-13T12:44:36Z
date_updated: 2022-01-24T13:27:50Z
department:
- _id: '101'
doi: 10.1002/rnc.5281
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281
oa: '1'
page: 380-403
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: International Journal of Robust and Nonlinear Control
status: public
title: Explicit multiobjective model predictive control for nonlinear systems with
symmetries
type: journal_article
user_id: '15694'
volume: 31(2)
year: '2021'
...
---
_id: '29543'
article_number: '109804'
author:
- first_name: Walid
full_name: Djema, Walid
last_name: Djema
- first_name: Laetitia
full_name: Giraldi, Laetitia
last_name: Giraldi
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Olivier
full_name: Bernard, Olivier
last_name: Bernard
citation:
ama: Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal
selection of species represented by quota models. Automatica. 2021;132.
doi:10.1016/j.automatica.2021.109804
apa: Djema, W., Giraldi, L., Maslovskaya, S., & Bernard, O. (2021). Turnpike
features in optimal selection of species represented by quota models. Automatica,
132, Article 109804. https://doi.org/10.1016/j.automatica.2021.109804
bibtex: '@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features
in optimal selection of species represented by quota models}, volume={132}, DOI={10.1016/j.automatica.2021.109804},
number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema,
Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021}
}'
chicago: Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard.
“Turnpike Features in Optimal Selection of Species Represented by Quota Models.”
Automatica 132 (2021). https://doi.org/10.1016/j.automatica.2021.109804.
ieee: 'W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features
in optimal selection of species represented by quota models,” Automatica,
vol. 132, Art. no. 109804, 2021, doi: 10.1016/j.automatica.2021.109804.'
mla: Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented
by Quota Models.” Automatica, vol. 132, 109804, Elsevier BV, 2021, doi:10.1016/j.automatica.2021.109804.
short: W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).
date_created: 2022-01-26T13:13:06Z
date_updated: 2022-01-26T13:15:33Z
department:
- _id: '636'
doi: 10.1016/j.automatica.2021.109804
intvolume: ' 132'
keyword:
- Electrical and Electronic Engineering
- Control and Systems Engineering
language:
- iso: eng
publication: Automatica
publication_identifier:
issn:
- 0005-1098
publication_status: published
publisher: Elsevier BV
status: public
title: Turnpike features in optimal selection of species represented by quota models
type: journal_article
user_id: '87909'
volume: 132
year: '2021'
...
---
_id: '31058'
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.
author:
- first_name: Philipp
full_name: Schütte, Philipp
id: '50168'
last_name: Schütte
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Benjamin
full_name: Delarue, Benjamin
last_name: Delarue
citation:
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., & Delarue, B. (2021). Resonances and weighted
zeta functions for obstacle scattering via smooth models.
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} }'
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.
mla: Schütte, Philipp, et al. Resonances and Weighted Zeta Functions for Obstacle
Scattering via Smooth Models. 2021.
short: P. Schütte, T. Weich, B. Delarue, (2021).
date_created: 2022-05-04T12:25:58Z
date_updated: 2022-05-17T12:05:52Z
department:
- _id: '10'
- _id: '548'
external_id:
arxiv:
- '2109.05907'
language:
- iso: eng
status: public
title: Resonances and weighted zeta functions for obstacle scattering via smooth models
type: preprint
user_id: '50168'
year: '2021'
...
---
_id: '31385'
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
citation:
ama: 'Hoffmann M. Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen
Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie. Mathematische
Semesterberichte. 2021;68:295–297. doi:10.1007/s00591-021-00299-3'
apa: 'Hoffmann, M. (2021). Rezension: Hendrik Kasten und Denis Vogel: Grundlagen
der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie.
In Mathematische Semesterberichte (Vol. 68, pp. 295–297). https://doi.org/10.1007/s00591-021-00299-3'
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={10.1007/s00591-021-00299-3},
journal={Mathematische Semesterberichte}, author={Hoffmann, Max}, year={2021},
pages={295–297} }'
chicago: 'Hoffmann, Max. “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen
der ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie.”
Mathematische Semesterberichte, 2021. https://doi.org/10.1007/s00591-021-00299-3.'
ieee: 'M. Hoffmann, “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen
Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie,” Mathematische
Semesterberichte, vol. 68. pp. 295–297, 2021, doi: 10.1007/s00591-021-00299-3.'
mla: 'Hoffmann, Max. “Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der
ebenen Geometrie – Eine zugängliche aber exakte Einführung in die ebene Geometrie.”
Mathematische Semesterberichte, vol. 68, 2021, pp. 295–297, doi:10.1007/s00591-021-00299-3.'
short: M. Hoffmann, Mathematische Semesterberichte 68 (2021) 295–297.
date_created: 2022-05-22T15:20:46Z
date_updated: 2022-05-22T15:58:33Z
department:
- _id: '97'
doi: 10.1007/s00591-021-00299-3
intvolume: ' 68'
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://link.springer.com/article/10.1007/s00591-021-00299-3
oa: '1'
page: 295–297
publication: Mathematische Semesterberichte
publication_status: published
status: public
title: 'Rezension: Hendrik Kasten und Denis Vogel: Grundlagen der ebenen Geometrie
– Eine zugängliche aber exakte Einführung in die ebene Geometrie'
type: review
user_id: '32202'
volume: 68
year: '2021'
...
---
_id: '31364'
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
citation:
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. Lehrinnovationen in der Hochschulmathematik. praxisrelevant
– didaktisch fundiert – forschungsbasiert. Springer Berlin Heidelberg; 2021:179–204.
doi:10.1007/978-3-662-62854-6_9'
apa: Hoffmann, M. (2021). Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen
– Praxisbeispiele aus der Universität Paderborn. In R. Biehler, A. Eichler, R.
Hochmuth, S. Rach, & N. Schaper (Eds.), Lehrinnovationen in der Hochschulmathematik.
praxisrelevant – didaktisch fundiert – forschungsbasiert (pp. 179–204). Springer
Berlin Heidelberg. https://doi.org/10.1007/978-3-662-62854-6_9
bibtex: '@inbook{Hoffmann_2021, place={Berlin, Heidelberg}, title={Einsatz von Schnittstellenaufgaben
in Mathematikveranstaltungen – Praxisbeispiele aus der Universität Paderborn},
DOI={10.1007/978-3-662-62854-6_9},
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} }'
chicago: 'Hoffmann, Max. “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen
– Praxisbeispiele aus der Universität Paderborn.” In Lehrinnovationen in der
Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert,
edited by Rolf Biehler, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and
Niclas Schaper, 179–204. Berlin, Heidelberg: Springer Berlin Heidelberg, 2021.
https://doi.org/10.1007/978-3-662-62854-6_9.'
ieee: 'M. Hoffmann, “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen
– Praxisbeispiele aus der Universität Paderborn,” in Lehrinnovationen in der
Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert,
R. Biehler, A. Eichler, R. Hochmuth, S. Rach, and N. Schaper, Eds. Berlin, Heidelberg:
Springer Berlin Heidelberg, 2021, pp. 179–204.'
mla: Hoffmann, Max. “Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen
– Praxisbeispiele aus der Universität Paderborn.” Lehrinnovationen in der
Hochschulmathematik. praxisrelevant – didaktisch fundiert – forschungsbasiert,
edited by Rolf Biehler et al., Springer Berlin Heidelberg, 2021, pp. 179–204,
doi:10.1007/978-3-662-62854-6_9.
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.'
date_created: 2022-05-22T13:56:39Z
date_updated: 2022-05-24T13:18:09Z
department:
- _id: '97'
doi: 10.1007/978-3-662-62854-6_9
editor:
- first_name: Rolf
full_name: Biehler, Rolf
last_name: Biehler
- first_name: Andreas
full_name: Eichler, Andreas
last_name: Eichler
- first_name: Reinhard
full_name: Hochmuth, Reinhard
last_name: Hochmuth
- first_name: Stefanie
full_name: Rach, Stefanie
last_name: Rach
- first_name: Niclas
full_name: Schaper, Niclas
last_name: Schaper
language:
- iso: ger
main_file_link:
- url: https://link.springer.com/chapter/10.1007/978-3-662-62854-6_9
page: 179–204
place: Berlin, Heidelberg
publication: ' Lehrinnovationen in der Hochschulmathematik. praxisrelevant – didaktisch
fundiert – forschungsbasiert'
publication_identifier:
isbn:
- '9783662628539'
- '9783662628546'
issn:
- 2197-8751
- 2197-876X
publication_status: published
publisher: Springer Berlin Heidelberg
quality_controlled: '1'
status: public
title: Einsatz von Schnittstellenaufgaben in Mathematikveranstaltungen – Praxisbeispiele
aus der Universität Paderborn
type: book_chapter
user_id: '32202'
year: '2021'
...
---
_id: '31261'
abstract:
- lang: eng
text: "Abstract\r\n 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."
author:
- first_name: Benjamin
full_name: Küster, Benjamin
last_name: Küster
- first_name: Tobias
full_name: Weich, Tobias
last_name: Weich
citation:
ama: Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles
Over Locally Symmetric Spaces. International Mathematics Research Notices.
2021;2021(11):8225-8296. doi:10.1093/imrn/rnz068
apa: Küster, B., & Weich, T. (2021). Quantum-Classical Correspondence on Associated
Vector Bundles Over Locally Symmetric Spaces. International Mathematics Research
Notices, 2021(11), 8225–8296. https://doi.org/10.1093/imrn/rnz068
bibtex: '@article{Küster_Weich_2021, title={Quantum-Classical Correspondence on
Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={10.1093/imrn/rnz068}, number={11},
journal={International Mathematics Research Notices}, publisher={Oxford University
Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2021}, pages={8225–8296}
}'
chicago: 'Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence
on Associated Vector Bundles Over Locally Symmetric Spaces.” International
Mathematics Research Notices 2021, no. 11 (2021): 8225–96. https://doi.org/10.1093/imrn/rnz068.'
ieee: 'B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector
Bundles Over Locally Symmetric Spaces,” International Mathematics Research
Notices, vol. 2021, no. 11, pp. 8225–8296, 2021, doi: 10.1093/imrn/rnz068.'
mla: Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated
Vector Bundles Over Locally Symmetric Spaces.” International Mathematics Research
Notices, vol. 2021, no. 11, Oxford University Press (OUP), 2021, pp. 8225–96,
doi:10.1093/imrn/rnz068.
short: B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021)
8225–8296.
date_created: 2022-05-17T12:00:36Z
date_updated: 2022-05-25T06:42:01Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: 10.1093/imrn/rnz068
external_id:
arxiv:
- '1710.04625'
intvolume: ' 2021'
issue: '11'
keyword:
- General Mathematics
language:
- iso: eng
page: 8225-8296
publication: International Mathematics Research Notices
publication_identifier:
issn:
- 1073-7928
- 1687-0247
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Quantum-Classical Correspondence on Associated Vector Bundles Over Locally
Symmetric Spaces
type: journal_article
user_id: '49178'
volume: 2021
year: '2021'
...
---
_id: '31576'
author:
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
- first_name: Marcus
full_name: Nührenbürger, Marcus
last_name: Nührenbürger
citation:
ama: Häsel-Weide U, Nührenbürger M. Inklusive Praktiken im Mathematikunterricht.
Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. Zeitschrift
für Grundschulforschung (ZfG). 2021;(14):49-65.
apa: Häsel-Weide, U., & Nührenbürger, M. (2021). Inklusive Praktiken im Mathematikunterricht.
Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen. Zeitschrift
für Grundschulforschung (ZfG), 14, 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.” Zeitschrift
für Grundschulforschung (ZfG), no. 14 (2021): 49–65.'
ieee: U. Häsel-Weide and M. Nührenbürger, “Inklusive Praktiken im Mathematikunterricht.
Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.,” Zeitschrift
für Grundschulforschung (ZfG), no. 14, pp. 49–65, 2021.
mla: Häsel-Weide, Uta, and Marcus Nührenbürger. “Inklusive Praktiken im Mathematikunterricht.
Empirische Analysen von Unterrichtsdiskursen in Einführungsphasen.” Zeitschrift
für Grundschulforschung (ZfG), no. 14, Springer, 2021, pp. 49–65.
short: U. Häsel-Weide, M. Nührenbürger, Zeitschrift für Grundschulforschung (ZfG)
(2021) 49–65.
date_created: 2022-06-02T08:04:02Z
date_updated: 2022-06-02T08:04:19Z
department:
- _id: '98'
- _id: '543'
issue: '14'
language:
- iso: ger
page: 49-65
publication: Zeitschrift für Grundschulforschung (ZfG)
publication_status: published
publisher: Springer
related_material:
link:
- relation: contains
url: https://link.springer.com/content/pdf/10.1007/s42278-020-00097-1.pdf
status: public
title: Inklusive Praktiken im Mathematikunterricht. Empirische Analysen von Unterrichtsdiskursen
in Einführungsphasen.
type: journal_article
user_id: '85821'
year: '2021'
...
---
_id: '31577'
author:
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
- first_name: Christian
full_name: Schöttler, Christian
last_name: Schöttler
citation:
ama: Häsel-Weide U, Schöttler C. Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse,
Anregungen. Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP).
2021;(2).
apa: Häsel-Weide, U., & Schöttler, C. (2021). Das Dezimalsystem verstehen –
Bedeutung, Erkenntnisse, Anregungen. Zeitschrift für Mathematikdidaktik in
Forschung & Praxis (ZMFP), 2.
bibtex: '@article{Häsel-Weide_Schöttler_2021, title={Das Dezimalsystem verstehen
– Bedeutung, Erkenntnisse, Anregungen}, number={2}, journal={Zeitschrift für Mathematikdidaktik
in Forschung & Praxis (ZMFP)}, author={Häsel-Weide, Uta and Schöttler, Christian},
year={2021} }'
chicago: Häsel-Weide, Uta, and Christian Schöttler. “Das Dezimalsystem verstehen
– Bedeutung, Erkenntnisse, Anregungen.” Zeitschrift für Mathematikdidaktik
in Forschung & Praxis (ZMFP), no. 2 (2021).
ieee: U. Häsel-Weide and C. Schöttler, “Das Dezimalsystem verstehen – Bedeutung,
Erkenntnisse, Anregungen,” Zeitschrift für Mathematikdidaktik in Forschung
& Praxis (ZMFP), no. 2, 2021.
mla: Häsel-Weide, Uta, and Christian Schöttler. “Das Dezimalsystem verstehen – Bedeutung,
Erkenntnisse, Anregungen.” Zeitschrift für Mathematikdidaktik in Forschung
& Praxis (ZMFP), no. 2, 2021.
short: U. Häsel-Weide, C. Schöttler, Zeitschrift für Mathematikdidaktik in Forschung
& Praxis (ZMFP) (2021).
date_created: 2022-06-02T08:09:31Z
date_updated: 2022-06-02T09:05:00Z
department:
- _id: '98'
- _id: '543'
issue: '2'
language:
- iso: ger
publication: Zeitschrift für Mathematikdidaktik in Forschung & Praxis (ZMFP)
publication_identifier:
issn:
- ' 2701-9012'
publication_status: published
related_material:
link:
- relation: contains
url: https://zmfp.de/fileadmin/user_upload/veroeffentlichungen/ZMFP_2021_Ha__sel-Weide_Scho__ttler_Dezimalsystem_ISSN.pdf
status: public
title: Das Dezimalsystem verstehen – Bedeutung, Erkenntnisse, Anregungen
type: journal_article
user_id: '85821'
year: '2021'
...
---
_id: '32810'
article_number: '103451'
author:
- first_name: Jiaao
full_name: Li, Jiaao
last_name: Li
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
last_name: Ma
- first_name: Yongtang
full_name: Shi, Yongtang
last_name: Shi
- first_name: Weifan
full_name: Wang, Weifan
last_name: Wang
- first_name: Yezhou
full_name: Wu, Yezhou
last_name: Wu
citation:
ama: Li J, Ma Y, Shi Y, Wang W, Wu Y. On 3-flow-critical graphs. European Journal
of Combinatorics. 2021;100. doi:10.1016/j.ejc.2021.103451
apa: Li, J., Ma, Y., Shi, Y., Wang, W., & Wu, Y. (2021). On 3-flow-critical
graphs. European Journal of Combinatorics, 100, Article 103451.
https://doi.org/10.1016/j.ejc.2021.103451
bibtex: '@article{Li_Ma_Shi_Wang_Wu_2021, title={On 3-flow-critical graphs}, volume={100},
DOI={10.1016/j.ejc.2021.103451},
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} }'
chicago: Li, Jiaao, Yulai Ma, Yongtang Shi, Weifan Wang, and Yezhou Wu. “On 3-Flow-Critical
Graphs.” European Journal of Combinatorics 100 (2021). https://doi.org/10.1016/j.ejc.2021.103451.
ieee: 'J. Li, Y. Ma, Y. Shi, W. Wang, and Y. Wu, “On 3-flow-critical graphs,” European
Journal of Combinatorics, vol. 100, Art. no. 103451, 2021, doi: 10.1016/j.ejc.2021.103451.'
mla: Li, Jiaao, et al. “On 3-Flow-Critical Graphs.” European Journal of Combinatorics,
vol. 100, 103451, Elsevier BV, 2021, doi:10.1016/j.ejc.2021.103451.
short: J. Li, Y. Ma, Y. Shi, W. Wang, Y. Wu, European Journal of Combinatorics 100
(2021).
date_created: 2022-08-15T09:35:02Z
date_updated: 2022-08-15T09:35:32Z
department:
- _id: '542'
doi: 10.1016/j.ejc.2021.103451
intvolume: ' 100'
keyword:
- Discrete Mathematics and Combinatorics
language:
- iso: eng
publication: European Journal of Combinatorics
publication_identifier:
issn:
- 0195-6698
publication_status: published
publisher: Elsevier BV
status: public
title: On 3-flow-critical graphs
type: journal_article
user_id: '15540'
volume: 100
year: '2021'
...
---
_id: '33278'
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.
author:
- first_name: Martin
full_name: Kolb, Martin
id: '48880'
last_name: Kolb
- first_name: Tobias
full_name: Weich, Tobias
last_name: Weich
- first_name: Lasse
full_name: Wolf, Lasse
last_name: Wolf
citation:
ama: Kolb M, Weich T, Wolf L. Spectral Asymptotics for Kinetic Brownian Motion on
Surfaces of Constant Curvature. Annales Henri Poincaré . 2021;23(4):1283-1296.
apa: Kolb, M., Weich, T., & Wolf, L. (2021). Spectral Asymptotics for Kinetic
Brownian Motion on Surfaces of Constant Curvature. Annales Henri Poincaré ,
23(4), 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} }'
chicago: 'Kolb, Martin, Tobias Weich, and Lasse Wolf. “Spectral Asymptotics for
Kinetic Brownian Motion on Surfaces of Constant Curvature.” Annales Henri Poincaré
23, no. 4 (2021): 1283–96.'
ieee: M. Kolb, T. Weich, and L. Wolf, “Spectral Asymptotics for Kinetic Brownian
Motion on Surfaces of Constant Curvature,” Annales Henri Poincaré , vol.
23, no. 4, pp. 1283–1296, 2021.
mla: Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Surfaces
of Constant Curvature.” Annales Henri Poincaré , vol. 23, no. 4, Springer
Science + Business Media, 2021, pp. 1283–96.
short: M. Kolb, T. Weich, L. Wolf, Annales Henri Poincaré 23 (2021) 1283–1296.
date_created: 2022-09-07T07:05:33Z
date_updated: 2022-09-08T06:06:13Z
department:
- _id: '96'
intvolume: ' 23'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/article/10.1007/s00023-021-01121-5
oa: '1'
page: 1283-1296
publication: 'Annales Henri Poincaré '
publication_status: published
publisher: Springer Science + Business Media
related_material:
link:
- relation: contains
url: https://link.springer.com/article/10.1007/s00023-021-01121-5
status: public
title: Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
type: journal_article
user_id: '85821'
volume: 23
year: '2021'
...