---
_id: '45687'
author:
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
- first_name: T.
full_name: Schopferer, T.
last_name: Schopferer
citation:
ama: Bruns J, Schopferer T. Eine mustergültige Wissenschaft. . TPS – Theorie
und Praxis der Sozialpädagogik. 2021;11:28-32.
apa: Bruns, J., & Schopferer, T. (2021). Eine mustergültige Wissenschaft. .
. TPS – Theorie und Praxis der Sozialpädagogik, 11, 28–32.
bibtex: '@article{Bruns_Schopferer_2021, title={Eine mustergültige Wissenschaft},
volume={11}, journal={. TPS – Theorie und Praxis der Sozialpädagogik}, author={Bruns,
Julia and Schopferer, T.}, year={2021}, pages={28–32} }'
chicago: 'Bruns, Julia, and T. Schopferer. “Eine mustergültige Wissenschaft.” .
. TPS – Theorie und Praxis der Sozialpädagogik 11 (2021): 28–32.'
ieee: J. Bruns and T. Schopferer, “Eine mustergültige Wissenschaft,” . TPS –
Theorie und Praxis der Sozialpädagogik, vol. 11, pp. 28–32, 2021.
mla: Bruns, Julia, and T. Schopferer. “Eine mustergültige Wissenschaft.” . .
TPS – Theorie und Praxis der Sozialpädagogik, vol. 11, 2021, pp. 28–32.
short: J. Bruns, T. Schopferer, . . TPS – Theorie und Praxis der Sozialpädagogik
11 (2021) 28–32.
date_created: 2023-06-20T18:47:03Z
date_updated: 2023-06-20T18:47:08Z
department:
- _id: '97'
- _id: '611'
intvolume: ' 11'
language:
- iso: ger
page: 28-32
publication: . TPS – Theorie und Praxis der Sozialpädagogik
publication_status: published
status: public
title: Eine mustergültige Wissenschaft
type: journal_article
user_id: '49063'
volume: 11
year: '2021'
...
---
_id: '36527'
author:
- first_name: Solveig
full_name: Jensen, Solveig
last_name: Jensen
- first_name: Hedwig
full_name: Gasteiger, Hedwig
last_name: Gasteiger
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
citation:
ama: 'Jensen S, Gasteiger H, Bruns J. Place value and regrouping as seperate constructs
of place value understanding. In: Inprasitha M, Changsri N, Boonsena N, eds. Proceedings
of the 44th Conference of the International Group for the Psychology of Mathematics
Education. Vol 3. ; 2021:101-109.'
apa: Jensen, S., Gasteiger, H., & Bruns, J. (2021). Place value and regrouping
as seperate constructs of place value understanding. In M. Inprasitha, N. Changsri,
& N. Boonsena (Eds.), Proceedings of the 44th Conference of the International
Group for the Psychology of Mathematics Education (Vol. 3, pp. 101–109).
bibtex: '@inproceedings{Jensen_Gasteiger_Bruns_2021, title={Place value and regrouping
as seperate constructs of place value understanding}, volume={3}, booktitle={Proceedings
of the 44th Conference of the International Group for the Psychology of Mathematics
Education}, author={Jensen, Solveig and Gasteiger, Hedwig and Bruns, Julia}, editor={Inprasitha,
Maitree and Changsri, Narumon and Boonsena, Nisakorn}, year={2021}, pages={101–109}
}'
chicago: Jensen, Solveig, Hedwig Gasteiger, and Julia Bruns. “Place Value and Regrouping
as Seperate Constructs of Place Value Understanding.” In Proceedings of the
44th Conference of the International Group for the Psychology of Mathematics Education,
edited by Maitree Inprasitha, Narumon Changsri, and Nisakorn Boonsena, 3:101–9,
2021.
ieee: S. Jensen, H. Gasteiger, and J. Bruns, “Place value and regrouping as seperate
constructs of place value understanding,” in Proceedings of the 44th Conference
of the International Group for the Psychology of Mathematics Education, Khon
Kaen, Thailand, 2021, vol. 3, pp. 101–109.
mla: Jensen, Solveig, et al. “Place Value and Regrouping as Seperate Constructs
of Place Value Understanding.” Proceedings of the 44th Conference of the International
Group for the Psychology of Mathematics Education, edited by Maitree Inprasitha
et al., vol. 3, 2021, pp. 101–09.
short: 'S. Jensen, H. Gasteiger, J. Bruns, in: M. Inprasitha, N. Changsri, N. Boonsena
(Eds.), Proceedings of the 44th Conference of the International Group for the
Psychology of Mathematics Education, 2021, pp. 101–109.'
conference:
location: Khon Kaen, Thailand
name: 44th Conference of the International Group for the Psychology of Mathematics
Education
date_created: 2023-01-13T08:47:46Z
date_updated: 2023-06-20T19:13:24Z
department:
- _id: '611'
- _id: '97'
editor:
- first_name: Maitree
full_name: Inprasitha, Maitree
last_name: Inprasitha
- first_name: Narumon
full_name: Changsri, Narumon
last_name: Changsri
- first_name: Nisakorn
full_name: Boonsena, Nisakorn
last_name: Boonsena
intvolume: ' 3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.igpme.org/wp-content/uploads/2022/04/Volume-3_final.pdf
oa: '1'
page: 101-109
publication: Proceedings of the 44th Conference of the International Group for the
Psychology of Mathematics Education
publication_status: published
quality_controlled: '1'
status: public
title: Place value and regrouping as seperate constructs of place value understanding
type: conference
user_id: '49063'
volume: 3
year: '2021'
...
---
_id: '34823'
article_type: review
author:
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
- first_name: Hedwig
full_name: Gasteiger, Hedwig
last_name: Gasteiger
- first_name: Carolin
full_name: Strahl, Carolin
last_name: Strahl
citation:
ama: 'Bruns J, Gasteiger H, Strahl C. Context and Implications Document for: Conceptualising
and measuring domain-specific content knowledge of early childhood educators:
A systematic review. Review of Education. 2021;9(2):539-540. doi:10.1002/rev3.3256'
apa: 'Bruns, J., Gasteiger, H., & Strahl, C. (2021). Context and Implications
Document for: Conceptualising and measuring domain-specific content knowledge
of early childhood educators: A systematic review. Review of Education,
9(2), 539–540. https://doi.org/10.1002/rev3.3256'
bibtex: '@article{Bruns_Gasteiger_Strahl_2021, title={Context and Implications Document
for: Conceptualising and measuring domain-specific content knowledge of early
childhood educators: A systematic review}, volume={9}, DOI={10.1002/rev3.3256},
number={2}, journal={Review of Education}, publisher={Wiley}, author={Bruns, Julia
and Gasteiger, Hedwig and Strahl, Carolin}, year={2021}, pages={539–540} }'
chicago: 'Bruns, Julia, Hedwig Gasteiger, and Carolin Strahl. “Context and Implications
Document for: Conceptualising and Measuring Domain-Specific Content Knowledge
of Early Childhood Educators: A Systematic Review.” Review of Education
9, no. 2 (2021): 539–40. https://doi.org/10.1002/rev3.3256.'
ieee: 'J. Bruns, H. Gasteiger, and C. Strahl, “Context and Implications Document
for: Conceptualising and measuring domain-specific content knowledge of early
childhood educators: A systematic review,” Review of Education, vol. 9,
no. 2, pp. 539–540, 2021, doi: 10.1002/rev3.3256.'
mla: 'Bruns, Julia, et al. “Context and Implications Document for: Conceptualising
and Measuring Domain-Specific Content Knowledge of Early Childhood Educators:
A Systematic Review.” Review of Education, vol. 9, no. 2, Wiley, 2021,
pp. 539–40, doi:10.1002/rev3.3256.'
short: J. Bruns, H. Gasteiger, C. Strahl, Review of Education 9 (2021) 539–540.
date_created: 2022-12-22T09:22:46Z
date_updated: 2023-06-20T19:10:58Z
department:
- _id: '611'
- _id: '97'
doi: 10.1002/rev3.3256
external_id:
isi:
- '000614157400001'
intvolume: ' 9'
isi: '1'
issue: '2'
language:
- iso: eng
page: 539-540
publication: Review of Education
publication_identifier:
issn:
- 2049-6613
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: 'Context and Implications Document for: Conceptualising and measuring domain-specific
content knowledge of early childhood educators: A systematic review'
type: journal_article
user_id: '49063'
volume: 9
year: '2021'
...
---
_id: '36536'
author:
- first_name: Solveig
full_name: Jensen, Solveig
last_name: Jensen
- first_name: Hedwig
full_name: Gasteiger, Hedwig
last_name: Gasteiger
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
citation:
ama: 'Jensen S, Gasteiger H, Bruns J. Stellenwertverständnis: Verständnis von Stellenwertprinzip
und Bündelungsprinzip als separate Konstrukte. In: Gesellschaft für Didaktik der
Mathematik, ed. Beiträge zum Mathematikunterricht 2021. WTM-Verlag; 2021.
doi:http://dx.doi.org/10.17877/DE290R-22292'
apa: 'Jensen, S., Gasteiger, H., & Bruns, J. (2021). Stellenwertverständnis:
Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte.
In Gesellschaft für Didaktik der Mathematik (Ed.), Beiträge zum Mathematikunterricht
2021. WTM-Verlag. http://dx.doi.org/10.17877/DE290R-22292'
bibtex: '@inproceedings{Jensen_Gasteiger_Bruns_2021, title={Stellenwertverständnis:
Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte},
DOI={http://dx.doi.org/10.17877/DE290R-22292},
booktitle={Beiträge zum Mathematikunterricht 2021}, publisher={WTM-Verlag}, author={Jensen,
Solveig and Gasteiger, Hedwig and Bruns, Julia}, editor={Gesellschaft für Didaktik
der Mathematik}, year={2021} }'
chicago: 'Jensen, Solveig, Hedwig Gasteiger, and Julia Bruns. “Stellenwertverständnis:
Verständnis von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte.”
In Beiträge zum Mathematikunterricht 2021, edited by Gesellschaft für Didaktik
der Mathematik. WTM-Verlag, 2021. http://dx.doi.org/10.17877/DE290R-22292.'
ieee: 'S. Jensen, H. Gasteiger, and J. Bruns, “Stellenwertverständnis: Verständnis
von Stellenwertprinzip und Bündelungsprinzip als separate Konstrukte,” in Beiträge
zum Mathematikunterricht 2021, Lüneburg, 2021, doi: http://dx.doi.org/10.17877/DE290R-22292.'
mla: 'Jensen, Solveig, et al. “Stellenwertverständnis: Verständnis von Stellenwertprinzip
und Bündelungsprinzip als separate Konstrukte.” Beiträge zum Mathematikunterricht
2021, edited by Gesellschaft für Didaktik der Mathematik, WTM-Verlag, 2021,
doi:http://dx.doi.org/10.17877/DE290R-22292.'
short: 'S. Jensen, H. Gasteiger, J. Bruns, in: Gesellschaft für Didaktik der Mathematik
(Ed.), Beiträge zum Mathematikunterricht 2021, WTM-Verlag, 2021.'
conference:
location: Lüneburg
name: 55. Jahrestagung der Gesellschaft für Didaktik der Mathematik
corporate_editor:
- Gesellschaft für Didaktik der Mathematik
date_created: 2023-01-13T09:05:16Z
date_updated: 2023-06-20T19:15:25Z
department:
- _id: '611'
- _id: '97'
doi: http://dx.doi.org/10.17877/DE290R-22292
external_id:
unknown:
- '00495419692518'
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://eldorado.tu-dortmund.de/bitstream/2003/40417/1/BzMU21_JENSEN_Stellenwertverständnis.pdf
oa: '1'
publication: Beiträge zum Mathematikunterricht 2021
publication_status: published
publisher: WTM-Verlag
status: public
title: 'Stellenwertverständnis: Verständnis von Stellenwertprinzip und Bündelungsprinzip
als separate Konstrukte'
type: conference
user_id: '49063'
year: '2021'
...
---
_id: '45343'
article_number: '101561'
author:
- first_name: Johanna
full_name: Schönherr, Johanna
id: '99409'
last_name: Schönherr
- first_name: S.
full_name: Schukajlow, S.
last_name: Schukajlow
- first_name: J.
full_name: Blomberg, J.
last_name: Blomberg
- first_name: C.
full_name: Leopold, C.
last_name: Leopold
citation:
ama: 'Schönherr J, Schukajlow S, Blomberg J, Leopold C. The role of strategy-based
motivation in mathematical problem solving: The case of learner-generated drawings.
Learning and Instruction. 2021;80. doi:10.1016/j.learninstruc.2021.101561'
apa: 'Schönherr, J., Schukajlow, S., Blomberg, J., & Leopold, C. (2021). The
role of strategy-based motivation in mathematical problem solving: The case of
learner-generated drawings. Learning and Instruction, 80, Article
101561. https://doi.org/10.1016/j.learninstruc.2021.101561'
bibtex: '@article{Schönherr_Schukajlow_Blomberg_Leopold_2021, title={The role of
strategy-based motivation in mathematical problem solving: The case of learner-generated
drawings}, volume={80}, DOI={10.1016/j.learninstruc.2021.101561},
number={101561}, journal={Learning and Instruction}, author={Schönherr, Johanna
and Schukajlow, S. and Blomberg, J. and Leopold, C.}, year={2021} }'
chicago: 'Schönherr, Johanna, S. Schukajlow, J. Blomberg, and C. Leopold. “The Role
of Strategy-Based Motivation in Mathematical Problem Solving: The Case of Learner-Generated
Drawings.” Learning and Instruction 80 (2021). https://doi.org/10.1016/j.learninstruc.2021.101561.'
ieee: 'J. Schönherr, S. Schukajlow, J. Blomberg, and C. Leopold, “The role of strategy-based
motivation in mathematical problem solving: The case of learner-generated drawings,”
Learning and Instruction, vol. 80, Art. no. 101561, 2021, doi: 10.1016/j.learninstruc.2021.101561.'
mla: 'Schönherr, Johanna, et al. “The Role of Strategy-Based Motivation in Mathematical
Problem Solving: The Case of Learner-Generated Drawings.” Learning and Instruction,
vol. 80, 101561, 2021, doi:10.1016/j.learninstruc.2021.101561.'
short: J. Schönherr, S. Schukajlow, J. Blomberg, C. Leopold, Learning and Instruction
80 (2021).
date_created: 2023-05-29T17:39:15Z
date_updated: 2023-06-20T19:29:54Z
department:
- _id: '97'
doi: 10.1016/j.learninstruc.2021.101561
extern: '1'
intvolume: ' 80'
language:
- iso: eng
publication: Learning and Instruction
publication_status: published
status: public
title: 'The role of strategy-based motivation in mathematical problem solving: The
case of learner-generated drawings'
type: journal_article
user_id: '49063'
volume: 80
year: '2021'
...
---
_id: '34673'
article_number: '96'
author:
- first_name: Tobias
full_name: Black, Tobias
id: '23686'
last_name: Black
orcid: 0000-0001-9963-0800
- first_name: Mario
full_name: Fuest, Mario
last_name: Fuest
- first_name: Johannes
full_name: Lankeit, Johannes
last_name: Lankeit
citation:
ama: Black T, Fuest M, Lankeit J. Relaxed parameter conditions for chemotactic collapse
in logistic-type parabolic–elliptic Keller–Segel systems. Zeitschrift für angewandte
Mathematik und Physik. 2021;72(3). doi:10.1007/s00033-021-01524-8
apa: Black, T., Fuest, M., & Lankeit, J. (2021). Relaxed parameter conditions
for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems.
Zeitschrift Für Angewandte Mathematik Und Physik, 72(3), Article
96. https://doi.org/10.1007/s00033-021-01524-8
bibtex: '@article{Black_Fuest_Lankeit_2021, title={Relaxed parameter conditions
for chemotactic collapse in logistic-type parabolic–elliptic Keller–Segel systems},
volume={72}, DOI={10.1007/s00033-021-01524-8},
number={396}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
Science and Business Media LLC}, author={Black, Tobias and Fuest, Mario and Lankeit,
Johannes}, year={2021} }'
chicago: Black, Tobias, Mario Fuest, and Johannes Lankeit. “Relaxed Parameter Conditions
for Chemotactic Collapse in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.”
Zeitschrift Für Angewandte Mathematik Und Physik 72, no. 3 (2021). https://doi.org/10.1007/s00033-021-01524-8.
ieee: 'T. Black, M. Fuest, and J. Lankeit, “Relaxed parameter conditions for chemotactic
collapse in logistic-type parabolic–elliptic Keller–Segel systems,” Zeitschrift
für angewandte Mathematik und Physik, vol. 72, no. 3, Art. no. 96, 2021, doi:
10.1007/s00033-021-01524-8.'
mla: Black, Tobias, et al. “Relaxed Parameter Conditions for Chemotactic Collapse
in Logistic-Type Parabolic–Elliptic Keller–Segel Systems.” Zeitschrift Für
Angewandte Mathematik Und Physik, vol. 72, no. 3, 96, Springer Science and
Business Media LLC, 2021, doi:10.1007/s00033-021-01524-8.
short: T. Black, M. Fuest, J. Lankeit, Zeitschrift Für Angewandte Mathematik Und
Physik 72 (2021).
date_created: 2022-12-21T09:48:36Z
date_updated: 2023-07-10T11:39:23Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1007/s00033-021-01524-8
intvolume: ' 72'
issue: '3'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- General Mathematics
language:
- iso: eng
publication: Zeitschrift für angewandte Mathematik und Physik
publication_identifier:
issn:
- 0044-2275
- 1420-9039
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Relaxed parameter conditions for chemotactic collapse in logistic-type parabolic–elliptic
Keller–Segel systems
type: journal_article
user_id: '23686'
volume: 72
year: '2021'
...
---
_id: '34675'
article_number: '135'
author:
- first_name: Tobias
full_name: Black, Tobias
id: '23686'
last_name: Black
orcid: 0000-0001-9963-0800
- first_name: Chunyan
full_name: Wu, Chunyan
last_name: Wu
citation:
ama: 'Black T, Wu C. Prescribed signal concentration on the boundary: Weak solvability
in a chemotaxis-Stokes system with proliferation. Zeitschrift für angewandte
Mathematik und Physik. 2021;72(4). doi:10.1007/s00033-021-01565-z'
apa: 'Black, T., & Wu, C. (2021). Prescribed signal concentration on the boundary:
Weak solvability in a chemotaxis-Stokes system with proliferation. Zeitschrift
Für Angewandte Mathematik Und Physik, 72(4), Article 135. https://doi.org/10.1007/s00033-021-01565-z'
bibtex: '@article{Black_Wu_2021, title={Prescribed signal concentration on the boundary:
Weak solvability in a chemotaxis-Stokes system with proliferation}, volume={72},
DOI={10.1007/s00033-021-01565-z},
number={4135}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer
Science and Business Media LLC}, author={Black, Tobias and Wu, Chunyan}, year={2021}
}'
chicago: 'Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the
Boundary: Weak Solvability in a Chemotaxis-Stokes System with Proliferation.”
Zeitschrift Für Angewandte Mathematik Und Physik 72, no. 4 (2021). https://doi.org/10.1007/s00033-021-01565-z.'
ieee: 'T. Black and C. Wu, “Prescribed signal concentration on the boundary: Weak
solvability in a chemotaxis-Stokes system with proliferation,” Zeitschrift
für angewandte Mathematik und Physik, vol. 72, no. 4, Art. no. 135, 2021,
doi: 10.1007/s00033-021-01565-z.'
mla: 'Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary:
Weak Solvability in a Chemotaxis-Stokes System with Proliferation.” Zeitschrift
Für Angewandte Mathematik Und Physik, vol. 72, no. 4, 135, Springer Science
and Business Media LLC, 2021, doi:10.1007/s00033-021-01565-z.'
short: T. Black, C. Wu, Zeitschrift Für Angewandte Mathematik Und Physik 72 (2021).
date_created: 2022-12-21T09:48:45Z
date_updated: 2023-07-10T11:39:30Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1007/s00033-021-01565-z
intvolume: ' 72'
issue: '4'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- General Mathematics
language:
- iso: eng
publication: Zeitschrift für angewandte Mathematik und Physik
publication_identifier:
issn:
- 0044-2275
- 1420-9039
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes
system with proliferation'
type: journal_article
user_id: '23686'
volume: 72
year: '2021'
...
---
_id: '56204'
author:
- first_name: Daniel
full_name: Frischemeier, Daniel
last_name: Frischemeier
- first_name: Susanne
full_name: Podworny, Susanne
id: '30619'
last_name: Podworny
orcid: 0000-0002-6313-5987
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Frischemeier D, Podworny S, Biehler R. Integration fachwissenschaftlicher
und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule
am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“.
In: Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik.
Springer Berlin Heidelberg; 2021. doi:10.1007/978-3-662-62854-6_11'
apa: Frischemeier, D., Podworny, S., & Biehler, R. (2021). Integration fachwissenschaftlicher
und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule
am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“.
In Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik.
Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-62854-6_11
bibtex: '@inbook{Frischemeier_Podworny_Biehler_2021, place={Berlin, Heidelberg},
title={Integration fachwissenschaftlicher und fachdidaktischer Komponenten in
der Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung
zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“}, DOI={10.1007/978-3-662-62854-6_11},
booktitle={Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik},
publisher={Springer Berlin Heidelberg}, author={Frischemeier, Daniel and Podworny,
Susanne and Biehler, Rolf}, year={2021} }'
chicago: 'Frischemeier, Daniel, Susanne Podworny, and Rolf Biehler. “Integration
fachwissenschaftlicher und fachdidaktischer Komponenten in der Lehramtsausbildung
Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit
und Wahrscheinlichkeit“.” In Konzepte und Studien zur Hochschuldidaktik und
Lehrerbildung Mathematik. Berlin, Heidelberg: Springer Berlin Heidelberg,
2021. https://doi.org/10.1007/978-3-662-62854-6_11.'
ieee: 'D. Frischemeier, S. Podworny, and R. Biehler, “Integration fachwissenschaftlicher
und fachdidaktischer Komponenten in der Lehramtsausbildung Mathematik Grundschule
am Beispiel einer Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“,”
in Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik,
Berlin, Heidelberg: Springer Berlin Heidelberg, 2021.'
mla: Frischemeier, Daniel, et al. “Integration fachwissenschaftlicher und fachdidaktischer
Komponenten in der Lehramtsausbildung Mathematik Grundschule am Beispiel einer
Veranstaltung zur Leitidee „Daten, Häufigkeit und Wahrscheinlichkeit“.” Konzepte
und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, Springer Berlin
Heidelberg, 2021, doi:10.1007/978-3-662-62854-6_11.
short: 'D. Frischemeier, S. Podworny, R. Biehler, in: Konzepte und Studien zur Hochschuldidaktik
und Lehrerbildung Mathematik, Springer Berlin Heidelberg, Berlin, Heidelberg,
2021.'
date_created: 2024-09-23T09:01:18Z
date_updated: 2024-09-25T08:27:11Z
department:
- _id: '363'
doi: 10.1007/978-3-662-62854-6_11
language:
- iso: ger
main_file_link:
- url: https://link.springer.com/chapter/10.1007/978-3-662-62854-6_11
place: Berlin, Heidelberg
publication: Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik
publication_identifier:
isbn:
- '9783662628539'
- '9783662628546'
issn:
- 2197-8751
- 2197-876X
publication_status: published
publisher: Springer Berlin Heidelberg
status: public
title: Integration fachwissenschaftlicher und fachdidaktischer Komponenten in der
Lehramtsausbildung Mathematik Grundschule am Beispiel einer Veranstaltung zur Leitidee
„Daten, Häufigkeit und Wahrscheinlichkeit“
type: book_chapter
user_id: '37888'
year: '2021'
...
---
_id: '64765'
author:
- first_name: Natalie
full_name: Nikitin, Natalie
last_name: Nikitin
citation:
ama: Nikitin N. Regularity Properties of Infinite-Dimensional Lie Groups and
Exponential Laws.; 2021.
apa: Nikitin, N. (2021). Regularity properties of infinite-dimensional Lie groups
and exponential laws.
bibtex: '@book{Nikitin_2021, title={Regularity properties of infinite-dimensional
Lie groups and exponential laws}, author={Nikitin, Natalie}, year={2021} }'
chicago: Nikitin, Natalie. Regularity Properties of Infinite-Dimensional Lie
Groups and Exponential Laws, 2021.
ieee: N. Nikitin, Regularity properties of infinite-dimensional Lie groups and
exponential laws. 2021.
mla: Nikitin, Natalie. Regularity Properties of Infinite-Dimensional Lie Groups
and Exponential Laws. 2021.
short: N. Nikitin, Regularity Properties of Infinite-Dimensional Lie Groups and
Exponential Laws, 2021.
date_created: 2026-02-26T21:15:13Z
date_updated: 2026-02-26T21:15:28Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://nbn-resolving.org/urn:nbn:de:hbz:466:2-39133
oa: '1'
status: public
supervisor:
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
title: Regularity properties of infinite-dimensional Lie groups and exponential laws
type: dissertation
user_id: '178'
year: '2021'
...
---
_id: '34790'
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. Locally pro-p contraction groups are nilpotent. Journal
für die reine und angewandte Mathematik. 2021;781:85–103. doi:10.1515/crelle-2021-0050
apa: Glöckner, H., & Willis, G. A. (2021). Locally pro-p contraction groups
are nilpotent. Journal Für Die Reine Und Angewandte Mathematik, 781,
85–103. https://doi.org/10.1515/crelle-2021-0050
bibtex: '@article{Glöckner_Willis_2021, title={Locally pro-p contraction groups
are nilpotent}, volume={781}, DOI={10.1515/crelle-2021-0050},
journal={Journal für die reine und angewandte Mathematik}, author={Glöckner, Helge
and Willis, George A.}, year={2021}, pages={85–103} }'
chicago: 'Glöckner, Helge, and George A. Willis. “Locally Pro-p Contraction Groups
Are Nilpotent.” Journal Für Die Reine Und Angewandte Mathematik 781 (2021):
85–103. https://doi.org/10.1515/crelle-2021-0050.'
ieee: 'H. Glöckner and G. A. Willis, “Locally pro-p contraction groups are nilpotent,”
Journal für die reine und angewandte Mathematik, vol. 781, pp. 85–103,
2021, doi: 10.1515/crelle-2021-0050.'
mla: Glöckner, Helge, and George A. Willis. “Locally Pro-p Contraction Groups Are
Nilpotent.” Journal Für Die Reine Und Angewandte Mathematik, vol. 781,
2021, pp. 85–103, doi:10.1515/crelle-2021-0050.
short: H. Glöckner, G.A. Willis, Journal Für Die Reine Und Angewandte Mathematik
781 (2021) 85–103.
date_created: 2022-12-21T19:17:28Z
date_updated: 2026-02-27T08:34:58Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1515/crelle-2021-0050
intvolume: ' 781'
keyword:
- 22D05
- 22A05
- '20E18'
language:
- iso: eng
page: 85–103
publication: Journal für die reine und angewandte Mathematik
publication_identifier:
issn:
- 0075-4102
quality_controlled: '1'
status: public
title: Locally pro-p contraction groups are nilpotent
type: journal_article
user_id: '178'
volume: 781
year: '2021'
...
---
_id: '19938'
abstract:
- lang: eng
text: 'We show that symplectic integrators preserve bifurcations of Hamiltonian
boundary value problems and that nonsymplectic integrators do not. We provide
a universal description of the breaking of umbilic bifurcations by nonysmplectic
integrators. We discover extra structure induced from certain types of boundary
value problems, including classical Dirichlet problems, that is useful to locate
bifurcations. Geodesics connecting two points are an example of a Hamiltonian
boundary value problem, and we introduce the jet-RATTLE method, a symplectic integrator
that easily computes geodesics and their bifurcations. Finally, we study the periodic
pitchfork bifurcation, a codimension-1 bifurcation arising in integrable Hamiltonian
systems. It is not preserved by either symplectic on nonsymplectic integrators,
but in some circumstances symplecticity greatly reduces the error. '
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Preservation of Bifurcations of Hamiltonian Boundary
Value Problems Under Discretisation. Foundations of Computational Mathematics.
2020;20(6):1363-1400. doi:10.1007/s10208-020-09454-z
apa: McLachlan, R. I., & Offen, C. (2020). Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation. Foundations of Computational
Mathematics, 20(6), 1363–1400. https://doi.org/10.1007/s10208-020-09454-z
bibtex: '@article{McLachlan_Offen_2020, title={Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation}, volume={20}, DOI={10.1007/s10208-020-09454-z},
number={6}, journal={Foundations of Computational Mathematics}, author={McLachlan,
Robert I and Offen, Christian}, year={2020}, pages={1363–1400} }'
chicago: 'McLachlan, Robert I, and Christian Offen. “Preservation of Bifurcations
of Hamiltonian Boundary Value Problems Under Discretisation.” Foundations of
Computational Mathematics 20, no. 6 (2020): 1363–1400. https://doi.org/10.1007/s10208-020-09454-z.'
ieee: R. I. McLachlan and C. Offen, “Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation,” Foundations of Computational
Mathematics, vol. 20, no. 6, pp. 1363–1400, 2020.
mla: McLachlan, Robert I., and Christian Offen. “Preservation of Bifurcations of
Hamiltonian Boundary Value Problems Under Discretisation.” Foundations of Computational
Mathematics, vol. 20, no. 6, 2020, pp. 1363–400, doi:10.1007/s10208-020-09454-z.
short: R.I. McLachlan, C. Offen, Foundations of Computational Mathematics 20 (2020)
1363–1400.
date_created: 2020-10-06T16:31:46Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1007/s10208-020-09454-z
extern: '1'
intvolume: ' 20'
issue: '6'
language:
- iso: eng
main_file_link:
- url: https://rdcu.be/b79aB
page: 1363-1400
publication: Foundations of Computational Mathematics
publication_status: published
status: public
title: Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation
type: journal_article
user_id: '85279'
volume: 20
year: '2020'
...
---
_id: '19939'
article_type: original
author:
- first_name: Lisa Maria
full_name: Kreusser, Lisa Maria
last_name: Kreusser
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: Kreusser LM, McLachlan RI, Offen C. Detection of high codimensional bifurcations
in variational PDEs. Nonlinearity. 2020;33(5):2335-2363. doi:10.1088/1361-6544/ab7293
apa: Kreusser, L. M., McLachlan, R. I., & Offen, C. (2020). Detection of high
codimensional bifurcations in variational PDEs. Nonlinearity, 33(5),
2335–2363. https://doi.org/10.1088/1361-6544/ab7293
bibtex: '@article{Kreusser_McLachlan_Offen_2020, title={Detection of high codimensional
bifurcations in variational PDEs}, volume={33}, DOI={10.1088/1361-6544/ab7293},
number={5}, journal={Nonlinearity}, author={Kreusser, Lisa Maria and McLachlan,
Robert I and Offen, Christian}, year={2020}, pages={2335–2363} }'
chicago: 'Kreusser, Lisa Maria, Robert I McLachlan, and Christian Offen. “Detection
of High Codimensional Bifurcations in Variational PDEs.” Nonlinearity 33,
no. 5 (2020): 2335–63. https://doi.org/10.1088/1361-6544/ab7293.'
ieee: L. M. Kreusser, R. I. McLachlan, and C. Offen, “Detection of high codimensional
bifurcations in variational PDEs,” Nonlinearity, vol. 33, no. 5, pp. 2335–2363,
2020.
mla: Kreusser, Lisa Maria, et al. “Detection of High Codimensional Bifurcations
in Variational PDEs.” Nonlinearity, vol. 33, no. 5, 2020, pp. 2335–63,
doi:10.1088/1361-6544/ab7293.
short: L.M. Kreusser, R.I. McLachlan, C. Offen, Nonlinearity 33 (2020) 2335–2363.
date_created: 2020-10-06T16:32:04Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1088/1361-6544/ab7293
extern: '1'
intvolume: ' 33'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1088/1361-6544/ab7293
oa: '1'
page: 2335-2363
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Detection of high codimensional bifurcations in variational PDEs
type: journal_article
user_id: '85279'
volume: 33
year: '2020'
...
---
_id: '17411'
abstract:
- lang: eng
text: Many dynamical systems possess symmetries, e.g. rotational and translational
invariances of mechanical systems. These can be beneficially exploited in the
design of numerical optimal control methods. We present a model predictive control
scheme which is based on a library of precomputed motion primitives. The primitives
are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim
primitives as relative equilibria w.r.t. this symmetry, play a crucial role in
the algorithm. The approach is illustrated using an academic mobile robot example.
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in Optimal Control: A Multiobjective
Model Predictive Control Approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum
S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation.
Cham: Springer; 2020. doi:10.1007/978-3-030-51264-4_9'
apa: 'Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in Optimal
Control: A Multiobjective Model Predictive Control Approach. In O. Junge, O. Schütze,
G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics,
Optimization and Computation. Cham: Springer. https://doi.org/10.1007/978-3-030-51264-4_9'
bibtex: '@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry
in Optimal Control: A Multiobjective Model Predictive Control Approach}, DOI={10.1007/978-3-030-51264-4_9},
booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer},
author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}, editor={Junge,
Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle,
KathrinEditors}, year={2020} }'
chicago: 'Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Sebastian Peitz. “Symmetry in
Optimal Control: A Multiobjective Model Predictive Control Approach.” In Advances
in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver
Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle. Cham: Springer,
2020. https://doi.org/10.1007/978-3-030-51264-4_9.'
ieee: 'K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in Optimal Control:
A Multiobjective Model Predictive Control Approach,” in Advances in Dynamics,
Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum,
and K. Padberg-Gehle, Eds. Cham: Springer, 2020.'
mla: 'Flaßkamp, Kathrin, et al. “Symmetry in Optimal Control: A Multiobjective Model
Predictive Control Approach.” Advances in Dynamics, Optimization and Computation,
edited by Oliver Junge et al., Springer, 2020, doi:10.1007/978-3-030-51264-4_9.'
short: 'K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland,
S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and
Computation, Springer, Cham, 2020.'
date_created: 2020-07-27T09:50:19Z
date_updated: 2022-01-06T06:53:11Z
department:
- _id: '101'
doi: 10.1007/978-3-030-51264-4_9
editor:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Padberg-Gehle, Kathrin
last_name: Padberg-Gehle
language:
- iso: eng
place: Cham
publication: Advances in Dynamics, Optimization and Computation
publication_identifier:
isbn:
- '9783030512637'
- '9783030512644'
issn:
- 2198-4182
- 2198-4190
publication_status: published
publisher: Springer
status: public
title: 'Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach'
type: book_chapter
user_id: '47427'
year: '2020'
...
---
_id: '21819'
abstract:
- lang: eng
text: Many dimensionality and model reduction techniques rely on estimating
dominant eigenfunctions of associated dynamical operators from data. Important
examples include the Koopman operator and its generator, but also the Schrödinger
operator. We propose a kernel-based method for the approximation of differential
operators in reproducing kernel Hilbert spaces and show how eigenfunctions can
be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms
are applied to molecular dynamics and quantum chemistry examples. Furthermore,
we exploit that, under certain conditions, the Schrödinger operator can be transformed
into a Kolmogorov backward operator corresponding to a drift-diffusion process
and vice versa. This allows us to apply methods developed for the analysis of
high-dimensional stochastic differential equations to quantum mechanical systems.
article_number: '722'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Boumediene
full_name: Hamzi, Boumediene
last_name: Hamzi
citation:
ama: Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator
and Schrödinger Operator. Entropy. 2020. doi:10.3390/e22070722
apa: Klus, S., Nüske, F., & Hamzi, B. (2020). Kernel-Based Approximation of
the Koopman Generator and Schrödinger Operator. Entropy. https://doi.org/10.3390/e22070722
bibtex: '@article{Klus_Nüske_Hamzi_2020, title={Kernel-Based Approximation of the
Koopman Generator and Schrödinger Operator}, DOI={10.3390/e22070722},
number={722}, journal={Entropy}, author={Klus, Stefan and Nüske, Feliks and Hamzi,
Boumediene}, year={2020} }'
chicago: Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. “Kernel-Based Approximation
of the Koopman Generator and Schrödinger Operator.” Entropy, 2020. https://doi.org/10.3390/e22070722.
ieee: S. Klus, F. Nüske, and B. Hamzi, “Kernel-Based Approximation of the Koopman
Generator and Schrödinger Operator,” Entropy, 2020.
mla: Klus, Stefan, et al. “Kernel-Based Approximation of the Koopman Generator and
Schrödinger Operator.” Entropy, 722, 2020, doi:10.3390/e22070722.
short: S. Klus, F. Nüske, B. Hamzi, Entropy (2020).
date_created: 2021-04-28T18:06:35Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e22070722
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/22/7/722
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator
type: journal_article
user_id: '81513'
year: '2020'
...
---
_id: '16964'
author:
- first_name: Reinhard
full_name: Hochmuth, Reinhard
last_name: Hochmuth
- first_name: Michael
full_name: Liebendörfer, Michael
last_name: Liebendörfer
- first_name: Rolf
full_name: Biehler, Rolf
last_name: Biehler
- first_name: Andreas
full_name: Eichler, Andreas
last_name: Eichler
citation:
ama: Hochmuth R, Liebendörfer M, Biehler R, Eichler A. Das Kompetenzzentrum Hochschuldidaktik
Mathematik (khdm). Neues Handbuch Hochschullehre. 2020;95:117-138.
apa: Hochmuth, R., Liebendörfer, M., Biehler, R., & Eichler, A. (2020). Das
Kompetenzzentrum Hochschuldidaktik Mathematik (khdm). Neues Handbuch Hochschullehre,
95, 117–138.
bibtex: '@article{Hochmuth_Liebendörfer_Biehler_Eichler_2020, title={Das Kompetenzzentrum
Hochschuldidaktik Mathematik (khdm)}, volume={95}, journal={Neues Handbuch Hochschullehre},
author={Hochmuth, Reinhard and Liebendörfer, Michael and Biehler, Rolf and Eichler,
Andreas}, year={2020}, pages={117–138} }'
chicago: 'Hochmuth, Reinhard, Michael Liebendörfer, Rolf Biehler, and Andreas Eichler.
“Das Kompetenzzentrum Hochschuldidaktik Mathematik (Khdm).” Neues Handbuch
Hochschullehre 95 (2020): 117–38.'
ieee: R. Hochmuth, M. Liebendörfer, R. Biehler, and A. Eichler, “Das Kompetenzzentrum
Hochschuldidaktik Mathematik (khdm),” Neues Handbuch Hochschullehre, vol.
95, pp. 117–138, 2020.
mla: Hochmuth, Reinhard, et al. “Das Kompetenzzentrum Hochschuldidaktik Mathematik
(Khdm).” Neues Handbuch Hochschullehre, vol. 95, 2020, pp. 117–38.
short: R. Hochmuth, M. Liebendörfer, R. Biehler, A. Eichler, Neues Handbuch Hochschullehre
95 (2020) 117–138.
date_created: 2020-05-16T07:32:23Z
date_updated: 2022-01-06T06:53:00Z
department:
- _id: '10'
intvolume: ' 95'
page: 117-138
publication: Neues Handbuch Hochschullehre
status: public
title: Das Kompetenzzentrum Hochschuldidaktik Mathematik (khdm)
type: journal_article
user_id: '30933'
volume: 95
year: '2020'
...
---
_id: '10596'
abstract:
- lang: eng
text: Multi-objective optimization is an active field of research that has many
applications. Owing to its success and because decision-making processes are becoming
more and more complex, there is a recent trend for incorporating many objectives
into such problems. The challenge with such problems, however, is that the dimensions
of the solution sets—the so-called Pareto sets and fronts—grow with the number
of objectives. It is thus no longer possible to compute or to approximate the
entire solution set of a given problem that contains many (e.g. more than three)
objectives. On the other hand, the computation of single solutions (e.g. via scalarization
methods) leads to unsatisfying results in many cases, even if user preferences
are incorporated. In this article, the Pareto Explorer tool is presented—a global/local
exploration tool for the treatment of many-objective optimization problems (MaOPs).
In the first step, a solution of the problem is computed via a global search algorithm
that ideally already includes user preferences. In the second step, a local search
along the Pareto set/front of the given MaOP is performed in user specified directions.
For this, several continuation-like procedures are proposed that can incorporate
preferences defined in decision, objective, or in weight space. The applicability
and usefulness of Pareto Explorer is demonstrated on benchmark problems as well
as on an application from industrial laundry design.
article_type: original
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Oliver
full_name: Cuate, Oliver
last_name: Cuate
- first_name: Adanay
full_name: Martín, Adanay
last_name: Martín
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Schütze O, Cuate O, Martín A, Peitz S, Dellnitz M. Pareto Explorer: a global/local
exploration tool for many-objective optimization problems. Engineering Optimization.
2020;52(5):832-855. doi:10.1080/0305215x.2019.1617286'
apa: 'Schütze, O., Cuate, O., Martín, A., Peitz, S., & Dellnitz, M. (2020).
Pareto Explorer: a global/local exploration tool for many-objective optimization
problems. Engineering Optimization, 52(5), 832–855. https://doi.org/10.1080/0305215x.2019.1617286'
bibtex: '@article{Schütze_Cuate_Martín_Peitz_Dellnitz_2020, title={Pareto Explorer:
a global/local exploration tool for many-objective optimization problems}, volume={52},
DOI={10.1080/0305215x.2019.1617286},
number={5}, journal={Engineering Optimization}, author={Schütze, Oliver and Cuate,
Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael}, year={2020},
pages={832–855} }'
chicago: 'Schütze, Oliver, Oliver Cuate, Adanay Martín, Sebastian Peitz, and Michael
Dellnitz. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective
Optimization Problems.” Engineering Optimization 52, no. 5 (2020): 832–55.
https://doi.org/10.1080/0305215x.2019.1617286.'
ieee: 'O. Schütze, O. Cuate, A. Martín, S. Peitz, and M. Dellnitz, “Pareto Explorer:
a global/local exploration tool for many-objective optimization problems,” Engineering
Optimization, vol. 52, no. 5, pp. 832–855, 2020.'
mla: 'Schütze, Oliver, et al. “Pareto Explorer: A Global/Local Exploration Tool
for Many-Objective Optimization Problems.” Engineering Optimization, vol.
52, no. 5, 2020, pp. 832–55, doi:10.1080/0305215x.2019.1617286.'
short: O. Schütze, O. Cuate, A. Martín, S. Peitz, M. Dellnitz, Engineering Optimization
52 (2020) 832–855.
date_created: 2019-07-10T08:14:39Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1080/0305215x.2019.1617286
intvolume: ' 52'
issue: '5'
language:
- iso: eng
page: 832-855
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: 'Pareto Explorer: a global/local exploration tool for many-objective optimization
problems'
type: journal_article
user_id: '47427'
volume: 52
year: '2020'
...
---
_id: '16288'
abstract:
- lang: eng
text: We derive a data-driven method for the approximation of the Koopman generator
called gEDMD, which can be regarded as a straightforward extension of EDMD (extended
dynamic mode decomposition). This approach is applicable to deterministic and
stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions,
and modes of the generator and for system identification. In addition to learning
the governing equations of deterministic systems, which then reduces to SINDy
(sparse identification of nonlinear dynamics), it is possible to identify the
drift and diffusion terms of stochastic differential equations from data. Moreover,
we apply gEDMD to derive coarse-grained models of high-dimensional systems, and
also to determine efficient model predictive control strategies. We highlight
relationships with other methods and demonstrate the efficacy of the proposed
methods using several guiding examples and prototypical molecular dynamics problems.
article_number: '132416'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Jan-Hendrik
full_name: Niemann, Jan-Hendrik
last_name: Niemann
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: 'Klus S, Nüske F, Peitz S, Niemann J-H, Clementi C, Schütte C. Data-driven
approximation of the Koopman generator: Model reduction, system identification,
and control. Physica D: Nonlinear Phenomena. 2020;406. doi:10.1016/j.physd.2020.132416'
apa: 'Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte,
C. (2020). Data-driven approximation of the Koopman generator: Model reduction,
system identification, and control. Physica D: Nonlinear Phenomena, 406.
https://doi.org/10.1016/j.physd.2020.132416'
bibtex: '@article{Klus_Nüske_Peitz_Niemann_Clementi_Schütte_2020, title={Data-driven
approximation of the Koopman generator: Model reduction, system identification,
and control}, volume={406}, DOI={10.1016/j.physd.2020.132416},
number={132416}, journal={Physica D: Nonlinear Phenomena}, author={Klus, Stefan
and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi,
Cecilia and Schütte, Christof}, year={2020} }'
chicago: 'Klus, Stefan, Feliks Nüske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia
Clementi, and Christof Schütte. “Data-Driven Approximation of the Koopman Generator:
Model Reduction, System Identification, and Control.” Physica D: Nonlinear
Phenomena 406 (2020). https://doi.org/10.1016/j.physd.2020.132416.'
ieee: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, and C. Schütte,
“Data-driven approximation of the Koopman generator: Model reduction, system identification,
and control,” Physica D: Nonlinear Phenomena, vol. 406, 2020.'
mla: 'Klus, Stefan, et al. “Data-Driven Approximation of the Koopman Generator:
Model Reduction, System Identification, and Control.” Physica D: Nonlinear
Phenomena, vol. 406, 132416, 2020, doi:10.1016/j.physd.2020.132416.'
short: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica
D: Nonlinear Phenomena 406 (2020).'
date_created: 2020-03-13T12:35:40Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1016/j.physd.2020.132416
intvolume: ' 406'
language:
- iso: eng
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
issn:
- 0167-2789
publication_status: published
status: public
title: 'Data-driven approximation of the Koopman generator: Model reduction, system
identification, and control'
type: journal_article
user_id: '47427'
volume: 406
year: '2020'
...
---
_id: '16289'
abstract:
- lang: eng
text: In the development of model predictive controllers for PDE-constrained problems,
the use of reduced order models is essential to enable real-time applicability.
Besides local linearization approaches, proper orthogonal decomposition (POD)
has been most widely used in the past in order to derive such models. Due to the
huge advances concerning both theory as well as the numerical approximation, a
very promising alternative based on the Koopman operator has recently emerged.
In this chapter, we present two control strategies for model predictive control
of nonlinear PDEs using data-efficient approximations of the Koopman operator.
In the first one, the dynamic control system is replaced by a small number of
autonomous systems with different yet constant inputs. The control problem is
consequently transformed into a switching problem. In the second approach, a bilinear
surrogate model is obtained via a convex combination of these autonomous systems.
Using a recent convergence result for extended dynamic mode decomposition (EDMD),
convergence of the reduced objective function can be shown. We study the properties
of these two strategies with respect to solution quality, data requirements, and
complexity of the resulting optimization problem using the 1-dimensional Burgers
equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an
extension for online adaptivity is presented.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: 'Peitz S, Klus S. Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced
Order Models Based on the Koopman Operator. In: Lecture Notes in Control and
Information Sciences. Vol 484. Lecture Notes in Control and Information Sciences.
Cham: Springer; 2020:257-282. doi:10.1007/978-3-030-35713-9_10'
apa: 'Peitz, S., & Klus, S. (2020). Feedback Control of Nonlinear PDEs Using
Data-Efficient Reduced Order Models Based on the Koopman Operator. In Lecture
Notes in Control and Information Sciences (Vol. 484, pp. 257–282). Cham: Springer.
https://doi.org/10.1007/978-3-030-35713-9_10'
bibtex: '@inbook{Peitz_Klus_2020, place={Cham}, series={Lecture Notes in Control
and Information Sciences}, title={Feedback Control of Nonlinear PDEs Using Data-Efficient
Reduced Order Models Based on the Koopman Operator}, volume={484}, DOI={10.1007/978-3-030-35713-9_10},
booktitle={Lecture Notes in Control and Information Sciences}, publisher={Springer},
author={Peitz, Sebastian and Klus, Stefan}, year={2020}, pages={257–282}, collection={Lecture
Notes in Control and Information Sciences} }'
chicago: 'Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs
Using Data-Efficient Reduced Order Models Based on the Koopman Operator.” In Lecture
Notes in Control and Information Sciences, 484:257–82. Lecture Notes in Control
and Information Sciences. Cham: Springer, 2020. https://doi.org/10.1007/978-3-030-35713-9_10.'
ieee: 'S. Peitz and S. Klus, “Feedback Control of Nonlinear PDEs Using Data-Efficient
Reduced Order Models Based on the Koopman Operator,” in Lecture Notes in Control
and Information Sciences, vol. 484, Cham: Springer, 2020, pp. 257–282.'
mla: Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs Using
Data-Efficient Reduced Order Models Based on the Koopman Operator.” Lecture
Notes in Control and Information Sciences, vol. 484, Springer, 2020, pp. 257–82,
doi:10.1007/978-3-030-35713-9_10.
short: 'S. Peitz, S. Klus, in: Lecture Notes in Control and Information Sciences,
Springer, Cham, 2020, pp. 257–282.'
date_created: 2020-03-13T12:38:52Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/978-3-030-35713-9_10
intvolume: ' 484'
language:
- iso: eng
page: 257-282
place: Cham
publication: Lecture Notes in Control and Information Sciences
publication_identifier:
isbn:
- '9783030357122'
- '9783030357139'
issn:
- 0170-8643
- 1610-7411
publication_status: published
publisher: Springer
series_title: Lecture Notes in Control and Information Sciences
status: public
title: Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models
Based on the Koopman Operator
type: book_chapter
user_id: '47427'
volume: 484
year: '2020'
...
---
_id: '16290'
abstract:
- lang: eng
text: The control of complex systems is of critical importance in many branches
of science, engineering, and industry, many of which are governed by nonlinear
partial differential equations. Controlling an unsteady fluid flow is particularly
important, as flow control is a key enabler for technologies in energy (e.g.,
wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles),
security (e.g., tracking airborne contamination), and health (e.g., artificial
hearts and artificial respiration). However, the high-dimensional, nonlinear,
and multi-scale dynamics make real-time feedback control infeasible. Fortunately,
these high- dimensional systems exhibit dominant, low-dimensional patterns of
activity that can be exploited for effective control in the sense that knowledge
of the entire state of a system is not required. Advances in machine learning
have the potential to revolutionize flow control given its ability to extract
principled, low-rank feature spaces characterizing such complex systems.We present
a novel deep learning modelpredictive control framework that exploits low-rank
features of the flow in order to achieve considerable improvements to control
performance. Instead of predicting the entire fluid state, we use a recurrent
neural network (RNN) to accurately predict the control relevant quantities of
the system, which are then embedded into an MPC framework to construct a feedback
loop. In order to lower the data requirements and to improve the prediction accuracy
and thus the control performance, incoming sensor data are used to update the
RNN online. The results are validated using varying fluid flow examples of increasing
complexity.
article_type: original
author:
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Steven L.
full_name: Brunton, Steven L.
last_name: Brunton
- first_name: J. Nathan
full_name: Kutz, J. Nathan
last_name: Kutz
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow
control with limited sensor data and online learning. Theoretical and Computational
Fluid Dynamics. 2020;34:577–591. doi:10.1007/s00162-020-00520-4
apa: Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., & Dellnitz, M. (2020).
Deep model predictive flow control with limited sensor data and online learning.
Theoretical and Computational Fluid Dynamics, 34, 577–591. https://doi.org/10.1007/s00162-020-00520-4
bibtex: '@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive
flow control with limited sensor data and online learning}, volume={34}, DOI={10.1007/s00162-020-00520-4},
journal={Theoretical and Computational Fluid Dynamics}, author={Bieker, Katharina
and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz,
Michael}, year={2020}, pages={577–591} }'
chicago: 'Bieker, Katharina, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz,
and Michael Dellnitz. “Deep Model Predictive Flow Control with Limited Sensor
Data and Online Learning.” Theoretical and Computational Fluid Dynamics
34 (2020): 577–591. https://doi.org/10.1007/s00162-020-00520-4.'
ieee: K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model
predictive flow control with limited sensor data and online learning,” Theoretical
and Computational Fluid Dynamics, vol. 34, pp. 577–591, 2020.
mla: Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited
Sensor Data and Online Learning.” Theoretical and Computational Fluid Dynamics,
vol. 34, 2020, pp. 577–591, doi:10.1007/s00162-020-00520-4.
short: K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and
Computational Fluid Dynamics 34 (2020) 577–591.
date_created: 2020-03-13T12:40:09Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/s00162-020-00520-4
intvolume: ' 34'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf
oa: '1'
page: 577–591
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Theoretical and Computational Fluid Dynamics
publication_identifier:
issn:
- 0935-4964
- 1432-2250
publication_status: published
status: public
title: Deep model predictive flow control with limited sensor data and online learning
type: journal_article
user_id: '47427'
volume: 34
year: '2020'
...
---
_id: '16309'
abstract:
- lang: eng
text: "In recent years, the success of the Koopman operator in dynamical systems\r\nanalysis
has also fueled the development of Koopman operator-based control\r\nframeworks.
In order to preserve the relatively low data requirements for an\r\napproximation
via Dynamic Mode Decomposition, a quantization approach was\r\nrecently proposed
in [Peitz & Klus, Automatica 106, 2019]. This way, control\r\nof nonlinear dynamical
systems can be realized by means of switched systems\r\ntechniques, using only
a finite set of autonomous Koopman operator-based\r\nreduced models. These individual
systems can be approximated very efficiently\r\nfrom data. The main idea is to
transform a control system into a set of\r\nautonomous systems for which the optimal
switching sequence has to be computed.\r\nIn this article, we extend these results
to continuous control inputs using\r\nrelaxation. This way, we combine the advantages
of the data efficiency of\r\napproximating a finite set of autonomous systems
with continuous controls. We\r\nshow that when using the Koopman generator, this
relaxation --- realized by\r\nlinear interpolation between two operators --- does
not introduce any error for\r\ncontrol affine systems. This allows us to control
high-dimensional nonlinear\r\nsystems using bilinear, low-dimensional surrogate
models. The efficiency of the\r\nproposed approach is demonstrated using several
examples with increasing\r\ncomplexity, from the Duffing oscillator to the chaotic
fluidic pinball."
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Samuel E.
full_name: Otto, Samuel E.
last_name: Otto
- first_name: Clarence W.
full_name: Rowley, Clarence W.
last_name: Rowley
citation:
ama: Peitz S, Otto SE, Rowley CW. Data-Driven Model Predictive Control using Interpolated
Koopman Generators. SIAM Journal on Applied Dynamical Systems. 2020;19(3):2162-2193.
doi:10.1137/20M1325678
apa: Peitz, S., Otto, S. E., & Rowley, C. W. (2020). Data-Driven Model Predictive
Control using Interpolated Koopman Generators. SIAM Journal on Applied Dynamical
Systems, 19(3), 2162–2193. https://doi.org/10.1137/20M1325678
bibtex: '@article{Peitz_Otto_Rowley_2020, title={Data-Driven Model Predictive Control
using Interpolated Koopman Generators}, volume={19}, DOI={10.1137/20M1325678},
number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Peitz,
Sebastian and Otto, Samuel E. and Rowley, Clarence W.}, year={2020}, pages={2162–2193}
}'
chicago: 'Peitz, Sebastian, Samuel E. Otto, and Clarence W. Rowley. “Data-Driven
Model Predictive Control Using Interpolated Koopman Generators.” SIAM Journal
on Applied Dynamical Systems 19, no. 3 (2020): 2162–93. https://doi.org/10.1137/20M1325678.'
ieee: S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control
using Interpolated Koopman Generators,” SIAM Journal on Applied Dynamical
Systems, vol. 19, no. 3, pp. 2162–2193, 2020.
mla: Peitz, Sebastian, et al. “Data-Driven Model Predictive Control Using Interpolated
Koopman Generators.” SIAM Journal on Applied Dynamical Systems, vol. 19,
no. 3, 2020, pp. 2162–93, doi:10.1137/20M1325678.
short: S. Peitz, S.E. Otto, C.W. Rowley, SIAM Journal on Applied Dynamical Systems
19 (2020) 2162–2193.
date_created: 2020-03-17T09:53:01Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1137/20M1325678
intvolume: ' 19'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/pdf/10.1137/20M1325678
page: 2162-2193
publication: SIAM Journal on Applied Dynamical Systems
status: public
title: Data-Driven Model Predictive Control using Interpolated Koopman Generators
type: journal_article
user_id: '47427'
volume: 19
year: '2020'
...