---
_id: '34839'
abstract:
- lang: eng
text: We describe the relations among the ℓ-torsion conjecture, a conjecture of
Malle giving an upper bound for the number of extensions, and the discriminant
multiplicity conjecture. We prove that the latter two conjectures are equivalent
in some sense. Altogether, the three conjectures are equivalent for the class
of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the
other two conjectures for nilpotent groups.
author:
- first_name: Jürgen
full_name: Klüners, Jürgen
id: '21202'
last_name: Klüners
- first_name: Jiuya
full_name: Wang, Jiuya
last_name: Wang
citation:
ama: Klüners J, Wang J. ℓ-torsion bounds for the class group of number fields with
an ℓ-group as Galois group. Proceedings of the American Mathematical Society.
2022;150(7):2793-2805. doi:10.1090/proc/15882
apa: Klüners, J., & Wang, J. (2022). ℓ-torsion bounds for the class group of
number fields with an ℓ-group as Galois group. Proceedings of the American
Mathematical Society, 150(7), 2793–2805. https://doi.org/10.1090/proc/15882
bibtex: '@article{Klüners_Wang_2022, title={ℓ-torsion bounds for the class group
of number fields with an ℓ-group as Galois group}, volume={150}, DOI={10.1090/proc/15882},
number={7}, journal={Proceedings of the American Mathematical Society}, publisher={American
Mathematical Society (AMS)}, author={Klüners, Jürgen and Wang, Jiuya}, year={2022},
pages={2793–2805} }'
chicago: 'Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group
of Number Fields with an ℓ-Group as Galois Group.” Proceedings of the American
Mathematical Society 150, no. 7 (2022): 2793–2805. https://doi.org/10.1090/proc/15882.'
ieee: 'J. Klüners and J. Wang, “ℓ-torsion bounds for the class group of number fields
with an ℓ-group as Galois group,” Proceedings of the American Mathematical
Society, vol. 150, no. 7, pp. 2793–2805, 2022, doi: 10.1090/proc/15882.'
mla: Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number
Fields with an ℓ-Group as Galois Group.” Proceedings of the American Mathematical
Society, vol. 150, no. 7, American Mathematical Society (AMS), 2022, pp. 2793–805,
doi:10.1090/proc/15882.
short: J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150
(2022) 2793–2805.
date_created: 2022-12-22T10:47:01Z
date_updated: 2023-03-06T08:47:42Z
department:
- _id: '102'
doi: 10.1090/proc/15882
external_id:
arxiv:
- '2003.12161 '
intvolume: ' 150'
issue: '7'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 2793-2805
publication: Proceedings of the American Mathematical Society
publication_identifier:
issn:
- 0002-9939
- 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois
group
type: journal_article
user_id: '93826'
volume: 150
year: '2022'
...
---
_id: '34835'
abstract:
- lang: eng
text: 'We prove an upper bound for the asymptotics of counting functions of number
fields with nilpotent Galois groups. '
author:
- first_name: Jürgen
full_name: Klüners, Jürgen
id: '21202'
last_name: Klüners
citation:
ama: Klüners J. The asymptotics of nilpotent Galois groups. Acta Arithmetica.
2022;204(2):165-184. doi:10.4064/aa211207-16-5
apa: Klüners, J. (2022). The asymptotics of nilpotent Galois groups. Acta Arithmetica,
204(2), 165–184. https://doi.org/10.4064/aa211207-16-5
bibtex: '@article{Klüners_2022, title={The asymptotics of nilpotent Galois groups},
volume={204}, DOI={10.4064/aa211207-16-5},
number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish
Academy of Sciences}, author={Klüners, Jürgen}, year={2022}, pages={165–184} }'
chicago: 'Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” Acta
Arithmetica 204, no. 2 (2022): 165–84. https://doi.org/10.4064/aa211207-16-5.'
ieee: 'J. Klüners, “The asymptotics of nilpotent Galois groups,” Acta Arithmetica,
vol. 204, no. 2, pp. 165–184, 2022, doi: 10.4064/aa211207-16-5.'
mla: Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” Acta Arithmetica,
vol. 204, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2022, pp.
165–84, doi:10.4064/aa211207-16-5.
short: J. Klüners, Acta Arithmetica 204 (2022) 165–184.
date_created: 2022-12-22T10:08:23Z
date_updated: 2023-03-06T08:48:33Z
department:
- _id: '102'
doi: 10.4064/aa211207-16-5
external_id:
arxiv:
- '2011.04325 '
intvolume: ' 204'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 165-184
publication: Acta Arithmetica
publication_identifier:
issn:
- 0065-1036
- 1730-6264
publication_status: published
publisher: Institute of Mathematics, Polish Academy of Sciences
status: public
title: The asymptotics of nilpotent Galois groups
type: journal_article
user_id: '93826'
volume: 204
year: '2022'
...
---
_id: '44328'
abstract:
- lang: eng
text: In this paper, we study equivalences between the categories of quasi–coherent
sheaves on non–commutative noetherian schemes. In particular, we give a new proof
of Căldăraru's conjecture about Morita equivalences of Azumaya algebras on noetherian
schemes. Moreover, we derive necessary and sufficient condition for two reduced
non–commutative curves to be Morita equivalent.
article_number: '108273'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: Yu.
full_name: Drozd, Yu.
last_name: Drozd
citation:
ama: Burban I, Drozd Yu. Morita theory for non-commutative noetherian schemes. Advances
in Mathematics. 2022;399. doi:10.1016/j.aim.2022.108273
apa: Burban, I., & Drozd, Yu. (2022). Morita theory for non-commutative noetherian
schemes. Advances in Mathematics, 399, Article 108273. https://doi.org/10.1016/j.aim.2022.108273
bibtex: '@article{Burban_Drozd_2022, title={Morita theory for non-commutative noetherian
schemes}, volume={399}, DOI={10.1016/j.aim.2022.108273},
number={108273}, journal={Advances in Mathematics}, author={Burban, Igor and Drozd,
Yu.}, year={2022} }'
chicago: Burban, Igor, and Yu. Drozd. “Morita Theory for Non-Commutative Noetherian
Schemes.” Advances in Mathematics 399 (2022). https://doi.org/10.1016/j.aim.2022.108273.
ieee: 'I. Burban and Yu. Drozd, “Morita theory for non-commutative noetherian schemes,”
Advances in Mathematics, vol. 399, Art. no. 108273, 2022, doi: 10.1016/j.aim.2022.108273.'
mla: Burban, Igor, and Yu. Drozd. “Morita Theory for Non-Commutative Noetherian
Schemes.” Advances in Mathematics, vol. 399, 108273, 2022, doi:10.1016/j.aim.2022.108273.
short: I. Burban, Yu. Drozd, Advances in Mathematics 399 (2022).
date_created: 2023-05-02T18:34:25Z
date_updated: 2023-05-07T01:35:27Z
department:
- _id: '602'
doi: 10.1016/j.aim.2022.108273
intvolume: ' 399'
language:
- iso: eng
publication: Advances in Mathematics
publication_status: published
status: public
title: Morita theory for non-commutative noetherian schemes
type: journal_article
user_id: '49063'
volume: 399
year: '2022'
...
---
_id: '44327'
article_number: '104499'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: A.
full_name: Peruzzi, A.
last_name: Peruzzi
citation:
ama: Burban I, Peruzzi A. On elliptic solutions of the associative Yang-Baxter equation.
Journal of Geometry and Physics. 2022;176.
apa: Burban, I., & Peruzzi, A. (2022). On elliptic solutions of the associative
Yang-Baxter equation. Journal of Geometry and Physics, 176, Article
104499.
bibtex: '@article{Burban_Peruzzi_2022, title={On elliptic solutions of the associative
Yang-Baxter equation}, volume={176}, number={104499}, journal={Journal of Geometry
and Physics}, author={Burban, Igor and Peruzzi, A.}, year={2022} }'
chicago: Burban, Igor, and A. Peruzzi. “On Elliptic Solutions of the Associative
Yang-Baxter Equation.” Journal of Geometry and Physics 176 (2022).
ieee: I. Burban and A. Peruzzi, “On elliptic solutions of the associative Yang-Baxter
equation,” Journal of Geometry and Physics, vol. 176, Art. no. 104499,
2022.
mla: Burban, Igor, and A. Peruzzi. “On Elliptic Solutions of the Associative Yang-Baxter
Equation.” Journal of Geometry and Physics, vol. 176, 104499, 2022.
short: I. Burban, A. Peruzzi, Journal of Geometry and Physics 176 (2022).
date_created: 2023-05-02T18:32:49Z
date_updated: 2023-05-07T01:41:35Z
department:
- _id: '602'
intvolume: ' 176'
language:
- iso: eng
publication: Journal of Geometry and Physics
publication_status: published
status: public
title: On elliptic solutions of the associative Yang-Baxter equation
type: journal_article
user_id: '49063'
volume: 176
year: '2022'
...
---
_id: '44624'
author:
- first_name: Timm
full_name: Faulwasser, Timm
last_name: Faulwasser
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Schaller M, Worthmann K. Manifold
turnpikes, trims, and symmetries. Mathematics of Control, Signals, and Systems.
2022;34:759-788.
apa: Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., Schaller, M., & Worthmann,
K. (2022). Manifold turnpikes, trims, and symmetries. Mathematics of Control,
Signals, and Systems, 34, 759–788.
bibtex: '@article{Faulwasser_Flaßkamp_Ober-Blöbaum_Schaller_Worthmann_2022, title={Manifold
turnpikes, trims, and symmetries}, volume={34}, journal={Mathematics of Control,
Signals, and Systems}, publisher={Springer}, author={Faulwasser, Timm and Flaßkamp,
Kathrin and Ober-Blöbaum, Sina and Schaller, Manuel and Worthmann, Karl}, year={2022},
pages={759–788} }'
chicago: 'Faulwasser, Timm, Kathrin Flaßkamp, Sina Ober-Blöbaum, Manuel Schaller,
and Karl Worthmann. “Manifold Turnpikes, Trims, and Symmetries.” Mathematics
of Control, Signals, and Systems 34 (2022): 759–88.'
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, and K. Worthmann,
“Manifold turnpikes, trims, and symmetries,” Mathematics of Control, Signals,
and Systems, vol. 34, pp. 759–788, 2022.
mla: Faulwasser, Timm, et al. “Manifold Turnpikes, Trims, and Symmetries.” Mathematics
of Control, Signals, and Systems, vol. 34, Springer, 2022, pp. 759–88.
short: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, K. Worthmann, Mathematics
of Control, Signals, and Systems 34 (2022) 759–788.
date_created: 2023-05-08T09:04:06Z
date_updated: 2023-05-08T09:04:26Z
department:
- _id: '636'
intvolume: ' 34'
language:
- iso: eng
page: 759-788
publication: Mathematics of Control, Signals, and Systems
publisher: Springer
status: public
title: Manifold turnpikes, trims, and symmetries
type: journal_article
user_id: '15694'
volume: 34
year: '2022'
...
---
_id: '33741'
abstract:
- lang: eng
text: There are many concepts of signed graph coloring which are defined by assigning
colors to the vertices of the graphs. These concepts usually differ in the number
of self-inverse colors used. We introduce a unifying concept for this kind of
coloring by assigning elements from symmetric sets to the vertices of the signed
graphs. In the first part of the paper, we study colorings with elements from
symmetric sets where the number of self-inverse elements is fixed. We prove a
Brooks’-type theorem and upper bounds for the corresponding chromatic numbers
in terms of the chromatic number of the underlying graph. These results are used
in the second part where we introduce the symset-chromatic number χsym(G,σ) of
a signed graph (G,σ). We show that the symset-chromatic number gives the minimum
partition of a signed graph into independent sets and non-bipartite antibalanced
subgraphs. In particular, χsym(G,σ)≤χ(G). In the final section we show that these
colorings can also be formalized as DP-colorings.
author:
- first_name: Chiara
full_name: Cappello, Chiara
id: '72874'
last_name: Cappello
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: Cappello C, Steffen E. Symmetric Set Coloring of Signed Graphs. Annals of
Combinatorics. Published online 2022. doi:10.1007/s00026-022-00593-4
apa: Cappello, C., & Steffen, E. (2022). Symmetric Set Coloring of Signed Graphs.
Annals of Combinatorics. https://doi.org/10.1007/s00026-022-00593-4
bibtex: '@article{Cappello_Steffen_2022, title={Symmetric Set Coloring of Signed
Graphs}, DOI={10.1007/s00026-022-00593-4},
journal={Annals of Combinatorics}, publisher={Springer Science and Business Media
LLC}, author={Cappello, Chiara and Steffen, Eckhard}, year={2022} }'
chicago: Cappello, Chiara, and Eckhard Steffen. “Symmetric Set Coloring of Signed
Graphs.” Annals of Combinatorics, 2022. https://doi.org/10.1007/s00026-022-00593-4.
ieee: 'C. Cappello and E. Steffen, “Symmetric Set Coloring of Signed Graphs,” Annals
of Combinatorics, 2022, doi: 10.1007/s00026-022-00593-4.'
mla: Cappello, Chiara, and Eckhard Steffen. “Symmetric Set Coloring of Signed Graphs.”
Annals of Combinatorics, Springer Science and Business Media LLC, 2022,
doi:10.1007/s00026-022-00593-4.
short: C. Cappello, E. Steffen, Annals of Combinatorics (2022).
date_created: 2022-10-17T07:54:41Z
date_updated: 2023-05-16T10:37:58Z
department:
- _id: '542'
doi: 10.1007/s00026-022-00593-4
external_id:
arxiv:
- '2106.05928'
keyword:
- Discrete Mathematics and Combinatorics
language:
- iso: eng
publication: Annals of Combinatorics
publication_identifier:
issn:
- 0218-0006
- 0219-3094
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Symmetric Set Coloring of Signed Graphs
type: journal_article
user_id: '15540'
year: '2022'
...
---
_id: '33950'
author:
- first_name: Chiara
full_name: Cappello, Chiara
id: '72874'
last_name: Cappello
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: Cappello C, Steffen E. Frustration-critical signed graphs. Discrete Applied
Mathematics. 2022;322:183-193. doi:10.1016/j.dam.2022.08.010
apa: Cappello, C., & Steffen, E. (2022). Frustration-critical signed graphs.
Discrete Applied Mathematics, 322, 183–193. https://doi.org/10.1016/j.dam.2022.08.010
bibtex: '@article{Cappello_Steffen_2022, title={Frustration-critical signed graphs},
volume={322}, DOI={10.1016/j.dam.2022.08.010},
journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Cappello,
Chiara and Steffen, Eckhard}, year={2022}, pages={183–193} }'
chicago: 'Cappello, Chiara, and Eckhard Steffen. “Frustration-Critical Signed Graphs.”
Discrete Applied Mathematics 322 (2022): 183–93. https://doi.org/10.1016/j.dam.2022.08.010.'
ieee: 'C. Cappello and E. Steffen, “Frustration-critical signed graphs,” Discrete
Applied Mathematics, vol. 322, pp. 183–193, 2022, doi: 10.1016/j.dam.2022.08.010.'
mla: Cappello, Chiara, and Eckhard Steffen. “Frustration-Critical Signed Graphs.”
Discrete Applied Mathematics, vol. 322, Elsevier BV, 2022, pp. 183–93,
doi:10.1016/j.dam.2022.08.010.
short: C. Cappello, E. Steffen, Discrete Applied Mathematics 322 (2022) 183–193.
date_created: 2022-10-28T06:51:31Z
date_updated: 2023-05-16T10:36:51Z
department:
- _id: '542'
doi: 10.1016/j.dam.2022.08.010
external_id:
arxiv:
- '2112.02664'
intvolume: ' 322'
keyword:
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 183-193
publication: Discrete Applied Mathematics
publication_identifier:
issn:
- 0166-218X
publication_status: published
publisher: Elsevier BV
status: public
title: Frustration-critical signed graphs
type: journal_article
user_id: '15540'
volume: 322
year: '2022'
...
---
_id: '45679'
author:
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
- first_name: D.
full_name: Reuter, D.
last_name: Reuter
citation:
ama: 'Bruns J, Reuter D. „Ich hab als Erstes die angeguckt“ – Muster- und Strukturerkennung
mit Eye-Tracking besser verstehen? In: Beiträge zum Mathematikunterricht 2022.
WTM-Verlag; 2022.'
apa: Bruns, J., & Reuter, D. (2022). „Ich hab als Erstes die angeguckt“ – Muster-
und Strukturerkennung mit Eye-Tracking besser verstehen? Beiträge zum Mathematikunterricht
2022.
bibtex: '@inproceedings{Bruns_Reuter_2022, title={„Ich hab als Erstes die angeguckt“
– Muster- und Strukturerkennung mit Eye-Tracking besser verstehen?}, booktitle={Beiträge
zum Mathematikunterricht 2022}, publisher={WTM-Verlag}, author={Bruns, Julia and
Reuter, D.}, year={2022} }'
chicago: Bruns, Julia, and D. Reuter. “„Ich hab als Erstes die angeguckt“ – Muster-
und Strukturerkennung mit Eye-Tracking besser verstehen?” In Beiträge zum Mathematikunterricht
2022. WTM-Verlag, 2022.
ieee: J. Bruns and D. Reuter, “„Ich hab als Erstes die angeguckt“ – Muster- und
Strukturerkennung mit Eye-Tracking besser verstehen?,” 2022.
mla: Bruns, Julia, and D. Reuter. “„Ich hab als Erstes die angeguckt“ – Muster-
und Strukturerkennung mit Eye-Tracking besser verstehen?” Beiträge zum Mathematikunterricht
2022, WTM-Verlag, 2022.
short: 'J. Bruns, D. Reuter, in: Beiträge zum Mathematikunterricht 2022, WTM-Verlag,
2022.'
date_created: 2023-06-20T18:27:40Z
date_updated: 2023-06-20T18:27:55Z
department:
- _id: '97'
- _id: '611'
language:
- iso: ger
publication: Beiträge zum Mathematikunterricht 2022
publication_status: published
publisher: WTM-Verlag
status: public
title: „Ich hab als Erstes die angeguckt“ – Muster- und Strukturerkennung mit Eye-Tracking
besser verstehen?
type: conference
user_id: '49063'
year: '2022'
...
---
_id: '45678'
author:
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
- first_name: M.
full_name: Hagena, M.
last_name: Hagena
- first_name: H.
full_name: Gasteiger, H.
last_name: Gasteiger
citation:
ama: 'Bruns J, Hagena M, Gasteiger H. Effects of Facilitator Professional Development
on Teachers’ Learning – An Intervention Study in the Context of Early Mathematics
Education. In: Hodgen J, Geraniou E, Bolondi G, Ferretti F, eds. Proceedings
of the Twelfth Congress of the European Society for Research in Mathematics Education
(CERME12). ; 2022.'
apa: Bruns, J., Hagena, M., & Gasteiger, H. (2022). Effects of Facilitator Professional
Development on Teachers’ Learning – An Intervention Study in the Context of Early
Mathematics Education. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti
(Eds.), Proceedings of the Twelfth Congress of the European Society for Research
in Mathematics Education (CERME12).
bibtex: '@inproceedings{Bruns_Hagena_Gasteiger_2022, title={Effects of Facilitator
Professional Development on Teachers’ Learning – An Intervention Study in the
Context of Early Mathematics Education}, booktitle={Proceedings of the Twelfth
Congress of the European Society for Research in Mathematics Education (CERME12)},
author={Bruns, Julia and Hagena, M. and Gasteiger, H.}, editor={Hodgen, J. and
Geraniou, E. and Bolondi, G. and Ferretti, F.}, year={2022} }'
chicago: Bruns, Julia, M. Hagena, and H. Gasteiger. “Effects of Facilitator Professional
Development on Teachers’ Learning – An Intervention Study in the Context of Early
Mathematics Education.” In Proceedings of the Twelfth Congress of the European
Society for Research in Mathematics Education (CERME12), edited by J. Hodgen,
E. Geraniou, G. Bolondi, and F. Ferretti, 2022.
ieee: J. Bruns, M. Hagena, and H. Gasteiger, “Effects of Facilitator Professional
Development on Teachers’ Learning – An Intervention Study in the Context of Early
Mathematics Education,” in Proceedings of the Twelfth Congress of the European
Society for Research in Mathematics Education (CERME12), Free University of
Bozen-Bolzano and ERME, 2022.
mla: Bruns, Julia, et al. “Effects of Facilitator Professional Development on Teachers’
Learning – An Intervention Study in the Context of Early Mathematics Education.”
Proceedings of the Twelfth Congress of the European Society for Research in
Mathematics Education (CERME12), edited by J. Hodgen et al., 2022.
short: 'J. Bruns, M. Hagena, H. Gasteiger, in: J. Hodgen, E. Geraniou, G. Bolondi,
F. Ferretti (Eds.), Proceedings of the Twelfth Congress of the European Society
for Research in Mathematics Education (CERME12), 2022.'
conference:
location: Free University of Bozen-Bolzano and ERME
name: Proceedings of the Twelfth Congress of the European Society for Research in
Mathematics Education (CERME12)
date_created: 2023-06-20T18:26:19Z
date_updated: 2023-06-20T19:06:39Z
department:
- _id: '97'
- _id: '611'
editor:
- first_name: J.
full_name: Hodgen, J.
last_name: Hodgen
- first_name: E.
full_name: Geraniou, E.
last_name: Geraniou
- first_name: G.
full_name: Bolondi, G.
last_name: Bolondi
- first_name: F.
full_name: Ferretti, F.
last_name: Ferretti
language:
- iso: eng
publication: Proceedings of the Twelfth Congress of the European Society for Research
in Mathematics Education (CERME12)
publication_status: published
status: public
title: Effects of Facilitator Professional Development on Teachers’ Learning – An
Intervention Study in the Context of Early Mathematics Education
type: conference
user_id: '49063'
year: '2022'
...
---
_id: '45677'
author:
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
- first_name: W.
full_name: Langer, W.
last_name: Langer
- first_name: J.
full_name: Erhorn, J.
last_name: Erhorn
citation:
ama: Bruns J, Langer W, Erhorn J. Entwicklung und Validierung eines videobasierten
Testinstruments zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse
im inklusiven Sportunterricht. German Journal of Exercise and Sport Research.
2022;52(3):386–397. doi:10.1007/s12662-022-00807-0
apa: Bruns, J., Langer, W., & Erhorn, J. (2022). Entwicklung und Validierung
eines videobasierten Testinstruments zur Erfassung des Noticing mit dem Fokus
auf Anerkennungsprozesse im inklusiven Sportunterricht. German Journal of Exercise
and Sport Research, 52(3), 386–397. https://doi.org/10.1007/s12662-022-00807-0
bibtex: '@article{Bruns_Langer_Erhorn_2022, title={Entwicklung und Validierung eines
videobasierten Testinstruments zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse
im inklusiven Sportunterricht}, volume={52}, DOI={10.1007/s12662-022-00807-0},
number={3}, journal={German Journal of Exercise and Sport Research}, author={Bruns,
Julia and Langer, W. and Erhorn, J.}, year={2022}, pages={386–397} }'
chicago: 'Bruns, Julia, W. Langer, and J. Erhorn. “Entwicklung und Validierung eines
videobasierten Testinstruments zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse
im inklusiven Sportunterricht.” German Journal of Exercise and Sport Research
52, no. 3 (2022): 386–397. https://doi.org/10.1007/s12662-022-00807-0.'
ieee: 'J. Bruns, W. Langer, and J. Erhorn, “Entwicklung und Validierung eines videobasierten
Testinstruments zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse
im inklusiven Sportunterricht,” German Journal of Exercise and Sport Research,
vol. 52, no. 3, pp. 386–397, 2022, doi: 10.1007/s12662-022-00807-0.'
mla: Bruns, Julia, et al. “Entwicklung und Validierung eines videobasierten Testinstruments
zur Erfassung des Noticing mit dem Fokus auf Anerkennungsprozesse im inklusiven
Sportunterricht.” German Journal of Exercise and Sport Research, vol. 52,
no. 3, 2022, pp. 386–397, doi:10.1007/s12662-022-00807-0.
short: J. Bruns, W. Langer, J. Erhorn, German Journal of Exercise and Sport Research
52 (2022) 386–397.
date_created: 2023-06-20T18:22:54Z
date_updated: 2023-06-20T19:06:58Z
department:
- _id: '97'
- _id: '611'
doi: 10.1007/s12662-022-00807-0
intvolume: ' 52'
issue: '3'
language:
- iso: ger
page: 386–397
publication: German Journal of Exercise and Sport Research
publication_status: published
status: public
title: Entwicklung und Validierung eines videobasierten Testinstruments zur Erfassung
des Noticing mit dem Fokus auf Anerkennungsprozesse im inklusiven Sportunterricht
type: journal_article
user_id: '49063'
volume: 52
year: '2022'
...
---
_id: '34820'
abstract:
- lang: eng
text: The construct of noticing is considered to be of crucial importance for professional
action of (prospective) physical education (PE) teachers in the context of (inclusive)
PE. In order to implement the demands of inclusive PE teaching, noticingwith regard
to processes of recognition proves to be particularly significant. Due to the
relevance of physicality, the design of recognition relationships that encourage
pupils' development results in specific requirements for the selective attention
and the theory-based interpretation of processes of recognition and disregard
in complex teaching situations. This facet of competence has hardly been studied
so far, partly due to the lack of instruments for standardised assessment of this
construct. In the context of this paper, the development and validation of a standardised,
video vignette-based test instrument for the measurement of noticingwith regard
to processes of recognition of prospective PE teachers is presented. The validation
focuses on the content of the test and the internal structure of the instrument
as well as on correlations with related constructs in terms of content. The results
from three consecutive validation studies provide indications of the reliability
and validity of the test score interpretation of the instrument ViProQiS_A. The
findings so far indicate that the standardised measurement of noticingwith regard
to processes of recognitionin inclusive PE could be realized on the basis of the
test instrument developed here.
article_type: original
author:
- first_name: Wiebke
full_name: Langer, Wiebke
last_name: Langer
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
- first_name: Jan
full_name: Erhorn, Jan
last_name: Erhorn
citation:
ama: Langer W, Bruns J, Erhorn J. Development and validation of a video-based test
instrument to measure noticing with regard to processes ofrecognition in inclusive
physical education. German Journal of Exercise and Sport Research. 2022;52(3):386-397.
doi:10.1007/s12662-022-00807-0
apa: Langer, W., Bruns, J., & Erhorn, J. (2022). Development and validation
of a video-based test instrument to measure noticing with regard to processes
ofrecognition in inclusive physical education. German Journal of Exercise and
Sport Research, 52(3), 386–397. https://doi.org/10.1007/s12662-022-00807-0
bibtex: '@article{Langer_Bruns_Erhorn_2022, title={Development and validation of
a video-based test instrument to measure noticing with regard to processes ofrecognition
in inclusive physical education}, volume={52}, DOI={10.1007/s12662-022-00807-0},
number={3}, journal={German Journal of Exercise and Sport Research}, publisher={Springer},
author={Langer, Wiebke and Bruns, Julia and Erhorn, Jan}, year={2022}, pages={386–397}
}'
chicago: 'Langer, Wiebke, Julia Bruns, and Jan Erhorn. “Development and Validation
of a Video-Based Test Instrument to Measure Noticing with Regard to Processes
Ofrecognition in Inclusive Physical Education.” German Journal of Exercise
and Sport Research 52, no. 3 (2022): 386–97. https://doi.org/10.1007/s12662-022-00807-0.'
ieee: 'W. Langer, J. Bruns, and J. Erhorn, “Development and validation of a video-based
test instrument to measure noticing with regard to processes ofrecognition in
inclusive physical education,” German Journal of Exercise and Sport Research,
vol. 52, no. 3, pp. 386–397, 2022, doi: 10.1007/s12662-022-00807-0.'
mla: Langer, Wiebke, et al. “Development and Validation of a Video-Based Test Instrument
to Measure Noticing with Regard to Processes Ofrecognition in Inclusive Physical
Education.” German Journal of Exercise and Sport Research, vol. 52, no.
3, Springer, 2022, pp. 386–97, doi:10.1007/s12662-022-00807-0.
short: W. Langer, J. Bruns, J. Erhorn, German Journal of Exercise and Sport Research
52 (2022) 386–397.
date_created: 2022-12-22T09:22:45Z
date_updated: 2023-06-20T19:10:42Z
department:
- _id: '97'
- _id: '611'
doi: 10.1007/s12662-022-00807-0
external_id:
isi:
- '000788945100004'
intvolume: ' 52'
isi: '1'
issue: '3'
keyword:
- Physical education teacher education
- Competence modelling and
- measurement
- Inclusive physical education
- Video-based items
- Noticing
language:
- iso: eng
page: 386-397
publication: German Journal of Exercise and Sport Research
publication_identifier:
eissn:
- 2509-3150
issn:
- 2509-3142
publication_status: published
publisher: Springer
quality_controlled: '1'
status: public
title: Development and validation of a video-based test instrument to measure noticing
with regard to processes ofrecognition in inclusive physical education
type: journal_article
user_id: '49063'
volume: 52
year: '2022'
...
---
_id: '34819'
abstract:
- lang: eng
text: Teachers expect facilitators to have own teaching experience as a teacher
in order to be able to carry out effective teacher professional development programs.
As part of the project EmMa(M), it is investigated, to which extent the teaching
experience of facilitators influences the development of early childhood teachers'
(n = 83) mathematical pedagogical content knowledge (MPCK) and early childhood
teachers' enjoyment of mathematics in the context of a teacher professional development
program. It turns out that the teaching experience of the facilitators has no
influence on the development of early childhood teachers' MPCK, but favors the
development of early childhood teachers' enjoyment of mathematics. Controlling
for this increased enjoyment an influence of teaching experience on the development
of early childhood teachers' MPCK emerges, but in favor of the participating facilitators
who have no teaching experience but have a university degree.
article_type: original
author:
- first_name: Maike
full_name: Hagena, Maike
last_name: Hagena
- 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
citation:
ama: Hagena M, Bruns J, Gasteiger H. Einfluss der Berufserfahrung von Multiplikatorinnen
und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen zur frühen mathematischen
Bildung. Zeitschrift Für Erziehungswissenschaft. Zeitschrift für Erziehungswissenschaft.
2022;25(6):1455–1480. doi:10.1007/s11618-022-01122-y
apa: Hagena, M., Bruns, J., & Gasteiger, H. (2022). Einfluss der Berufserfahrung
von Multiplikatorinnen und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen
zur frühen mathematischen Bildung. Zeitschrift Für Erziehungswissenschaft. Zeitschrift
für Erziehungswissenschaft, 25(6), 1455–1480. https://doi.org/10.1007/s11618-022-01122-y
bibtex: '@article{Hagena_Bruns_Gasteiger_2022, title={Einfluss der Berufserfahrung
von Multiplikatorinnen und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen
zur frühen mathematischen Bildung. Zeitschrift Für Erziehungswissenschaft}, volume={25},
DOI={10.1007/s11618-022-01122-y},
number={6}, journal={Zeitschrift für Erziehungswissenschaft}, publisher={Springer
Vieweg-springer Fachmedien Wiesbaden Gmbh}, author={Hagena, Maike and Bruns, Julia
and Gasteiger, Hedwig}, year={2022}, pages={1455–1480} }'
chicago: 'Hagena, Maike, Julia Bruns, and Hedwig Gasteiger. “Einfluss der Berufserfahrung
von Multiplikatorinnen und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen
zur frühen mathematischen Bildung. Zeitschrift Für Erziehungswissenschaft.” Zeitschrift
für Erziehungswissenschaft 25, no. 6 (2022): 1455–1480. https://doi.org/10.1007/s11618-022-01122-y.'
ieee: 'M. Hagena, J. Bruns, and H. Gasteiger, “Einfluss der Berufserfahrung von
Multiplikatorinnen und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen
zur frühen mathematischen Bildung. Zeitschrift Für Erziehungswissenschaft,” Zeitschrift
für Erziehungswissenschaft, vol. 25, no. 6, pp. 1455–1480, 2022, doi: 10.1007/s11618-022-01122-y.'
mla: Hagena, Maike, et al. “Einfluss der Berufserfahrung von Multiplikatorinnen
und Multiplikatoren auf die Wirksamkeit von Fortbildungsmaßnahmen zur frühen mathematischen
Bildung. Zeitschrift Für Erziehungswissenschaft.” Zeitschrift für Erziehungswissenschaft,
vol. 25, no. 6, Springer Vieweg-springer Fachmedien Wiesbaden Gmbh, 2022, pp.
1455–1480, doi:10.1007/s11618-022-01122-y.
short: M. Hagena, J. Bruns, H. Gasteiger, Zeitschrift für Erziehungswissenschaft
25 (2022) 1455–1480.
date_created: 2022-12-22T09:22:45Z
date_updated: 2023-06-20T19:10:11Z
department:
- _id: '611'
- _id: '97'
doi: 10.1007/s11618-022-01122-y
external_id:
isi:
- '000852117800001'
intvolume: ' 25'
isi: '1'
issue: '6'
keyword:
- Facilitator professional development
- Early childhood teachers
- Teaching
- experience
- Early mathematics education
language:
- iso: ger
page: 1455–1480
publication: Zeitschrift für Erziehungswissenschaft
publication_identifier:
eissn:
- 1862-5215
issn:
- 1434-663X
publication_status: published
publisher: Springer Vieweg-springer Fachmedien Wiesbaden Gmbh
quality_controlled: '1'
status: public
title: Einfluss der Berufserfahrung von Multiplikatorinnen und Multiplikatoren auf
die Wirksamkeit von Fortbildungsmaßnahmen zur frühen mathematischen Bildung. Zeitschrift
Für Erziehungswissenschaft
type: journal_article
user_id: '49063'
volume: 25
year: '2022'
...
---
_id: '36472'
author:
- first_name: Dinah
full_name: Reuter, Dinah
last_name: Reuter
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
citation:
ama: 'Reuter D, Bruns J. Muster- und Strukturerkennungsprozesse bei potenziell mathematisch
begabten Grundschulkindern untersuchen – Das Potenzial von Eye-Tracking und retrospektivem
Interview im Vergleich. In: Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik.
Springer Berlin Heidelberg; 2022. doi:10.1007/978-3-662-63214-7_3'
apa: Reuter, D., & Bruns, J. (2022). Muster- und Strukturerkennungsprozesse
bei potenziell mathematisch begabten Grundschulkindern untersuchen – Das Potenzial
von Eye-Tracking und retrospektivem Interview im Vergleich. In Eye-Tracking
in der Mathematik- und Naturwissenschaftsdidaktik. Springer Berlin Heidelberg.
https://doi.org/10.1007/978-3-662-63214-7_3
bibtex: '@inbook{Reuter_Bruns_2022, place={Berlin, Heidelberg}, title={Muster- und
Strukturerkennungsprozesse bei potenziell mathematisch begabten Grundschulkindern
untersuchen – Das Potenzial von Eye-Tracking und retrospektivem Interview im Vergleich},
DOI={10.1007/978-3-662-63214-7_3},
booktitle={Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik}, publisher={Springer
Berlin Heidelberg}, author={Reuter, Dinah and Bruns, Julia}, year={2022} }'
chicago: 'Reuter, Dinah, and Julia Bruns. “Muster- und Strukturerkennungsprozesse
bei potenziell mathematisch begabten Grundschulkindern untersuchen – Das Potenzial
von Eye-Tracking und retrospektivem Interview im Vergleich.” In Eye-Tracking
in der Mathematik- und Naturwissenschaftsdidaktik. Berlin, Heidelberg: Springer
Berlin Heidelberg, 2022. https://doi.org/10.1007/978-3-662-63214-7_3.'
ieee: 'D. Reuter and J. Bruns, “Muster- und Strukturerkennungsprozesse bei potenziell
mathematisch begabten Grundschulkindern untersuchen – Das Potenzial von Eye-Tracking
und retrospektivem Interview im Vergleich,” in Eye-Tracking in der Mathematik-
und Naturwissenschaftsdidaktik, Berlin, Heidelberg: Springer Berlin Heidelberg,
2022.'
mla: Reuter, Dinah, and Julia Bruns. “Muster- und Strukturerkennungsprozesse bei
potenziell mathematisch begabten Grundschulkindern untersuchen – Das Potenzial
von Eye-Tracking und retrospektivem Interview im Vergleich.” Eye-Tracking in
der Mathematik- und Naturwissenschaftsdidaktik, Springer Berlin Heidelberg,
2022, doi:10.1007/978-3-662-63214-7_3.
short: 'D. Reuter, J. Bruns, in: Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik,
Springer Berlin Heidelberg, Berlin, Heidelberg, 2022.'
date_created: 2023-01-12T14:51:59Z
date_updated: 2023-06-20T19:10:24Z
department:
- _id: '97'
- _id: '611'
doi: 10.1007/978-3-662-63214-7_3
language:
- iso: ger
place: Berlin, Heidelberg
publication: Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik
publication_identifier:
isbn:
- '9783662632130'
- '9783662632147'
publication_status: published
publisher: Springer Berlin Heidelberg
quality_controlled: '1'
status: public
title: Muster- und Strukturerkennungsprozesse bei potenziell mathematisch begabten
Grundschulkindern untersuchen – Das Potenzial von Eye-Tracking und retrospektivem
Interview im Vergleich
type: book_chapter
user_id: '49063'
year: '2022'
...
---
_id: '45854'
abstract:
- lang: eng
text: In a previous paper the authors developed an algorithm to classify certain
quaternary quadratic lattices over totally real fields. The present article applies
this algorithm to the classification of binary Hermitian lattices over totally
imaginary fields. We use it in particular to classify the 48-dimensional extremal
even unimodular lattices over the integers that admit a semilarge automorphism.
author:
- first_name: Markus
full_name: Kirschmer, Markus
id: '82258'
last_name: Kirschmer
- first_name: Gabriele
full_name: Nebe, Gabriele
last_name: Nebe
citation:
ama: Kirschmer M, Nebe G. Binary Hermitian Lattices over Number Fields. Experimental
Mathematics. 2022;31(1):280-301. doi:10.1080/10586458.2019.1618756
apa: Kirschmer, M., & Nebe, G. (2022). Binary Hermitian Lattices over Number
Fields. Experimental Mathematics, 31(1), 280–301. https://doi.org/10.1080/10586458.2019.1618756
bibtex: '@article{Kirschmer_Nebe_2022, title={Binary Hermitian Lattices over Number
Fields}, volume={31}, DOI={10.1080/10586458.2019.1618756},
number={1}, journal={Experimental Mathematics}, publisher={Informa UK Limited},
author={Kirschmer, Markus and Nebe, Gabriele}, year={2022}, pages={280–301} }'
chicago: 'Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over
Number Fields.” Experimental Mathematics 31, no. 1 (2022): 280–301. https://doi.org/10.1080/10586458.2019.1618756.'
ieee: 'M. Kirschmer and G. Nebe, “Binary Hermitian Lattices over Number Fields,”
Experimental Mathematics, vol. 31, no. 1, pp. 280–301, 2022, doi: 10.1080/10586458.2019.1618756.'
mla: Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number
Fields.” Experimental Mathematics, vol. 31, no. 1, Informa UK Limited,
2022, pp. 280–301, doi:10.1080/10586458.2019.1618756.
short: M. Kirschmer, G. Nebe, Experimental Mathematics 31 (2022) 280–301.
date_created: 2023-07-04T08:28:04Z
date_updated: 2023-07-04T08:29:22Z
department:
- _id: '102'
doi: 10.1080/10586458.2019.1618756
intvolume: ' 31'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 280-301
publication: Experimental Mathematics
publication_identifier:
issn:
- 1058-6458
- 1944-950X
publication_status: published
publisher: Informa UK Limited
status: public
title: Binary Hermitian Lattices over Number Fields
type: journal_article
user_id: '93826'
volume: 31
year: '2022'
...
---
_id: '34677'
article_number: '96'
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: eventual smoothness
in a chemotaxis-Navier–Stokes system with logistic proliferation. Calculus
of Variations and Partial Differential Equations. 2022;61(3). doi:10.1007/s00526-022-02201-y'
apa: 'Black, T., & Wu, C. (2022). Prescribed signal concentration on the boundary:
eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation.
Calculus of Variations and Partial Differential Equations, 61(3),
Article 96. https://doi.org/10.1007/s00526-022-02201-y'
bibtex: '@article{Black_Wu_2022, title={Prescribed signal concentration on the boundary:
eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation},
volume={61}, DOI={10.1007/s00526-022-02201-y},
number={396}, journal={Calculus of Variations and Partial Differential Equations},
publisher={Springer Science and Business Media LLC}, author={Black, Tobias and
Wu, Chunyan}, year={2022} }'
chicago: 'Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the
Boundary: Eventual Smoothness in a Chemotaxis-Navier–Stokes System with Logistic
Proliferation.” Calculus of Variations and Partial Differential Equations
61, no. 3 (2022). https://doi.org/10.1007/s00526-022-02201-y.'
ieee: 'T. Black and C. Wu, “Prescribed signal concentration on the boundary: eventual
smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation,”
Calculus of Variations and Partial Differential Equations, vol. 61, no.
3, Art. no. 96, 2022, doi: 10.1007/s00526-022-02201-y.'
mla: 'Black, Tobias, and Chunyan Wu. “Prescribed Signal Concentration on the Boundary:
Eventual Smoothness in a Chemotaxis-Navier–Stokes System with Logistic Proliferation.”
Calculus of Variations and Partial Differential Equations, vol. 61, no.
3, 96, Springer Science and Business Media LLC, 2022, doi:10.1007/s00526-022-02201-y.'
short: T. Black, C. Wu, Calculus of Variations and Partial Differential Equations
61 (2022).
date_created: 2022-12-21T09:50:59Z
date_updated: 2023-07-10T11:37:27Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1007/s00526-022-02201-y
intvolume: ' 61'
issue: '3'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
issn:
- 0944-2669
- 1432-0835
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'Prescribed signal concentration on the boundary: eventual smoothness in a
chemotaxis-Navier–Stokes system with logistic proliferation'
type: journal_article
user_id: '23686'
volume: 61
year: '2022'
...
---
_id: '19941'
abstract:
- lang: eng
text: "In backward error analysis, an approximate solution to an equation is compared
to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential
equations, the two agree up to any power of the step size. If the differential
equation has a geometric property then the modified equation may share it. In
this way, known properties of differential equations can be applied to the approximation.
But for partial differential equations, the known modified equations are of higher
order, limiting applicability of the theory. Therefore, we study symmetric solutions
of discretized\r\npartial differential equations that arise from a discrete variational
principle. These symmetric solutions obey infinite-dimensional functional equations.
We show that these equations admit second-order modified equations which are Hamiltonian
and also possess first-order Lagrangians in modified coordinates. The modified
equation and its associated structures are computed explicitly for the case of
rotating travelling waves in the nonlinear wave equation."
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. Backward error analysis for variational discretisations
of partial differential equations. Journal of Geometric Mechanics. 2022;14(3):447-471.
doi:10.3934/jgm.2022014
apa: McLachlan, R. I., & Offen, C. (2022). Backward error analysis for variational
discretisations of partial differential equations. Journal of Geometric Mechanics,
14(3), 447–471. https://doi.org/10.3934/jgm.2022014
bibtex: '@article{McLachlan_Offen_2022, title={Backward error analysis for variational
discretisations of partial differential equations}, volume={14}, DOI={10.3934/jgm.2022014},
number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan,
Robert I and Offen, Christian}, year={2022}, pages={447–471} }'
chicago: 'McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for
Variational Discretisations of Partial Differential Equations.” Journal of
Geometric Mechanics 14, no. 3 (2022): 447–71. https://doi.org/10.3934/jgm.2022014.'
ieee: 'R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations
of partial differential equations,” Journal of Geometric Mechanics, vol.
14, no. 3, pp. 447–471, 2022, doi: 10.3934/jgm.2022014.'
mla: McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational
Discretisations of Partial Differential Equations.” Journal of Geometric Mechanics,
vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:10.3934/jgm.2022014.
short: R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471.
date_created: 2020-10-06T16:33:19Z
date_updated: 2023-08-10T08:44:55Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jgm.2022014
external_id:
arxiv:
- '2006.14172'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-06-13T09:11:38Z
date_updated: 2022-06-13T09:11:38Z
description: |-
In backward error analysis, an approximate solution to an equa-
tion is compared to the exact solution to a nearby ‘modified’ equation. In
numerical ordinary differential equations, the two agree up to any power of
the step size. If the differential equation has a geometric property then the
modified equation may share it. In this way, known properties of differential
equations can be applied to the approximation. But for partial differential
equations, the known modified equations are of higher order, limiting appli-
cability of the theory. Therefore, we study symmetric solutions of discretized
partial differential equations that arise from a discrete variational principle.
These symmetric solutions obey infinite-dimensional functional equations. We
show that these equations admit second-order modified equations which are
Hamiltonian and also possess first-order Lagrangians in modified coordinates.
The modified equation and its associated structures are computed explicitly
for the case of rotating travelling waves in the nonlinear wave equation.
file_id: '31859'
file_name: 2_BlendedBEASymmPDE.pdf
file_size: 1507248
relation: main_file
title: Backward error analysis for variational discretisations of PDEs
file_date_updated: 2022-06-13T09:11:38Z
has_accepted_license: '1'
intvolume: ' 14'
issue: '3'
language:
- iso: eng
oa: '1'
page: 447 - 471
publication: Journal of Geometric Mechanics
publication_status: published
publisher: AIMS
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/multisymplectic
status: public
title: Backward error analysis for variational discretisations of partial differential
equations
type: journal_article
user_id: '85279'
volume: 14
year: '2022'
...
---
_id: '23382'
abstract:
- lang: eng
text: Hamiltonian systems are differential equations which describe systems in classical
mechanics, plasma physics, and sampling problems. They exhibit many structural
properties, such as a lack of attractors and the presence of conservation laws.
To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation
of prior knowledge about Hamiltonian structure greatly improves predictions. This
is typically done by learning the system's Hamiltonian and then integrating the
Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian
data needs to be approximated based on the trajectory observations. Moreover,
the numerical integrator introduces an additional discretisation error. In this
paper, we show that an inverse modified Hamiltonian structure adapted to the geometric
integrator can be learned directly from observations. A separate approximation
step for the Hamiltonian data avoided. The inverse modified data compensates for
the discretisation error such that the discretisation error is eliminated. The
technique is developed for Gaussian Processes.
article_type: original
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science. 2022;32(1). doi:10.1063/5.0065913'
apa: 'Offen, C., & Ober-Blöbaum, S. (2022). Symplectic integration of learned
Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science,
32(1). https://doi.org/10.1063/5.0065913'
bibtex: '@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned
Hamiltonian systems}, volume={32(1)}, DOI={10.1063/5.0065913},
journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP},
author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }'
chicago: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned
Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science
32(1) (2022). https://doi.org/10.1063/5.0065913.'
ieee: 'C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian
systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.
32(1), 2022, doi: 10.1063/5.0065913.'
mla: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned
Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science,
vol. 32(1), AIP, 2022, doi:10.1063/5.0065913.'
short: 'C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear
Science 32(1) (2022).'
date_created: 2021-08-11T08:24:02Z
date_updated: 2023-08-10T08:48:14Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0065913
external_id:
arxiv:
- '2108.02492'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2021-12-13T14:56:15Z
date_updated: 2021-12-13T14:56:15Z
file_id: '28734'
file_name: SymplecticShadowIntegration_AIP.pdf
file_size: 2285059
relation: main_file
file_date_updated: 2021-12-13T14:56:15Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://aip.scitation.org/doi/abs/10.1063/5.0065913
oa: '1'
publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science'
publication_status: published
publisher: AIP
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/symplectic-shadow-integration
status: public
title: Symplectic integration of learned Hamiltonian systems
type: journal_article
user_id: '85279'
volume: 32(1)
year: '2022'
...
---
_id: '40613'
author:
- first_name: Jennifer
full_name: Dröse, Jennifer
id: '85820'
last_name: Dröse
citation:
ama: 'Dröse J. Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von
drei Professionalisierungsgruppen. In: Beiträge Zum Mathematikunterricht.
; 2022.'
apa: Dröse, J. (2022). Verstehensgrundlagen diagnostizieren - Diagnostisches Denken
von drei Professionalisierungsgruppen. Beiträge Zum Mathematikunterricht.
bibtex: '@inproceedings{Dröse_2022, title={Verstehensgrundlagen diagnostizieren
- Diagnostisches Denken von drei Professionalisierungsgruppen}, booktitle={Beiträge
zum Mathematikunterricht}, author={Dröse, Jennifer}, year={2022} }'
chicago: Dröse, Jennifer. “Verstehensgrundlagen Diagnostizieren - Diagnostisches
Denken von Drei Professionalisierungsgruppen.” In Beiträge Zum Mathematikunterricht,
2022.
ieee: J. Dröse, “Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von
drei Professionalisierungsgruppen,” 2022.
mla: Dröse, Jennifer. “Verstehensgrundlagen Diagnostizieren - Diagnostisches Denken
von Drei Professionalisierungsgruppen.” Beiträge Zum Mathematikunterricht,
2022.
short: 'J. Dröse, in: Beiträge Zum Mathematikunterricht, 2022.'
date_created: 2023-01-27T19:00:01Z
date_updated: 2023-08-15T06:04:03Z
department:
- _id: '98'
language:
- iso: eng
publication: Beiträge zum Mathematikunterricht
status: public
title: Verstehensgrundlagen diagnostizieren - Diagnostisches Denken von drei Professionalisierungsgruppen
type: conference
user_id: '85820'
year: '2022'
...
---
_id: '47520'
author:
- first_name: Lara Marie
full_name: Graf, Lara Marie
id: '89837'
last_name: Graf
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
- first_name: Marcus
full_name: Nührenbörger, Marcus
last_name: Nührenbörger
- first_name: Karina
full_name: Höveler, Karina
last_name: Höveler
citation:
ama: 'Graf LM, Häsel-Weide U, Nührenbörger M, Höveler K. Lernwege von fachfremd
unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen. In: IDMI-Primar
Goethe-Universität Frankfurt, ed. Beiträge Zum Mathematikunterricht 2022 -
56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik. ; 2022:773-776.'
apa: Graf, L. M., Häsel-Weide, U., Nührenbörger, M., & Höveler, K. (2022). Lernwege
von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen.
In IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht
2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp.
773–776).
bibtex: '@inproceedings{Graf_Häsel-Weide_Nührenbörger_Höveler_2022, title={Lernwege
von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen},
booktitle={Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik}, author={Graf, Lara Marie and Häsel-Weide, Uta and
Nührenbörger, Marcus and Höveler, Karina}, editor={IDMI-Primar Goethe-Universität
Frankfurt}, year={2022}, pages={773–776} }'
chicago: Graf, Lara Marie, Uta Häsel-Weide, Marcus Nührenbörger, and Karina Höveler.
“Lernwege von Fachfremd Unterrichtenden Lehrkräften Zur Ablösung Vom Zählenden
Rechnen.” In Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung Der
Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität
Frankfurt, 773–76, 2022.
ieee: L. M. Graf, U. Häsel-Weide, M. Nührenbörger, and K. Höveler, “Lernwege von
fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden Rechnen,” in
Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik, Frankfurt am Main, 2022, pp. 773–776.
mla: Graf, Lara Marie, et al. “Lernwege von Fachfremd Unterrichtenden Lehrkräften
Zur Ablösung Vom Zählenden Rechnen.” Beiträge Zum Mathematikunterricht 2022
- 56. Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, edited by
IDMI-Primar Goethe-Universität Frankfurt, 2022, pp. 773–76.
short: 'L.M. Graf, U. Häsel-Weide, M. Nührenbörger, K. Höveler, in: IDMI-Primar
Goethe-Universität Frankfurt (Ed.), Beiträge Zum Mathematikunterricht 2022 - 56.
Jahrestagung Der Gesellschaft Für Didaktik Der Mathematik, 2022, pp. 773–776.'
conference:
end_date: 02.09.2022
location: Frankfurt am Main
name: 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik
start_date: 29.08.2022
corporate_editor:
- IDMI-Primar Goethe-Universität Frankfurt
date_created: 2023-09-27T10:01:52Z
date_updated: 2023-09-27T10:02:12Z
department:
- _id: '543'
language:
- iso: eng
page: 773-776
publication: Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik
status: public
title: Lernwege von fachfremd unterrichtenden Lehrkräften zur Ablösung vom zählenden
Rechnen
type: conference
user_id: '44184'
year: '2022'
...
---
_id: '47519'
author:
- first_name: Imke
full_name: Schwerin, Imke
id: '48912'
last_name: Schwerin
citation:
ama: 'Schwerin I. Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und
Verständnis. In: IDMI-Primar Goethe-Universität Frankfurt, ed. Beiträge Zum
Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik Der
Mathematik. ; 2022:401-404.'
apa: Schwerin, I. (2022). Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen
und Verständnis. In IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge
zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft für Didaktik
der Mathematik (pp. 401–404).
bibtex: '@inproceedings{Schwerin_2022, title={Verdoppeln und Halbieren im 2. Schuljahr
- Vorgehensweisen und Verständnis}, booktitle={Beiträge zum Mathematikunterricht
2022 - 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik}, author={Schwerin,
Imke}, editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2022}, pages={401–404}
}'
chicago: Schwerin, Imke. “Verdoppeln Und Halbieren Im 2. Schuljahr - Vorgehensweisen
Und Verständnis.” In Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung
Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität
Frankfurt, 401–4, 2022.
ieee: I. Schwerin, “Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und
Verständnis,” in Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung
der Gesellschaft für Didaktik der Mathematik, Frankfurt am Main, 2022, pp.
401–404.
mla: Schwerin, Imke. “Verdoppeln Und Halbieren Im 2. Schuljahr - Vorgehensweisen
Und Verständnis.” Beiträge Zum Mathematikunterricht 2022 - 56. Jahrestagung
Der Gesellschaft Für Didaktik Der Mathematik, edited by IDMI-Primar Goethe-Universität
Frankfurt, 2022, pp. 401–04.
short: 'I. Schwerin, in: IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge
Zum Mathematikunterricht 2022 - 56. Jahrestagung Der Gesellschaft Für Didaktik
Der Mathematik, 2022, pp. 401–404.'
conference:
end_date: 02.09.2022
location: Frankfurt am Main
name: 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik
start_date: 29.08.2022
corporate_editor:
- IDMI-Primar Goethe-Universität Frankfurt
date_created: 2023-09-27T09:53:36Z
date_updated: 2023-09-27T09:54:00Z
department:
- _id: '543'
language:
- iso: eng
page: 401-404
publication: Beiträge zum Mathematikunterricht 2022 - 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik
status: public
title: Verdoppeln und Halbieren im 2. Schuljahr - Vorgehensweisen und Verständnis
type: conference
user_id: '44184'
year: '2022'
...