---
_id: '55193'
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
citation:
ama: Hoffmann M, Hilgert J, Weich T. Ebene euklidische Geometrie. Algebraisierung,
Axiomatisierung und Schnittstellen zur Schulmathematik. Springer Berlin Heidelberg;
2024. doi:10.1007/978-3-662-67357-7
apa: Hoffmann, M., Hilgert, J., & Weich, T. (2024). Ebene euklidische Geometrie.
Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik. Springer
Berlin Heidelberg. https://doi.org/10.1007/978-3-662-67357-7
bibtex: '@book{Hoffmann_Hilgert_Weich_2024, place={Berlin, Heidelberg}, title={Ebene
euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur
Schulmathematik}, DOI={10.1007/978-3-662-67357-7},
publisher={Springer Berlin Heidelberg}, author={Hoffmann, Max and Hilgert, Joachim
and Weich, Tobias}, year={2024} }'
chicago: 'Hoffmann, Max, Joachim Hilgert, and Tobias Weich. Ebene euklidische
Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen zur Schulmathematik.
Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. https://doi.org/10.1007/978-3-662-67357-7.'
ieee: 'M. Hoffmann, J. Hilgert, and T. Weich, Ebene euklidische Geometrie. Algebraisierung,
Axiomatisierung und Schnittstellen zur Schulmathematik. Berlin, Heidelberg:
Springer Berlin Heidelberg, 2024.'
mla: Hoffmann, Max, et al. Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung
und Schnittstellen zur Schulmathematik. Springer Berlin Heidelberg, 2024,
doi:10.1007/978-3-662-67357-7.
short: M. Hoffmann, J. Hilgert, T. Weich, Ebene euklidische Geometrie. Algebraisierung,
Axiomatisierung und Schnittstellen zur Schulmathematik, Springer Berlin Heidelberg,
Berlin, Heidelberg, 2024.
date_created: 2024-07-12T08:36:42Z
date_updated: 2024-08-08T08:05:30Z
department:
- _id: '97'
- _id: '643'
- _id: '548'
doi: 10.1007/978-3-662-67357-7
language:
- iso: ger
place: Berlin, Heidelberg
publication_identifier:
isbn:
- '9783662673560'
- '9783662673577'
publication_status: published
publisher: Springer Berlin Heidelberg
status: public
title: Ebene euklidische Geometrie. Algebraisierung, Axiomatisierung und Schnittstellen
zur Schulmathematik
type: book
user_id: '220'
year: '2024'
...
---
_id: '46469'
abstract:
- lang: eng
text: 'We show how to learn discrete field theories from observational data of fields
on a space-time lattice. For this, we train a neural network model of a discrete
Lagrangian density such that the discrete Euler--Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine
learning architecture. Lagrangian densities are not uniquely defined by the solutions
of a field theory. We introduce a technique to derive regularisers for the training
process which optimise numerical regularity of the discrete field theory. Minimisation
of the regularisers guarantees that close to the training data the discrete field
theory behaves robust and efficient when used in numerical simulations. Further,
we show how to identify structurally simple solutions of the underlying continuous
field theory such as travelling waves. This is possible even when travelling waves
are not present in the training data. This is compared to data-driven model order
reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training
data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger
equation. '
article_number: '013104'
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. Learning of discrete models of variational PDEs from
data. Chaos. 2024;34(1). doi:10.1063/5.0172287
apa: Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational
PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287
bibtex: '@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of
variational PDEs from data}, volume={34}, DOI={10.1063/5.0172287},
number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen,
Christian and Ober-Blöbaum, Sina}, year={2024} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of
Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287.
ieee: 'C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational
PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.'
mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational
PDEs from Data.” Chaos, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:10.1063/5.0172287.
short: C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).
date_created: 2023-08-10T08:24:48Z
date_updated: 2024-08-12T13:45:43Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0172287
external_id:
arxiv:
- '2308.05082 '
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-01-09T10:48:38Z
date_updated: 2024-01-09T10:48:38Z
file_id: '50376'
file_name: Accepted manuscript with AIP banner CHA23-AR-01370.pdf
file_size: 13222105
relation: main_file
title: Accepted Manuscript Chaos
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-01-09T11:19:49Z
date_updated: 2024-01-09T11:19:49Z
description: |-
We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train
a neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian
densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for
the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers
guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical
simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory
such as travelling waves. This is possible even when travelling waves are not present in the training data. This is
compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on
examples based on the wave equation and the Schrödinger equation.
file_id: '50390'
file_name: LDensityPDE_AIP.pdf
file_size: 12960884
relation: main_file
title: Learning of discrete models of variational PDEs from data
file_date_updated: 2024-01-09T11:19:49Z
has_accepted_license: '1'
intvolume: ' 34'
issue: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/DLNN_pde
status: public
title: Learning of discrete models of variational PDEs from data
type: journal_article
user_id: '85279'
volume: 34
year: '2024'
...
---
_id: '55159'
abstract:
- lang: eng
text: "We introduce a method based on Gaussian process regression to identify discrete
variational principles from observed solutions of a field theory. The method is
based on the data-based identification of a discrete Lagrangian density. It is
a geometric machine learning technique in the sense that the variational structure
of the true field theory is reflected in the data-driven model by design. We provide
a rigorous convergence statement of the method. The proof circumvents challenges
posed by the ambiguity of discrete Lagrangian densities in the inverse problem
of variational calculus.\r\nMoreover, our method can be used to quantify model
uncertainty in the equations of motions and any linear observable of the discrete
field theory. This is illustrated on the example of the discrete wave equation
and Schrödinger equation.\r\nThe article constitutes an extension of our previous
article arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians
for variational dynamics from an ode setting to the setting of discrete pdes."
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: Offen C. Machine learning of discrete field theories with guaranteed convergence
and uncertainty quantification.
apa: Offen, C. (n.d.). Machine learning of discrete field theories with guaranteed
convergence and uncertainty quantification.
bibtex: '@article{Offen, title={Machine learning of discrete field theories with
guaranteed convergence and uncertainty quantification}, author={Offen, Christian}
}'
chicago: Offen, Christian. “Machine Learning of Discrete Field Theories with Guaranteed
Convergence and Uncertainty Quantification,” n.d.
ieee: C. Offen, “Machine learning of discrete field theories with guaranteed convergence
and uncertainty quantification.” .
mla: Offen, Christian. Machine Learning of Discrete Field Theories with Guaranteed
Convergence and Uncertainty Quantification.
short: C. Offen, (n.d.).
date_created: 2024-07-10T13:43:50Z
date_updated: 2024-08-12T13:43:32Z
ddc:
- '510'
department:
- _id: '636'
external_id:
arxiv:
- '2407.07642'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-07-10T13:39:32Z
date_updated: 2024-07-10T13:39:32Z
description: |-
We introduce a method based on Gaussian process regression to identify discrete
variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design.
We provide a rigorous convergence statement of the method.
The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.
Moreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory.
This is illustrated on the example of the discrete wave equation and Schrödinger equation.
The article constitutes an extension of our previous article for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.
file_id: '55160'
file_name: L_Collocation.pdf
file_size: 4569314
relation: main_file
title: Machine learning of discrete field theories with guaranteed convergence and
uncertainty quantification
file_date_updated: 2024-07-10T13:39:32Z
has_accepted_license: '1'
keyword:
- System identification
- inverse problem of variational calculus
- Gaussian process
- Lagrangian learning
- physics informed machine learning
- geometry aware learning
language:
- iso: eng
oa: '1'
page: '28'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication_status: submitted
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/Lagrangian_GP_PDE
status: public
title: Machine learning of discrete field theories with guaranteed convergence and
uncertainty quantification
type: preprint
user_id: '85279'
year: '2024'
...
---
_id: '55667'
abstract:
- lang: eng
text: This study investigates how 11- to 12-year-old students construct
data-based decision trees using data cards for classification purposes. We examine
the students' heuristics and reasoning during this process. The research is based
on an eight-week teaching unit during which students labeled data, built decision
trees, and assessed them using test data. They learned to manually construct decision
trees to classify food items as recommendable or not. They utilized data cards
with a heuristic that is a simplified form of a machine learning algorithm. We
report on evidence that this topic is teachable to middle school students, along
with insights for refining our teaching approach and broader implications for
teaching machine learning at the school level.
article_number: '3'
author:
- first_name: Franz Yannik
full_name: Fleischer, Franz Yannik
id: '42660'
last_name: Fleischer
orcid: https://orcid.org/0000-0003-0318-0329
- 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: Fleischer FY, Podworny S, Biehler R. Teaching and Learning to Construct Data-Based
Decision Trees Using Data Cards as the First Introduction to Machine Learning
in Middle School. Statistics Education Research Journal. 2024;23(1). doi:10.52041/serj.v23i1.450
apa: Fleischer, F. Y., Podworny, S., & Biehler, R. (2024). Teaching and Learning
to Construct Data-Based Decision Trees Using Data Cards as the First Introduction
to Machine Learning in Middle School. Statistics Education Research Journal,
23(1), Article 3. https://doi.org/10.52041/serj.v23i1.450
bibtex: '@article{Fleischer_Podworny_Biehler_2024, title={Teaching and Learning
to Construct Data-Based Decision Trees Using Data Cards as the First Introduction
to Machine Learning in Middle School}, volume={23}, DOI={10.52041/serj.v23i1.450},
number={13}, journal={Statistics Education Research Journal}, publisher={International
Association for Statistical Education}, author={Fleischer, Franz Yannik and Podworny,
Susanne and Biehler, Rolf}, year={2024} }'
chicago: Fleischer, Franz Yannik, Susanne Podworny, and Rolf Biehler. “Teaching
and Learning to Construct Data-Based Decision Trees Using Data Cards as the First
Introduction to Machine Learning in Middle School.” Statistics Education Research
Journal 23, no. 1 (2024). https://doi.org/10.52041/serj.v23i1.450.
ieee: 'F. Y. Fleischer, S. Podworny, and R. Biehler, “Teaching and Learning to Construct
Data-Based Decision Trees Using Data Cards as the First Introduction to Machine
Learning in Middle School,” Statistics Education Research Journal, vol.
23, no. 1, Art. no. 3, 2024, doi: 10.52041/serj.v23i1.450.'
mla: Fleischer, Franz Yannik, et al. “Teaching and Learning to Construct Data-Based
Decision Trees Using Data Cards as the First Introduction to Machine Learning
in Middle School.” Statistics Education Research Journal, vol. 23, no.
1, 3, International Association for Statistical Education, 2024, doi:10.52041/serj.v23i1.450.
short: F.Y. Fleischer, S. Podworny, R. Biehler, Statistics Education Research Journal
23 (2024).
date_created: 2024-08-21T09:59:33Z
date_updated: 2024-08-21T10:02:38Z
department:
- _id: '363'
doi: 10.52041/serj.v23i1.450
intvolume: ' 23'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.52041/serj.v23i1.450
oa: '1'
publication: Statistics Education Research Journal
publication_identifier:
issn:
- 1570-1824
publication_status: published
publisher: International Association for Statistical Education
status: public
title: Teaching and Learning to Construct Data-Based Decision Trees Using Data Cards
as the First Introduction to Machine Learning in Middle School
type: journal_article
user_id: '37888'
volume: 23
year: '2024'
...
---
_id: '55756'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Daniel
full_name: Frischemeier, Daniel
last_name: Frischemeier
citation:
ama: 'Biehler R, Frischemeier D. Eine inklusive Lehr-Lernumgebung für die Leitidee
„Daten und Zufall“ in der Primarstufe. In: Inklusives Lehren und Lernen von
Mathematik. Springer Fachmedien Wiesbaden; 2024. doi:10.1007/978-3-658-43964-4_13'
apa: Biehler, R., & Frischemeier, D. (2024). Eine inklusive Lehr-Lernumgebung
für die Leitidee „Daten und Zufall“ in der Primarstufe. In Inklusives Lehren
und Lernen von Mathematik. Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-43964-4_13
bibtex: '@inbook{Biehler_Frischemeier_2024, place={Wiesbaden}, title={Eine inklusive
Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der Primarstufe}, DOI={10.1007/978-3-658-43964-4_13},
booktitle={Inklusives Lehren und Lernen von Mathematik}, publisher={Springer Fachmedien
Wiesbaden}, author={Biehler, Rolf and Frischemeier, Daniel}, year={2024} }'
chicago: 'Biehler, Rolf, and Daniel Frischemeier. “Eine inklusive Lehr-Lernumgebung
für die Leitidee „Daten und Zufall“ in der Primarstufe.” In Inklusives Lehren
und Lernen von Mathematik. Wiesbaden: Springer Fachmedien Wiesbaden, 2024.
https://doi.org/10.1007/978-3-658-43964-4_13.'
ieee: 'R. Biehler and D. Frischemeier, “Eine inklusive Lehr-Lernumgebung für die
Leitidee „Daten und Zufall“ in der Primarstufe,” in Inklusives Lehren und Lernen
von Mathematik, Wiesbaden: Springer Fachmedien Wiesbaden, 2024.'
mla: Biehler, Rolf, and Daniel Frischemeier. “Eine inklusive Lehr-Lernumgebung für
die Leitidee „Daten und Zufall“ in der Primarstufe.” Inklusives Lehren und
Lernen von Mathematik, Springer Fachmedien Wiesbaden, 2024, doi:10.1007/978-3-658-43964-4_13.
short: 'R. Biehler, D. Frischemeier, in: Inklusives Lehren und Lernen von Mathematik,
Springer Fachmedien Wiesbaden, Wiesbaden, 2024.'
date_created: 2024-08-26T09:18:57Z
date_updated: 2024-08-26T09:33:50Z
department:
- _id: '363'
doi: 10.1007/978-3-658-43964-4_13
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/978-3-658-43964-4_13
oa: '1'
place: Wiesbaden
publication: Inklusives Lehren und Lernen von Mathematik
publication_identifier:
isbn:
- '9783658439637'
- '9783658439644'
publication_status: published
publisher: Springer Fachmedien Wiesbaden
status: public
title: Eine inklusive Lehr-Lernumgebung für die Leitidee „Daten und Zufall“ in der
Primarstufe
type: book_chapter
user_id: '37888'
year: '2024'
...
---
_id: '55758'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Daniel
full_name: Frischemeier, Daniel
last_name: Frischemeier
citation:
ama: 'Biehler R, Frischemeier D. Daten-Spürnasen Auf Spurensuche: Datenanalyse
in Der Grundschule Mit Digitalen Werkzeugen. Klett Kallmeyer; 2024.'
apa: 'Biehler, R., & Frischemeier, D. (2024). Daten-Spürnasen auf Spurensuche:
Datenanalyse in der Grundschule mit digitalen Werkzeugen. Klett Kallmeyer.'
bibtex: '@book{Biehler_Frischemeier_2024, title={Daten-Spürnasen auf Spurensuche:
Datenanalyse in der Grundschule mit digitalen Werkzeugen}, publisher={Klett Kallmeyer},
author={Biehler, Rolf and Frischemeier, Daniel}, year={2024} }'
chicago: 'Biehler, Rolf, and Daniel Frischemeier. Daten-Spürnasen Auf Spurensuche:
Datenanalyse in Der Grundschule Mit Digitalen Werkzeugen. Klett Kallmeyer,
2024.'
ieee: 'R. Biehler and D. Frischemeier, Daten-Spürnasen auf Spurensuche: Datenanalyse
in der Grundschule mit digitalen Werkzeugen. Klett Kallmeyer, 2024.'
mla: 'Biehler, Rolf, and Daniel Frischemeier. Daten-Spürnasen Auf Spurensuche:
Datenanalyse in Der Grundschule Mit Digitalen Werkzeugen. Klett Kallmeyer,
2024.'
short: 'R. Biehler, D. Frischemeier, Daten-Spürnasen Auf Spurensuche: Datenanalyse
in Der Grundschule Mit Digitalen Werkzeugen, Klett Kallmeyer, 2024.'
date_created: 2024-08-26T09:38:05Z
date_updated: 2024-08-26T09:38:17Z
department:
- _id: '363'
language:
- iso: eng
publisher: Klett Kallmeyer
status: public
title: 'Daten-Spürnasen auf Spurensuche: Datenanalyse in der Grundschule mit digitalen
Werkzeugen'
type: book
user_id: '37888'
year: '2024'
...
---
_id: '45972'
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Kovács B. Numerical surgery for mean curvature flow of surfaces. SIAM Journal
on Scientific Computing. 2024;46(2):A645--A669. doi:10.1137/22M1531919
apa: Kovács, B. (2024). Numerical surgery for mean curvature flow of surfaces. SIAM
Journal on Scientific Computing, 46(2), A645--A669. https://doi.org/10.1137/22M1531919
bibtex: '@article{Kovács_2024, title={Numerical surgery for mean curvature flow
of surfaces}, volume={46}, DOI={10.1137/22M1531919},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Kovács, Balázs},
year={2024}, pages={A645--A669} }'
chicago: 'Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.”
SIAM Journal on Scientific Computing 46, no. 2 (2024): A645--A669. https://doi.org/10.1137/22M1531919.'
ieee: 'B. Kovács, “Numerical surgery for mean curvature flow of surfaces,” SIAM
Journal on Scientific Computing, vol. 46, no. 2, pp. A645--A669, 2024, doi:
10.1137/22M1531919.'
mla: Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.” SIAM
Journal on Scientific Computing, vol. 46, no. 2, 2024, pp. A645--A669, doi:10.1137/22M1531919.
short: B. Kovács, SIAM Journal on Scientific Computing 46 (2024) A645--A669.
date_created: 2023-07-10T12:32:34Z
date_updated: 2024-08-27T07:42:56Z
department:
- _id: '841'
doi: 10.1137/22M1531919
extern: '1'
intvolume: ' 46'
issue: '2'
language:
- iso: eng
page: A645--A669
publication: SIAM Journal on Scientific Computing
status: public
title: Numerical surgery for mean curvature flow of surfaces
type: journal_article
user_id: '100441'
volume: 46
year: '2024'
...
---
_id: '53300'
article_number: '128125'
author:
- first_name: Dominik
full_name: Brennecken, Dominik
id: '55911'
last_name: Brennecken
citation:
ama: Brennecken D. Hankel transform, K-Bessel functions and zeta distributions in
the Dunkl setting. Journal of Mathematical Analysis and Applications. 2024;535(2).
doi:10.1016/j.jmaa.2024.128125
apa: Brennecken, D. (2024). Hankel transform, K-Bessel functions and zeta distributions
in the Dunkl setting. Journal of Mathematical Analysis and Applications,
535(2), Article 128125. https://doi.org/10.1016/j.jmaa.2024.128125
bibtex: '@article{Brennecken_2024, title={Hankel transform, K-Bessel functions and
zeta distributions in the Dunkl setting}, volume={535}, DOI={10.1016/j.jmaa.2024.128125},
number={2128125}, journal={Journal of Mathematical Analysis and Applications},
publisher={Elsevier BV}, author={Brennecken, Dominik}, year={2024} }'
chicago: Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions
in the Dunkl Setting.” Journal of Mathematical Analysis and Applications
535, no. 2 (2024). https://doi.org/10.1016/j.jmaa.2024.128125.
ieee: 'D. Brennecken, “Hankel transform, K-Bessel functions and zeta distributions
in the Dunkl setting,” Journal of Mathematical Analysis and Applications,
vol. 535, no. 2, Art. no. 128125, 2024, doi: 10.1016/j.jmaa.2024.128125.'
mla: Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions
in the Dunkl Setting.” Journal of Mathematical Analysis and Applications,
vol. 535, no. 2, 128125, Elsevier BV, 2024, doi:10.1016/j.jmaa.2024.128125.
short: D. Brennecken, Journal of Mathematical Analysis and Applications 535 (2024).
date_created: 2024-04-05T13:55:33Z
date_updated: 2024-09-03T14:40:46Z
department:
- _id: '555'
doi: 10.1016/j.jmaa.2024.128125
intvolume: ' 535'
issue: '2'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
publication: Journal of Mathematical Analysis and Applications
publication_identifier:
issn:
- 0022-247X
publication_status: published
publisher: Elsevier BV
status: public
title: Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting
type: journal_article
user_id: '55911'
volume: 535
year: '2024'
...
---
_id: '56016'
abstract:
- lang: eng
text: AbstractSpecial tasks for pre-service teachers
(PSTs) in university mathematics courses (“interface tasks”) are a common innovation
in recent years to overcome the second discontinuity. By this, we mean tasks that
are situated by typical everyday challenges of mathematics teaching and in which
PSTs must use their mathematical knowledge and skills in a professionally relevant
way. In this paper, we analyze answers that PSTs have created to an interface
task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical
perspective and then give a suitable elementarized answer. We situate these two
steps theoretically and reconstruct the mathematical reasoning in PSTs' answers.
Through qualitative content analysis, we examined how PSTs justify figures' symmetries
from a university mathematics perspective and when responding to the fictitious
student. The scenario of a student questioning the existence of 100° rotationally
symmetrical figures elicited rich and varied responses, proving suitable for an
interface task. We compared PSTs' reasoning related to mathematical clarification
with the reasoning related to elementarization. In many cases, this revealed a
productive use of course content. An interesting result is that there is no uniform
picture as to whether the arguments are more detailed in the mathematical clarification
or in the elementarization.
article_type: original
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: Hoffmann M, Biehler R. Using academic mathematical knowledge when working on
interface tasks–analyses of pre-service teachers’ arguments about rotationally
symmetric figures. ZDM – Mathematics Education. Published online 2024.
doi:10.1007/s11858-024-01633-4
apa: Hoffmann, M., & Biehler, R. (2024). Using academic mathematical knowledge
when working on interface tasks–analyses of pre-service teachers’ arguments about
rotationally symmetric figures. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-024-01633-4
bibtex: '@article{Hoffmann_Biehler_2024, title={Using academic mathematical knowledge
when working on interface tasks–analyses of pre-service teachers’ arguments about
rotationally symmetric figures}, DOI={10.1007/s11858-024-01633-4},
journal={ZDM – Mathematics Education}, publisher={Springer Science and Business
Media LLC}, author={Hoffmann, Max and Biehler, Rolf}, year={2024} }'
chicago: Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge
When Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about
Rotationally Symmetric Figures.” ZDM – Mathematics Education, 2024. https://doi.org/10.1007/s11858-024-01633-4.
ieee: 'M. Hoffmann and R. Biehler, “Using academic mathematical knowledge when working
on interface tasks–analyses of pre-service teachers’ arguments about rotationally
symmetric figures,” ZDM – Mathematics Education, 2024, doi: 10.1007/s11858-024-01633-4.'
mla: Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge When
Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about Rotationally
Symmetric Figures.” ZDM – Mathematics Education, Springer Science and Business
Media LLC, 2024, doi:10.1007/s11858-024-01633-4.
short: M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2024).
date_created: 2024-09-04T09:32:26Z
date_updated: 2024-09-04T09:33:45Z
department:
- _id: '97'
- _id: '643'
doi: 10.1007/s11858-024-01633-4
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s11858-024-01633-4.pdf
oa: '1'
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: Using academic mathematical knowledge when working on interface tasks–analyses
of pre-service teachers’ arguments about rotationally symmetric figures
type: journal_article
user_id: '32202'
year: '2024'
...
---
_id: '56001'
author:
- first_name: Dominik
full_name: Brennecken, Dominik
id: '55911'
last_name: Brennecken
- first_name: Margit
full_name: Rösler, Margit
id: '37390'
last_name: Rösler
citation:
ama: 'Brennecken D, Rösler M. The Laplace transform in Dunkl theory. In: Chatzakou
M, Ruzhansky M, Stoeva D, eds. Women in Analysis and PDE. Vol 5. Trends
in Mathematics: Research Perspectives Ghent Analysis and PDE Cente. Birkhäuser
Cham; 2024:425.'
apa: Brennecken, D., & Rösler, M. (2024). The Laplace transform in Dunkl theory.
In M. Chatzakou, M. Ruzhansky, & D. Stoeva (Eds.), Women in Analysis and
PDE (Vol. 5, p. 425). Birkhäuser Cham.
bibtex: '@inbook{Brennecken_Rösler_2024, series={Trends in Mathematics: Research
Perspectives Ghent Analysis and PDE Cente}, title={The Laplace transform in Dunkl
theory}, volume={5}, booktitle={Women in Analysis and PDE}, publisher={Birkhäuser
Cham}, author={Brennecken, Dominik and Rösler, Margit}, editor={Chatzakou, Marianna
and Ruzhansky, Michael and Stoeva, Diana}, year={2024}, pages={425}, collection={Trends
in Mathematics: Research Perspectives Ghent Analysis and PDE Cente} }'
chicago: 'Brennecken, Dominik, and Margit Rösler. “The Laplace Transform in Dunkl
Theory.” In Women in Analysis and PDE, edited by Marianna Chatzakou, Michael
Ruzhansky, and Diana Stoeva, 5:425. Trends in Mathematics: Research Perspectives
Ghent Analysis and PDE Cente. Birkhäuser Cham, 2024.'
ieee: D. Brennecken and M. Rösler, “The Laplace transform in Dunkl theory,” in Women
in Analysis and PDE, vol. 5, M. Chatzakou, M. Ruzhansky, and D. Stoeva, Eds.
Birkhäuser Cham, 2024, p. 425.
mla: Brennecken, Dominik, and Margit Rösler. “The Laplace Transform in Dunkl Theory.”
Women in Analysis and PDE, edited by Marianna Chatzakou et al., vol. 5,
Birkhäuser Cham, 2024, p. 425.
short: 'D. Brennecken, M. Rösler, in: M. Chatzakou, M. Ruzhansky, D. Stoeva (Eds.),
Women in Analysis and PDE, Birkhäuser Cham, 2024, p. 425.'
date_created: 2024-09-03T15:31:27Z
date_updated: 2024-09-05T06:58:54Z
department:
- _id: '555'
editor:
- first_name: Marianna
full_name: Chatzakou, Marianna
last_name: Chatzakou
- first_name: Michael
full_name: Ruzhansky, Michael
last_name: Ruzhansky
- first_name: Diana
full_name: Stoeva, Diana
last_name: Stoeva
intvolume: ' 5'
language:
- iso: eng
page: '425'
publication: Women in Analysis and PDE
publication_identifier:
isbn:
- 978-3-031-57004-9
publication_status: published
publisher: Birkhäuser Cham
series_title: 'Trends in Mathematics: Research Perspectives Ghent Analysis and PDE
Cente'
status: public
title: The Laplace transform in Dunkl theory
type: book_chapter
user_id: '82981'
volume: 5
year: '2024'
...
---
_id: '56021'
author:
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
- first_name: M.
full_name: Nührenbörger, M.
last_name: Nührenbörger
citation:
ama: 'Häsel-Weide U, Nührenbörger M. Produktives Fördern im inklusiven Mathematikunterricht.
In: Barzel B, Büchter A, Rütten C, Schacht F, Weskamp-Kleine S, eds. Inklusives
Lehren und Lernen von Mathematik: Konzepte und Beispiele mit Fokus auf Grund-
und Förderschule. Springer Fachmedien Wiesbaden; 2024:97-113. doi:https://doi.org/10.1007/978-3-658-43964-4_7 '
apa: 'Häsel-Weide, U., & Nührenbörger, M. (2024). Produktives Fördern im inklusiven
Mathematikunterricht. In B. Barzel, A. Büchter, C. Rütten, F. Schacht, & S.
Weskamp-Kleine (Eds.), Inklusives Lehren und Lernen von Mathematik: Konzepte
und Beispiele mit Fokus auf Grund- und Förderschule (pp. 97–113). Springer
Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-43964-4_7
'
bibtex: '@inbook{Häsel-Weide_Nührenbörger_2024, title={Produktives Fördern im inklusiven
Mathematikunterricht}, DOI={https://doi.org/10.1007/978-3-658-43964-4_7 }, booktitle={Inklusives Lehren
und Lernen von Mathematik: Konzepte und Beispiele mit Fokus auf Grund- und Förderschule},
publisher={Springer Fachmedien Wiesbaden}, author={Häsel-Weide, Uta and Nührenbörger,
M.}, editor={Barzel, B. and Büchter, A. and Rütten, C. and Schacht, F. and Weskamp-Kleine,
S.}, year={2024}, pages={97–113} }'
chicago: 'Häsel-Weide, Uta, and M. Nührenbörger. “Produktives Fördern im inklusiven
Mathematikunterricht.” In Inklusives Lehren und Lernen von Mathematik: Konzepte
und Beispiele mit Fokus auf Grund- und Förderschule, edited by B. Barzel,
A. Büchter, C. Rütten, F. Schacht, and S. Weskamp-Kleine, 97–113. Springer Fachmedien
Wiesbaden, 2024. https://doi.org/10.1007/978-3-658-43964-4_7
.'
ieee: 'U. Häsel-Weide and M. Nührenbörger, “Produktives Fördern im inklusiven Mathematikunterricht,”
in Inklusives Lehren und Lernen von Mathematik: Konzepte und Beispiele mit
Fokus auf Grund- und Förderschule, B. Barzel, A. Büchter, C. Rütten, F. Schacht,
and S. Weskamp-Kleine, Eds. Springer Fachmedien Wiesbaden, 2024, pp. 97–113.'
mla: 'Häsel-Weide, Uta, and M. Nührenbörger. “Produktives Fördern im inklusiven
Mathematikunterricht.” Inklusives Lehren und Lernen von Mathematik: Konzepte
und Beispiele mit Fokus auf Grund- und Förderschule, edited by B. Barzel et
al., Springer Fachmedien Wiesbaden, 2024, pp. 97–113, doi:https://doi.org/10.1007/978-3-658-43964-4_7 .'
short: 'U. Häsel-Weide, M. Nührenbörger, in: B. Barzel, A. Büchter, C. Rütten, F.
Schacht, S. Weskamp-Kleine (Eds.), Inklusives Lehren und Lernen von Mathematik:
Konzepte und Beispiele mit Fokus auf Grund- und Förderschule, Springer Fachmedien
Wiesbaden, 2024, pp. 97–113.'
date_created: 2024-09-05T07:18:03Z
date_updated: 2024-09-05T07:22:02Z
department:
- _id: '543'
doi: 'https://doi.org/10.1007/978-3-658-43964-4_7 '
editor:
- first_name: B.
full_name: Barzel, B.
last_name: Barzel
- first_name: A.
full_name: Büchter, A.
last_name: Büchter
- first_name: C.
full_name: Rütten, C.
last_name: Rütten
- first_name: F.
full_name: Schacht, F.
last_name: Schacht
- first_name: S.
full_name: Weskamp-Kleine, S.
last_name: Weskamp-Kleine
language:
- iso: ger
page: 97-113
publication: 'Inklusives Lehren und Lernen von Mathematik: Konzepte und Beispiele
mit Fokus auf Grund- und Förderschule'
publisher: Springer Fachmedien Wiesbaden
status: public
title: Produktives Fördern im inklusiven Mathematikunterricht
type: book_chapter
user_id: '44184'
year: '2024'
...
---
_id: '56022'
article_number: '18'
author:
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
- first_name: Melina
full_name: Wallner, Melina
id: '45445'
last_name: Wallner
citation:
ama: Häsel-Weide U, Wallner M. Achsensymmetrisch?! Praktiken, soziale und sozio-mathematische
Normen der Begründung der Achsensymmetrie ebener Figuren in der Grundschule. Journal
für Mathematik-Didaktik. 2024;45(2). doi:https://doi.org/10.1007/s13138-024-00241-9
apa: Häsel-Weide, U., & Wallner, M. (2024). Achsensymmetrisch?! Praktiken, soziale
und sozio-mathematische Normen der Begründung der Achsensymmetrie ebener Figuren
in der Grundschule. Journal Für Mathematik-Didaktik, 45(2), Article
18. https://doi.org/10.1007/s13138-024-00241-9
bibtex: '@article{Häsel-Weide_Wallner_2024, title={Achsensymmetrisch?! Praktiken,
soziale und sozio-mathematische Normen der Begründung der Achsensymmetrie ebener
Figuren in der Grundschule}, volume={45}, DOI={https://doi.org/10.1007/s13138-024-00241-9},
number={218}, journal={Journal für Mathematik-Didaktik}, author={Häsel-Weide,
Uta and Wallner, Melina}, year={2024} }'
chicago: Häsel-Weide, Uta, and Melina Wallner. “Achsensymmetrisch?! Praktiken, Soziale
Und Sozio-Mathematische Normen Der Begründung Der Achsensymmetrie Ebener Figuren
in Der Grundschule.” Journal Für Mathematik-Didaktik 45, no. 2 (2024).
https://doi.org/10.1007/s13138-024-00241-9.
ieee: 'U. Häsel-Weide and M. Wallner, “Achsensymmetrisch?! Praktiken, soziale und
sozio-mathematische Normen der Begründung der Achsensymmetrie ebener Figuren in
der Grundschule,” Journal für Mathematik-Didaktik, vol. 45, no. 2, Art.
no. 18, 2024, doi: https://doi.org/10.1007/s13138-024-00241-9.'
mla: Häsel-Weide, Uta, and Melina Wallner. “Achsensymmetrisch?! Praktiken, Soziale
Und Sozio-Mathematische Normen Der Begründung Der Achsensymmetrie Ebener Figuren
in Der Grundschule.” Journal Für Mathematik-Didaktik, vol. 45, no. 2, 18,
2024, doi:https://doi.org/10.1007/s13138-024-00241-9.
short: U. Häsel-Weide, M. Wallner, Journal Für Mathematik-Didaktik 45 (2024).
date_created: 2024-09-05T07:21:55Z
date_updated: 2024-09-05T07:22:06Z
department:
- _id: '543'
doi: https://doi.org/10.1007/s13138-024-00241-9
intvolume: ' 45'
issue: '2'
language:
- iso: eng
publication: Journal für Mathematik-Didaktik
status: public
title: Achsensymmetrisch?! Praktiken, soziale und sozio-mathematische Normen der Begründung
der Achsensymmetrie ebener Figuren in der Grundschule
type: journal_article
user_id: '44184'
volume: 45
year: '2024'
...
---
_id: '56197'
abstract:
- lang: eng
text: AbstractSpecial tasks for pre-service teachers
(PSTs) in university mathematics courses (“interface tasks”) are a common innovation
in recent years to overcome the second discontinuity. By this, we mean tasks that
are situated by typical everyday challenges of mathematics teaching and in which
PSTs must use their mathematical knowledge and skills in a professionally relevant
way. In this paper, we analyze answers that PSTs have created to an interface
task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical
perspective and then give a suitable elementarized answer. We situate these two
steps theoretically and reconstruct the mathematical reasoning in PSTs' answers.
Through qualitative content analysis, we examined how PSTs justify figures' symmetries
from a university mathematics perspective and when responding to the fictitious
student. The scenario of a student questioning the existence of 100° rotationally
symmetrical figures elicited rich and varied responses, proving suitable for an
interface task. We compared PSTs' reasoning related to mathematical clarification
with the reasoning related to elementarization. In many cases, this revealed a
productive use of course content. An interesting result is that there is no uniform
picture as to whether the arguments are more detailed in the mathematical clarification
or in the elementarization.
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: Hoffmann M, Biehler R. Using academic mathematical knowledge when working on
interface tasks–analyses of pre-service teachers’ arguments about rotationally
symmetric figures. ZDM – Mathematics Education. Published online 2024.
doi:10.1007/s11858-024-01633-4
apa: Hoffmann, M., & Biehler, R. (2024). Using academic mathematical knowledge
when working on interface tasks–analyses of pre-service teachers’ arguments about
rotationally symmetric figures. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-024-01633-4
bibtex: '@article{Hoffmann_Biehler_2024, title={Using academic mathematical knowledge
when working on interface tasks–analyses of pre-service teachers’ arguments about
rotationally symmetric figures}, DOI={10.1007/s11858-024-01633-4},
journal={ZDM – Mathematics Education}, publisher={Springer Science and Business
Media LLC}, author={Hoffmann, Max and Biehler, Rolf}, year={2024} }'
chicago: Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge
When Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about
Rotationally Symmetric Figures.” ZDM – Mathematics Education, 2024. https://doi.org/10.1007/s11858-024-01633-4.
ieee: 'M. Hoffmann and R. Biehler, “Using academic mathematical knowledge when working
on interface tasks–analyses of pre-service teachers’ arguments about rotationally
symmetric figures,” ZDM – Mathematics Education, 2024, doi: 10.1007/s11858-024-01633-4.'
mla: Hoffmann, Max, and Rolf Biehler. “Using Academic Mathematical Knowledge When
Working on Interface Tasks–Analyses of Pre-Service Teachers’ Arguments about Rotationally
Symmetric Figures.” ZDM – Mathematics Education, Springer Science and Business
Media LLC, 2024, doi:10.1007/s11858-024-01633-4.
short: M. Hoffmann, R. Biehler, ZDM – Mathematics Education (2024).
date_created: 2024-09-23T07:36:35Z
date_updated: 2024-09-23T07:44:49Z
department:
- _id: '363'
doi: 10.1007/s11858-024-01633-4
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1007/s11858-024-01633-4
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Using academic mathematical knowledge when working on interface tasks–analyses
of pre-service teachers’ arguments about rotationally symmetric figures
type: journal_article
user_id: '37888'
year: '2024'
...
---
_id: '56114'
author:
- first_name: Matthieu
full_name: Pinaud, Matthieu
last_name: Pinaud
citation:
ama: Pinaud M. Manifolds of absolutely continuous functions with values in an infinite-dimensional
manifold and regularity properties of half-Lie groups. Published online 2024.
apa: Pinaud, M. (2024). Manifolds of absolutely continuous functions with values
in an infinite-dimensional manifold and regularity properties of half-Lie groups.
bibtex: '@article{Pinaud_2024, title={Manifolds of absolutely continuous functions
with values in an infinite-dimensional manifold and regularity properties of half-Lie
groups}, author={Pinaud, Matthieu}, year={2024} }'
chicago: Pinaud, Matthieu. “Manifolds of Absolutely Continuous Functions with Values
in an Infinite-Dimensional Manifold and Regularity Properties of Half-Lie Groups,”
2024.
ieee: M. Pinaud, “Manifolds of absolutely continuous functions with values in an
infinite-dimensional manifold and regularity properties of half-Lie groups.” 2024.
mla: Pinaud, Matthieu. Manifolds of Absolutely Continuous Functions with Values
in an Infinite-Dimensional Manifold and Regularity Properties of Half-Lie Groups.
2024.
short: M. Pinaud, (2024).
date_created: 2024-09-11T22:40:37Z
date_updated: 2024-09-11T22:45:02Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
arxiv:
- '2409.06512'
language:
- iso: eng
status: public
title: Manifolds of absolutely continuous functions with values in an infinite-dimensional
manifold and regularity properties of half-Lie groups
type: preprint
user_id: '178'
year: '2024'
...
---
_id: '56199'
citation:
ama: Liebendörfer M, Schmitz A, Biehler R, eds. Lernvideos in der Mathematik
– Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität
Paderborn und der TH Köln.; 2024.
apa: Liebendörfer, M., Schmitz, A., & Biehler, R. (Eds.). (2024). Lernvideos
in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos
der Universität Paderborn und der TH Köln.
bibtex: '@book{Liebendörfer_Schmitz_Biehler_2024, title={Lernvideos in der Mathematik
– Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität
Paderborn und der TH Köln}, year={2024} }'
chicago: Liebendörfer, Michael, Angelika Schmitz, and Rolf Biehler, eds. Lernvideos
in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos
der Universität Paderborn und der TH Köln, 2024.
ieee: M. Liebendörfer, A. Schmitz, and R. Biehler, Eds., Lernvideos in der Mathematik
– Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität
Paderborn und der TH Köln. 2024.
mla: Liebendörfer, Michael, et al., editors. Lernvideos in der Mathematik – Beiträge
zur Abschlusstagung des Projektes studiVEMINTvideos der Universität Paderborn
und der TH Köln. 2024.
short: M. Liebendörfer, A. Schmitz, R. Biehler, eds., Lernvideos in der Mathematik
– Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos der Universität
Paderborn und der TH Köln, 2024.
date_created: 2024-09-23T07:42:26Z
date_updated: 2024-09-25T08:26:10Z
department:
- _id: '363'
editor:
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: Angelika
full_name: Schmitz, Angelika
last_name: Schmitz
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
language:
- iso: ger
main_file_link:
- url: https://kobra.uni-kassel.de/handle/123456789/15993
publication_status: published
status: public
title: Lernvideos in der Mathematik – Beiträge zur Abschlusstagung des Projektes studiVEMINTvideos
der Universität Paderborn und der TH Köln
type: book_editor
user_id: '37888'
year: '2024'
...
---
_id: '56366'
abstract:
- lang: eng
text: AbstractWe discuss in which cases the Dunkl
convolution of distributions , possibly both with non‐compact support, can be
defined and study its analytic properties. We prove results on the (singular‐)support
of Dunkl convolutions. Based on this, we are able to prove a theorem on elliptic
regularity for a certain class of Dunkl operators, called elliptic Dunkl operators.
Finally, for the root system we consider the Riesz distributions and prove that
their Dunkl convolution exists and that holds.
author:
- first_name: Dominik
full_name: Brennecken, Dominik
id: '55911'
last_name: Brennecken
citation:
ama: Brennecken D. Dunkl convolution and elliptic regularity for Dunkl operators.
Mathematische Nachrichten. Published online 2024. doi:10.1002/mana.202300370
apa: Brennecken, D. (2024). Dunkl convolution and elliptic regularity for Dunkl
operators. Mathematische Nachrichten. https://doi.org/10.1002/mana.202300370
bibtex: '@article{Brennecken_2024, title={Dunkl convolution and elliptic regularity
for Dunkl operators}, DOI={10.1002/mana.202300370},
journal={Mathematische Nachrichten}, publisher={Wiley}, author={Brennecken, Dominik},
year={2024} }'
chicago: Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl
Operators.” Mathematische Nachrichten, 2024. https://doi.org/10.1002/mana.202300370.
ieee: 'D. Brennecken, “Dunkl convolution and elliptic regularity for Dunkl operators,”
Mathematische Nachrichten, 2024, doi: 10.1002/mana.202300370.'
mla: Brennecken, Dominik. “Dunkl Convolution and Elliptic Regularity for Dunkl Operators.”
Mathematische Nachrichten, Wiley, 2024, doi:10.1002/mana.202300370.
short: D. Brennecken, Mathematische Nachrichten (2024).
date_created: 2024-10-07T11:44:00Z
date_updated: 2024-10-07T11:46:15Z
department:
- _id: '555'
doi: 10.1002/mana.202300370
language:
- iso: eng
publication: Mathematische Nachrichten
publication_identifier:
issn:
- 0025-584X
- 1522-2616
publication_status: published
publisher: Wiley
status: public
title: Dunkl convolution and elliptic regularity for Dunkl operators
type: journal_article
user_id: '55911'
year: '2024'
...
---
_id: '56497'
article_number: '114258'
author:
- first_name: Chiara
full_name: Cappello, Chiara
last_name: Cappello
- first_name: Reza
full_name: Naserasr, Reza
last_name: Naserasr
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Zhouningxin
full_name: Wang, Zhouningxin
last_name: Wang
citation:
ama: Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs.
Discrete Mathematics. 2024;348(1). doi:10.1016/j.disc.2024.114258
apa: Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2024). Critically
3-frustrated signed graphs. Discrete Mathematics, 348(1), Article
114258. https://doi.org/10.1016/j.disc.2024.114258
bibtex: '@article{Cappello_Naserasr_Steffen_Wang_2024, title={Critically 3-frustrated
signed graphs}, volume={348}, DOI={10.1016/j.disc.2024.114258},
number={1114258}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Cappello,
Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2024}
}'
chicago: Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang.
“Critically 3-Frustrated Signed Graphs.” Discrete Mathematics 348, no.
1 (2024). https://doi.org/10.1016/j.disc.2024.114258.
ieee: 'C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated
signed graphs,” Discrete Mathematics, vol. 348, no. 1, Art. no. 114258,
2024, doi: 10.1016/j.disc.2024.114258.'
mla: Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” Discrete
Mathematics, vol. 348, no. 1, 114258, Elsevier BV, 2024, doi:10.1016/j.disc.2024.114258.
short: C. Cappello, R. Naserasr, E. Steffen, Z. Wang, Discrete Mathematics 348 (2024).
date_created: 2024-10-10T12:27:11Z
date_updated: 2024-10-10T12:28:13Z
department:
- _id: '542'
doi: 10.1016/j.disc.2024.114258
intvolume: ' 348'
issue: '1'
language:
- iso: eng
publication: Discrete Mathematics
publication_identifier:
issn:
- 0012-365X
publication_status: published
publisher: Elsevier BV
status: public
title: Critically 3-frustrated signed graphs
type: journal_article
user_id: '15540'
volume: 348
year: '2024'
...
---
_id: '56584'
author:
- first_name: Ali
full_name: Suri, Ali
last_name: Suri
citation:
ama: Suri A. Curvature and stability of quasi-geostrophic motion. Journal of
Geometry and Physics. 2024;198:105109.
apa: Suri, A. (2024). Curvature and stability of quasi-geostrophic motion. Journal
of Geometry and Physics, 198, 105109.
bibtex: '@article{Suri_2024, title={Curvature and stability of quasi-geostrophic
motion}, volume={198}, journal={Journal of Geometry and Physics}, author={Suri,
Ali}, year={2024}, pages={105109} }'
chicago: 'Suri, Ali. “Curvature and Stability of Quasi-Geostrophic Motion.” Journal
of Geometry and Physics 198 (2024): 105109.'
ieee: A. Suri, “Curvature and stability of quasi-geostrophic motion,” Journal
of Geometry and Physics, vol. 198, p. 105109, 2024.
mla: Suri, Ali. “Curvature and Stability of Quasi-Geostrophic Motion.” Journal
of Geometry and Physics, vol. 198, 2024, p. 105109.
short: A. Suri, Journal of Geometry and Physics 198 (2024) 105109.
date_created: 2024-10-10T15:59:49Z
date_updated: 2024-10-10T16:00:50Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
intvolume: ' 198'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1016/j.geomphys.2024.105109
page: '105109'
publication: Journal of Geometry and Physics
quality_controlled: '1'
status: public
title: Curvature and stability of quasi-geostrophic motion
type: journal_article
user_id: '178'
volume: 198
year: '2024'
...
---
_id: '56585'
author:
- first_name: Ali
full_name: Suri, Ali
last_name: Suri
citation:
ama: Suri A. Conjugate points along spherical harmonics. Journal of Geometry
and Physics. 2024;206:105333.
apa: Suri, A. (2024). Conjugate points along spherical harmonics. Journal of
Geometry and Physics, 206, 105333.
bibtex: '@article{Suri_2024, title={Conjugate points along spherical harmonics},
volume={206}, journal={Journal of Geometry and Physics}, author={Suri, Ali}, year={2024},
pages={105333} }'
chicago: 'Suri, Ali. “Conjugate Points along Spherical Harmonics.” Journal of
Geometry and Physics 206 (2024): 105333.'
ieee: A. Suri, “Conjugate points along spherical harmonics,” Journal of Geometry
and Physics, vol. 206, p. 105333, 2024.
mla: Suri, Ali. “Conjugate Points along Spherical Harmonics.” Journal of Geometry
and Physics, vol. 206, 2024, p. 105333.
short: A. Suri, Journal of Geometry and Physics 206 (2024) 105333.
date_created: 2024-10-10T16:05:18Z
date_updated: 2024-10-10T16:05:47Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
intvolume: ' 206'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1016/j.geomphys.2024.105333
page: '105333'
publication: Journal of Geometry and Physics
quality_controlled: '1'
status: public
title: Conjugate points along spherical harmonics
type: journal_article
user_id: '178'
volume: 206
year: '2024'
...
---
_id: '56583'
author:
- first_name: Helge
full_name: Glöckner, Helge
id: '178'
last_name: Glöckner
- first_name: Ali
full_name: Suri, Ali
last_name: Suri
citation:
ama: Glöckner H, Suri A. L^1-regularity of strong ILB-Lie groups. Published online
2024.
apa: Glöckner, H., & Suri, A. (2024). L^1-regularity of strong ILB-Lie groups.
bibtex: '@article{Glöckner_Suri_2024, title={L^1-regularity of strong ILB-Lie groups},
author={Glöckner, Helge and Suri, Ali}, year={2024} }'
chicago: Glöckner, Helge, and Ali Suri. “L^1-Regularity of Strong ILB-Lie Groups,”
2024.
ieee: H. Glöckner and A. Suri, “L^1-regularity of strong ILB-Lie groups.” 2024.
mla: Glöckner, Helge, and Ali Suri. L^1-Regularity of Strong ILB-Lie Groups.
2024.
short: H. Glöckner, A. Suri, (2024).
date_created: 2024-10-10T15:49:15Z
date_updated: 2024-10-10T15:51:43Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
external_id:
arxiv:
- '2410.02909'
language:
- iso: eng
status: public
title: L^1-regularity of strong ILB-Lie groups
type: preprint
user_id: '178'
year: '2024'
...