---
_id: '37654'
abstract:
- lang: eng
text: "Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate
prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian
systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven
modeling approach. However, preserving symmetries requires additional attention.
In this research, we\r\nenhance the HNN with a Lie algebra framework to detect
and embed symmetries in the neural network. This approach\r\nallows to simultaneously
learn the symmetry group action and the total energy of the system. As illustrating
examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are
considered."
article_number: '063115'
article_type: original
author:
- first_name: Eva
full_name: Dierkes, Eva
last_name: Dierkes
- 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
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
citation:
ama: Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks
with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969
apa: Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian
Neural Networks with Automatic Symmetry Detection. Chaos, 33(6),
Article 063115. https://doi.org/10.1063/5.0142969
bibtex: '@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural
Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969},
number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes,
Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023}
}'
chicago: Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp.
“Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos
33, no. 6 (2023). https://doi.org/10.1063/5.0142969.
ieee: 'E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural
Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art.
no. 063115, 2023, doi: 10.1063/5.0142969.'
mla: Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.”
Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969.
short: E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).
date_created: 2023-01-20T09:10:06Z
date_updated: 2023-08-10T08:37:01Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0142969
external_id:
arxiv:
- '2301.07928'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-04-26T16:20:56Z
date_updated: 2023-04-26T16:20:56Z
description: |-
Incorporating physical system knowledge into data-driven
system identification has been shown to be beneficial. The
approach presented in this article combines learning of an
energy-conserving model from data with detecting a Lie
group representation of the unknown system symmetry.
The proposed approach can improve the learned model
and reveal underlying symmetry simultaneously.
file_id: '44205'
file_name: JournalPaper_main.pdf
file_size: 5200111
relation: main_file
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
file_date_updated: 2023-04-26T16:20:56Z
has_accepted_license: '1'
intvolume: ' 33'
issue: '6'
language:
- iso: eng
oa: '1'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/eva-dierkes/HNN_withSymmetries
status: public
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
type: journal_article
user_id: '85279'
volume: 33
year: '2023'
...
---
_id: '23428'
abstract:
- lang: eng
text: "The Koopman operator has become an essential tool for data-driven approximation
of dynamical (control) systems in recent years, e.g., via extended dynamic mode
decomposition. Despite its popularity, convergence results and, in particular,
error bounds are still quite scarce. In this paper, we derive probabilistic bounds
for the approximation error and the prediction error depending on the number of
training data points; for both ordinary and stochastic differential equations.
Moreover, we extend our analysis to nonlinear control-affine systems using either
ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the
Koopman generator to obtain a bilinear system and, thus, circumvent the curse
of dimensionality since we do not autonomize the system by augmenting the state
by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data
error analysis in the stochastic and/or control setting. Finally, we demonstrate
the effectiveness of the proposed approach by comparing it with state-of-the-art
techniques showing its superiority whenever state and control are coupled."
article_number: '14'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Friedrich
full_name: Philipp, Friedrich
last_name: Philipp
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds
for Koopman-based prediction and control. Journal of Nonlinear Science.
2023;33. doi:10.1007/s00332-022-09862-1
apa: Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023).
Finite-data error bounds for Koopman-based prediction and control. Journal
of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1
bibtex: '@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data
error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1},
number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and
Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl},
year={2023} }'
chicago: Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and
Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.”
Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1.
ieee: 'F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data
error bounds for Koopman-based prediction and control,” Journal of Nonlinear
Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.'
mla: Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction
and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.
short: F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear
Science 33 (2023).
date_created: 2021-08-17T12:25:09Z
date_updated: 2023-08-24T07:50:12Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s00332-022-09862-1
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf
oa: '1'
publication: Journal of Nonlinear Science
publication_status: published
status: public
title: Finite-data error bounds for Koopman-based prediction and control
type: journal_article
user_id: '47427'
volume: 33
year: '2023'
...
---
_id: '21600'
abstract:
- lang: eng
text: Many problems in science and engineering require an efficient numerical approximation
of integrals or solutions to differential equations. For systems with rapidly
changing dynamics, an equidistant discretization is often inadvisable as it results
in prohibitively large errors or computational effort. To this end, adaptive schemes,
such as solvers based on Runge–Kutta pairs, have been developed which adapt the
step size based on local error estimations at each step. While the classical schemes
apply very generally and are highly efficient on regular systems, they can behave
suboptimally when an inefficient step rejection mechanism is triggered by structurally
complex systems such as chaotic systems. To overcome these issues, we propose
a method to tailor numerical schemes to the problem class at hand. This is achieved
by combining simple, classical quadrature rules or ODE solvers with data-driven
time-stepping controllers. Compared with learning solution operators to ODEs directly,
it generalizes better to unseen initial data as our approach employs classical
numerical schemes as base methods. At the same time it can make use of identified
structures of a problem class and, therefore, outperforms state-of-the-art adaptive
schemes. Several examples demonstrate superior efficiency. Source code is available
at https://github.com/lueckem/quadrature-ML.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Eyke
full_name: Hüllermeier, Eyke
id: '48129'
last_name: Hüllermeier
- first_name: Marvin
full_name: Lücke, Marvin
last_name: Lücke
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Karlson
full_name: Pfannschmidt, Karlson
id: '13472'
last_name: Pfannschmidt
orcid: 0000-0001-9407-7903
citation:
ama: Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical
integration using reinforcement learning. SIAM Journal on Scientific Computing.
2023;45(2):A579-A595. doi:10.1137/21M1412682
apa: Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz,
S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration
using reinforcement learning. SIAM Journal on Scientific Computing, 45(2),
A579–A595. https://doi.org/10.1137/21M1412682
bibtex: '@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023,
title={Efficient time stepping for numerical integration using reinforcement
learning}, volume={45}, DOI={10.1137/21M1412682},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz,
Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen,
Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595}
}'
chicago: 'Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum,
Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping
for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific
Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.'
ieee: 'M. Dellnitz et al., “Efficient time stepping for numerical integration
using reinforcement learning,” SIAM Journal on Scientific Computing, vol.
45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.'
mla: Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration
Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol.
45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.
short: M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz,
K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.
date_created: 2021-04-09T07:59:19Z
date_updated: 2023-08-25T09:24:50Z
ddc:
- '510'
department:
- _id: '101'
- _id: '636'
- _id: '355'
- _id: '655'
doi: 10.1137/21M1412682
external_id:
arxiv:
- arXiv:2104.03562
has_accepted_license: '1'
intvolume: ' 45'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/reader/10.1137/21M1412682
page: A579-A595
publication: SIAM Journal on Scientific Computing
publication_status: published
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/lueckem/quadrature-ML
status: public
title: Efficient time stepping for numerical integration using reinforcement learning
type: journal_article
user_id: '47427'
volume: 45
year: '2023'
...
---
_id: '46757'
author:
- first_name: Imke
full_name: Schwerin, Imke
id: '48912'
last_name: Schwerin
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
citation:
ama: 'Schwerin I, Häsel-Weide U. Second grader´s understanding of doubling and halfing
in various representations. In: Novotna J, Moraova H, eds. International Symposium
in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education. Charles University; 2023:297-305.'
apa: 'Schwerin, I., & Häsel-Weide, U. (2023). Second grader´s understanding
of doubling and halfing in various representations. In J. Novotna & H. Moraova
(Eds.), International Symposium in Elementary Mathematics Teaching. Proceedings:
New Directions in Elementary Mathematics Education (pp. 297–305). Charles
University.'
bibtex: '@inproceedings{Schwerin_Häsel-Weide_2023, title={Second grader´s understanding
of doubling and halfing in various representations}, booktitle={International
Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education}, publisher={Charles University}, author={Schwerin, Imke
and Häsel-Weide, Uta}, editor={Novotna, J. and Moraova, H.}, year={2023}, pages={297–305}
}'
chicago: 'Schwerin, Imke, and Uta Häsel-Weide. “Second Grader´s Understanding of
Doubling and Halfing in Various Representations.” In International Symposium
in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education, edited by J. Novotna and H. Moraova, 297–305. Charles
University, 2023.'
ieee: 'I. Schwerin and U. Häsel-Weide, “Second grader´s understanding of doubling
and halfing in various representations,” in International Symposium in Elementary
Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education,
Prag, 2023, pp. 297–305.'
mla: 'Schwerin, Imke, and Uta Häsel-Weide. “Second Grader´s Understanding of Doubling
and Halfing in Various Representations.” International Symposium in Elementary
Mathematics Teaching. Proceedings: New Directions in Elementary Mathematics Education,
edited by J. Novotna and H. Moraova, Charles University, 2023, pp. 297–305.'
short: 'I. Schwerin, U. Häsel-Weide, in: J. Novotna, H. Moraova (Eds.), International
Symposium in Elementary Mathematics Teaching. Proceedings: New Directions in Elementary
Mathematics Education, Charles University, 2023, pp. 297–305.'
conference:
location: Prag
name: International Symposium in Elementary Mathematics Teaching
date_created: 2023-08-30T09:40:23Z
date_updated: 2023-08-30T09:55:41Z
department:
- _id: '543'
editor:
- first_name: J.
full_name: Novotna, J.
last_name: Novotna
- first_name: H.
full_name: Moraova, H.
last_name: Moraova
language:
- iso: eng
page: 297-305
publication: 'International Symposium in Elementary Mathematics Teaching. Proceedings:
New Directions in Elementary Mathematics Education'
publisher: Charles University
status: public
title: Second grader´s understanding of doubling and halfing in various representations
type: conference
user_id: '44184'
year: '2023'
...
---
_id: '46758'
author:
- first_name: Rebekka
full_name: Schmidt, Rebekka
id: '58565'
last_name: Schmidt
- first_name: Claudia
full_name: Tenberge, Claudia
id: '67302'
last_name: Tenberge
- first_name: Uta
full_name: Häsel-Weide, Uta
id: '60267'
last_name: Häsel-Weide
citation:
ama: 'Schmidt R, Tenberge C, Häsel-Weide U. Lehre in Zeiten von Digitalisierung
und Inklusion - Beispiele aus drei Fächern. In: Vöing N, Schmidt R, Neiske I,
eds. Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre.
Visual Ink Publishing; 2023:297-318.'
apa: Schmidt, R., Tenberge, C., & Häsel-Weide, U. (2023). Lehre in Zeiten von
Digitalisierung und Inklusion - Beispiele aus drei Fächern. In N. Vöing, R. Schmidt,
& I. Neiske (Eds.), Aktive Teilhabe fördern – ICM und Student Engagement
in der Hochschullehre (pp. 297–318). Visual Ink Publishing.
bibtex: '@inbook{Schmidt_Tenberge_Häsel-Weide_2023, title={Lehre in Zeiten von Digitalisierung
und Inklusion - Beispiele aus drei Fächern}, booktitle={Aktive Teilhabe fördern
– ICM und Student Engagement in der Hochschullehre}, publisher={Visual Ink Publishing},
author={Schmidt, Rebekka and Tenberge, Claudia and Häsel-Weide, Uta}, editor={Vöing,
N. and Schmidt, R. and Neiske, I.}, year={2023}, pages={297–318} }'
chicago: Schmidt, Rebekka, Claudia Tenberge, and Uta Häsel-Weide. “Lehre in Zeiten
von Digitalisierung und Inklusion - Beispiele aus drei Fächern.” In Aktive
Teilhabe fördern – ICM und Student Engagement in der Hochschullehre, edited
by N. Vöing, R. Schmidt, and I. Neiske, 297–318. Visual Ink Publishing, 2023.
ieee: R. Schmidt, C. Tenberge, and U. Häsel-Weide, “Lehre in Zeiten von Digitalisierung
und Inklusion - Beispiele aus drei Fächern,” in Aktive Teilhabe fördern – ICM
und Student Engagement in der Hochschullehre, N. Vöing, R. Schmidt, and I.
Neiske, Eds. Visual Ink Publishing, 2023, pp. 297–318.
mla: Schmidt, Rebekka, et al. “Lehre in Zeiten von Digitalisierung und Inklusion
- Beispiele aus drei Fächern.” Aktive Teilhabe fördern – ICM und Student Engagement
in der Hochschullehre, edited by N. Vöing et al., Visual Ink Publishing, 2023,
pp. 297–318.
short: 'R. Schmidt, C. Tenberge, U. Häsel-Weide, in: N. Vöing, R. Schmidt, I. Neiske
(Eds.), Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre,
Visual Ink Publishing, 2023, pp. 297–318.'
date_created: 2023-08-30T09:54:47Z
date_updated: 2023-08-30T09:55:46Z
department:
- _id: '543'
editor:
- first_name: N.
full_name: Vöing, N.
last_name: Vöing
- first_name: R.
full_name: Schmidt, R.
last_name: Schmidt
- first_name: I.
full_name: Neiske, I.
last_name: Neiske
language:
- iso: ger
page: 297-318
publication: Aktive Teilhabe fördern – ICM und Student Engagement in der Hochschullehre
publisher: Visual Ink Publishing
status: public
title: Lehre in Zeiten von Digitalisierung und Inklusion - Beispiele aus drei Fächern
type: book_chapter
user_id: '44184'
year: '2023'
...
---
_id: '56200'
abstract:
- lang: eng
text: AbstractIntending to counteract Klein’s second
discontinuity in teacher education, we explored and applied the innovation of
“interface ePortfolio” in the context of a geometry
course for preservice teachers (PSTs). The tool offers the possibility of implementing
the design principle of profession orientation. In
the article, we theoretically clarify what we understand by this principle and
locate our innovative concept against this theoretical background. We empirically
investigate the extent to which counteraction against the second discontinuity
is successful by analyzing reflection texts created in the interface ePortfolio,
focusing on PSTs’ perspectives. Our qualitative content analysis shows that most
of them perceive the innovation as helpful in the intended sense and indicates
that the course concept, in general, and the interface ePortfolio, in particular,
have helped establish relevant links between the course content and their later
work as teachers.
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. Implementing profession orientation as a design principle
for overcoming Klein’s second discontinuity – preservice teacher’s perspectives
on interface activities in the context of a geometry course. ZDM – Mathematics
Education. 2023;55(4):737-751. doi:10.1007/s11858-023-01505-3
apa: Hoffmann, M., & Biehler, R. (2023). Implementing profession orientation
as a design principle for overcoming Klein’s second discontinuity – preservice
teacher’s perspectives on interface activities in the context of a geometry course.
ZDM – Mathematics Education, 55(4), 737–751. https://doi.org/10.1007/s11858-023-01505-3
bibtex: '@article{Hoffmann_Biehler_2023, title={Implementing profession orientation
as a design principle for overcoming Klein’s second discontinuity – preservice
teacher’s perspectives on interface activities in the context of a geometry course},
volume={55}, DOI={10.1007/s11858-023-01505-3},
number={4}, journal={ZDM – Mathematics Education}, publisher={Springer Science
and Business Media LLC}, author={Hoffmann, Max and Biehler, Rolf}, year={2023},
pages={737–751} }'
chicago: 'Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation
as a Design Principle for Overcoming Klein’s Second Discontinuity – Preservice
Teacher’s Perspectives on Interface Activities in the Context of a Geometry Course.”
ZDM – Mathematics Education 55, no. 4 (2023): 737–51. https://doi.org/10.1007/s11858-023-01505-3.'
ieee: 'M. Hoffmann and R. Biehler, “Implementing profession orientation as a design
principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives
on interface activities in the context of a geometry course,” ZDM – Mathematics
Education, vol. 55, no. 4, pp. 737–751, 2023, doi: 10.1007/s11858-023-01505-3.'
mla: Hoffmann, Max, and Rolf Biehler. “Implementing Profession Orientation as a
Design Principle for Overcoming Klein’s Second Discontinuity – Preservice Teacher’s
Perspectives on Interface Activities in the Context of a Geometry Course.” ZDM
– Mathematics Education, vol. 55, no. 4, Springer Science and Business Media
LLC, 2023, pp. 737–51, doi:10.1007/s11858-023-01505-3.
short: M. Hoffmann, R. Biehler, ZDM – Mathematics Education 55 (2023) 737–751.
date_created: 2024-09-23T07:51:34Z
date_updated: 2024-09-25T08:26:34Z
department:
- _id: '363'
doi: 10.1007/s11858-023-01505-3
intvolume: ' 55'
issue: '4'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/s11858-023-01505-3
page: 737-751
publication: ZDM – Mathematics Education
publication_identifier:
issn:
- 1863-9690
- 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Implementing profession orientation as a design principle for overcoming Klein’s
second discontinuity – preservice teacher’s perspectives on interface activities
in the context of a geometry course
type: journal_article
user_id: '37888'
volume: 55
year: '2023'
...
---
_id: '40607'
abstract:
- lang: eng
text: AbstractTeachers’ in-depth diagnostic thinking
has been shown to be crucial for student-centered teaching as they need to perceive
and interpret students’ understanding for well-informed decision-making on adaptive
teaching practices. The paper presents a content-related approach to analyzing
diagnostic thinking processes with respect to the mathematical knowledge elements
that prospective teachers identify as students’ resources and obstacles. Prospective
teachers’ challenge is that some relevant knowledge elements first have to be
unpacked, because compact concepts (such as the place value concept) or procedures
(such as for multi-digit multiplication) comprise several smaller knowledge elements
(such as the positional property) that have to be made explicit for students to
foster their learning processes adequately. Our study examines what knowledge
elements prospective teachers perceive and interpret in a transcript vignettes
on multi-digit multiplication (of decimal and natural numbers) and its underlying
basic arithmetic concepts (place value understanding and meaning of multiplication)
in written diagnostic judgments on students’ resources and obstacles (N = 196).
A comparative design within the vignette is used to investigate how far the process
of perceiving can be supported by thematic cues. The analysis reveals that those
knowledge elements cued in the vignette by being already unpacked and explicitly
addressed are perceived and interpreted more often (but with lower correctness)
than those that are uncued and therefore have to be unpacked by the prospective
teachers themselves. This confirms the need to prepare prospective teachers for
unpacking mathematical concepts themselves.
author:
- first_name: Jennifer
full_name: Dröse, Jennifer
last_name: Dröse
- first_name: Susanne
full_name: Prediger, Susanne
last_name: Prediger
citation:
ama: 'Dröse J, Prediger S. Prospective Teachers’ Diagnostic Thinking on Students’
Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking
of Knowledge Elements. Journal für Mathematik-Didaktik. Published online
2023. doi:10.1007/s13138-022-00214-w'
apa: 'Dröse, J., & Prediger, S. (2023). Prospective Teachers’ Diagnostic Thinking
on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis
on Unpacking of Knowledge Elements. Journal Für Mathematik-Didaktik. https://doi.org/10.1007/s13138-022-00214-w'
bibtex: '@article{Dröse_Prediger_2023, title={Prospective Teachers’ Diagnostic Thinking
on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis
on Unpacking of Knowledge Elements}, DOI={10.1007/s13138-022-00214-w},
journal={Journal für Mathematik-Didaktik}, publisher={Springer Science and Business
Media LLC}, author={Dröse, Jennifer and Prediger, Susanne}, year={2023} }'
chicago: 'Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic
Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related
Analysis on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik,
2023. https://doi.org/10.1007/s13138-022-00214-w.'
ieee: 'J. Dröse and S. Prediger, “Prospective Teachers’ Diagnostic Thinking on Students’
Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking
of Knowledge Elements,” Journal für Mathematik-Didaktik, 2023, doi: 10.1007/s13138-022-00214-w.'
mla: 'Dröse, Jennifer, and Susanne Prediger. “Prospective Teachers’ Diagnostic Thinking
on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis
on Unpacking of Knowledge Elements.” Journal Für Mathematik-Didaktik, Springer
Science and Business Media LLC, 2023, doi:10.1007/s13138-022-00214-w.'
short: J. Dröse, S. Prediger, Journal Für Mathematik-Didaktik (2023).
date_created: 2023-01-27T18:47:24Z
date_updated: 2025-01-15T08:36:09Z
department:
- _id: '98'
doi: 10.1007/s13138-022-00214-w
keyword:
- Education
- General Mathematics
language:
- iso: eng
publication: Journal für Mathematik-Didaktik
publication_identifier:
issn:
- 0173-5322
- 1869-2699
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: 'Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit
Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements'
type: journal_article
user_id: '85820'
year: '2023'
...
---
_id: '45374'
author:
- first_name: S.
full_name: Prediger, S.
last_name: Prediger
- first_name: Jennifer
full_name: Dröse, Jennifer
id: '85820'
last_name: Dröse
- first_name: R.
full_name: Stahnke, R.
last_name: Stahnke
- first_name: C.
full_name: Ademmer, C.
last_name: Ademmer
citation:
ama: 'Prediger S, Dröse J, Stahnke R, Ademmer C. Teacher expertise for fostering
at-risk students’ understanding of basic concepts: conceptual model and evidence
for growth. Journal of Mathematics Teacher Education. Published online
2023. doi:https://doi.org/10.1007/s10857-022-09538-3'
apa: 'Prediger, S., Dröse, J., Stahnke, R., & Ademmer, C. (2023). Teacher expertise
for fostering at-risk students’ understanding of basic concepts: conceptual model
and evidence for growth. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-022-09538-3'
bibtex: '@article{Prediger_Dröse_Stahnke_Ademmer_2023, title={Teacher expertise
for fostering at-risk students’ understanding of basic concepts: conceptual model
and evidence for growth}, DOI={https://doi.org/10.1007/s10857-022-09538-3},
journal={Journal of Mathematics Teacher Education}, author={Prediger, S. and Dröse,
Jennifer and Stahnke, R. and Ademmer, C.}, year={2023} }'
chicago: 'Prediger, S., Jennifer Dröse, R. Stahnke, and C. Ademmer. “Teacher Expertise
for Fostering At-Risk Students’ Understanding of Basic Concepts: Conceptual Model
and Evidence for Growth.” Journal of Mathematics Teacher Education, 2023.
https://doi.org/10.1007/s10857-022-09538-3.'
ieee: 'S. Prediger, J. Dröse, R. Stahnke, and C. Ademmer, “Teacher expertise for
fostering at-risk students’ understanding of basic concepts: conceptual model
and evidence for growth,” Journal of Mathematics Teacher Education, 2023,
doi: https://doi.org/10.1007/s10857-022-09538-3.'
mla: 'Prediger, S., et al. “Teacher Expertise for Fostering At-Risk Students’ Understanding
of Basic Concepts: Conceptual Model and Evidence for Growth.” Journal of Mathematics
Teacher Education, 2023, doi:https://doi.org/10.1007/s10857-022-09538-3.'
short: S. Prediger, J. Dröse, R. Stahnke, C. Ademmer, Journal of Mathematics Teacher
Education (2023).
date_created: 2023-05-31T06:27:51Z
date_updated: 2025-01-15T08:34:36Z
department:
- _id: '98'
doi: https://doi.org/10.1007/s10857-022-09538-3
language:
- iso: eng
publication: Journal of Mathematics Teacher Education
quality_controlled: '1'
status: public
title: 'Teacher expertise for fostering at-risk students’ understanding of basic concepts:
conceptual model and evidence for growth'
type: journal_article
user_id: '85820'
year: '2023'
...
---
_id: '46155'
article_number: '104270'
author:
- first_name: Julia
full_name: Bruns, Julia
id: '72183'
last_name: Bruns
orcid: https://orcid.org/0000-0002-6604-5864
- first_name: Maike
full_name: Hagena, Maike
last_name: Hagena
- first_name: Hedwig
full_name: Gasteiger, Hedwig
last_name: Gasteiger
citation:
ama: 'Bruns J, Hagena M, Gasteiger H. Professional Development Enacted by Facilitators
in the Context of Early Mathematics Education: Scaling up or Dilution of Effects?
Teaching and Teacher Education. 2023;132. doi:10.1016/j.tate.2023.104270'
apa: 'Bruns, J., Hagena, M., & Gasteiger, H. (2023). Professional Development
Enacted by Facilitators in the Context of Early Mathematics Education: Scaling
up or Dilution of Effects? Teaching and Teacher Education, 132,
Article 104270. https://doi.org/10.1016/j.tate.2023.104270'
bibtex: '@article{Bruns_Hagena_Gasteiger_2023, title={Professional Development Enacted
by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution
of Effects?}, volume={132}, DOI={10.1016/j.tate.2023.104270},
number={104270}, journal={Teaching and Teacher Education}, publisher={Elsevier
BV}, author={Bruns, Julia and Hagena, Maike and Gasteiger, Hedwig}, year={2023}
}'
chicago: 'Bruns, Julia, Maike Hagena, and Hedwig Gasteiger. “Professional Development
Enacted by Facilitators in the Context of Early Mathematics Education: Scaling
up or Dilution of Effects?” Teaching and Teacher Education 132 (2023).
https://doi.org/10.1016/j.tate.2023.104270.'
ieee: 'J. Bruns, M. Hagena, and H. Gasteiger, “Professional Development Enacted
by Facilitators in the Context of Early Mathematics Education: Scaling up or Dilution
of Effects?,” Teaching and Teacher Education, vol. 132, Art. no. 104270,
2023, doi: 10.1016/j.tate.2023.104270.'
mla: 'Bruns, Julia, et al. “Professional Development Enacted by Facilitators in
the Context of Early Mathematics Education: Scaling up or Dilution of Effects?”
Teaching and Teacher Education, vol. 132, 104270, Elsevier BV, 2023, doi:10.1016/j.tate.2023.104270.'
short: J. Bruns, M. Hagena, H. Gasteiger, Teaching and Teacher Education 132 (2023).
date_created: 2023-07-26T08:55:26Z
date_updated: 2025-06-02T12:59:11Z
department:
- _id: '611'
doi: 10.1016/j.tate.2023.104270
intvolume: ' 132'
keyword:
- Education
language:
- iso: eng
publication: Teaching and Teacher Education
publication_identifier:
issn:
- 0742-051X
publication_status: published
publisher: Elsevier BV
status: public
title: 'Professional Development Enacted by Facilitators in the Context of Early Mathematics
Education: Scaling up or Dilution of Effects?'
type: journal_article
user_id: '72183'
volume: 132
year: '2023'
...
---
_id: '59984'
author:
- first_name: Irene
full_name: Garnelo Abellanas, Irene
id: '93843'
last_name: Garnelo Abellanas
- first_name: Michael
full_name: Liebendörfer, Michael
last_name: Liebendörfer
citation:
ama: 'Garnelo Abellanas I, Liebendörfer M. Introducing mathematics undergraduate
students to the theorem prover lean. In: Thirteenth Congress of the European
Society for Research in Mathematics (CERME13). ; 2023.'
apa: Garnelo Abellanas, I., & Liebendörfer, M. (2023). Introducing mathematics
undergraduate students to the theorem prover lean. Thirteenth Congress of the
European Society for Research in Mathematics (CERME13). Thirteenth Congress
of the European Society for Research in Mathematics Education (CERME13), Budapest.
bibtex: '@inproceedings{Garnelo Abellanas_Liebendörfer_2023, title={Introducing
mathematics undergraduate students to the theorem prover lean}, booktitle={Thirteenth
Congress of the European Society for Research in Mathematics (CERME13)}, author={Garnelo
Abellanas, Irene and Liebendörfer, Michael}, year={2023} }'
chicago: Garnelo Abellanas, Irene, and Michael Liebendörfer. “Introducing Mathematics
Undergraduate Students to the Theorem Prover Lean.” In Thirteenth Congress
of the European Society for Research in Mathematics (CERME13), 2023.
ieee: I. Garnelo Abellanas and M. Liebendörfer, “Introducing mathematics undergraduate
students to the theorem prover lean,” presented at the Thirteenth Congress of
the European Society for Research in Mathematics Education (CERME13), Budapest,
2023.
mla: Garnelo Abellanas, Irene, and Michael Liebendörfer. “Introducing Mathematics
Undergraduate Students to the Theorem Prover Lean.” Thirteenth Congress of
the European Society for Research in Mathematics (CERME13), 2023.
short: 'I. Garnelo Abellanas, M. Liebendörfer, in: Thirteenth Congress of the European
Society for Research in Mathematics (CERME13), 2023.'
conference:
location: Budapest
name: Thirteenth Congress of the European Society for Research in Mathematics Education
(CERME13)
date_created: 2025-05-19T07:19:01Z
date_updated: 2026-01-15T10:36:11Z
department:
- _id: '983'
language:
- iso: eng
publication: Thirteenth Congress of the European Society for Research in Mathematics
(CERME13)
related_material:
link:
- relation: confirmation
url: https://hal.science/hal-04406679v1/file/TWG_14-Garnelo-218.pdf
status: public
title: Introducing mathematics undergraduate students to the theorem prover lean
type: conference
user_id: '93843'
year: '2023'
...
---
_id: '63635'
article_type: original
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Oliver
full_name: Matte, Oliver
last_name: Matte
citation:
ama: Hinrichs B, Matte O. Feynman–Kac Formula and Asymptotic Behavior of the Minimal
Energy for the Relativistic Nelson Model in Two Spatial Dimensions. Annales
Henri Poincaré. 2023;25(6):2877-2940. doi:10.1007/s00023-023-01369-z
apa: Hinrichs, B., & Matte, O. (2023). Feynman–Kac Formula and Asymptotic Behavior
of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.
Annales Henri Poincaré, 25(6), 2877–2940. https://doi.org/10.1007/s00023-023-01369-z
bibtex: '@article{Hinrichs_Matte_2023, title={Feynman–Kac Formula and Asymptotic
Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial
Dimensions}, volume={25}, DOI={10.1007/s00023-023-01369-z},
number={6}, journal={Annales Henri Poincaré}, publisher={Springer Science and
Business Media LLC}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2023},
pages={2877–2940} }'
chicago: 'Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic
Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial
Dimensions.” Annales Henri Poincaré 25, no. 6 (2023): 2877–2940. https://doi.org/10.1007/s00023-023-01369-z.'
ieee: 'B. Hinrichs and O. Matte, “Feynman–Kac Formula and Asymptotic Behavior of
the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions,”
Annales Henri Poincaré, vol. 25, no. 6, pp. 2877–2940, 2023, doi: 10.1007/s00023-023-01369-z.'
mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman–Kac Formula and Asymptotic Behavior
of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions.”
Annales Henri Poincaré, vol. 25, no. 6, Springer Science and Business Media
LLC, 2023, pp. 2877–940, doi:10.1007/s00023-023-01369-z.
short: B. Hinrichs, O. Matte, Annales Henri Poincaré 25 (2023) 2877–2940.
date_created: 2026-01-16T08:39:40Z
date_updated: 2026-01-16T09:05:26Z
department:
- _id: '799'
doi: 10.1007/s00023-023-01369-z
extern: '1'
external_id:
arxiv:
- '2211.14046'
intvolume: ' 25'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 2877-2940
publication: Annales Henri Poincaré
publication_identifier:
issn:
- 1424-0637
- 1424-0661
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic
Nelson Model in Two Spatial Dimensions
type: journal_article
user_id: '99427'
volume: 25
year: '2023'
...
---
_id: '46100'
article_number: '127558'
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Daan W.
full_name: Janssen, Daan W.
last_name: Janssen
- first_name: Jobst
full_name: Ziebell, Jobst
last_name: Ziebell
citation:
ama: 'Hinrichs B, Janssen DW, Ziebell J. Super-Gaussian decay of exponentials: A
sufficient condition. Journal of Mathematical Analysis and Applications.
2023;528(1). doi:10.1016/j.jmaa.2023.127558'
apa: 'Hinrichs, B., Janssen, D. W., & Ziebell, J. (2023). Super-Gaussian decay
of exponentials: A sufficient condition. Journal of Mathematical Analysis and
Applications, 528(1), Article 127558. https://doi.org/10.1016/j.jmaa.2023.127558'
bibtex: '@article{Hinrichs_Janssen_Ziebell_2023, title={Super-Gaussian decay of
exponentials: A sufficient condition}, volume={528}, DOI={10.1016/j.jmaa.2023.127558},
number={1127558}, journal={Journal of Mathematical Analysis and Applications},
publisher={Elsevier BV}, author={Hinrichs, Benjamin and Janssen, Daan W. and Ziebell,
Jobst}, year={2023} }'
chicago: 'Hinrichs, Benjamin, Daan W. Janssen, and Jobst Ziebell. “Super-Gaussian
Decay of Exponentials: A Sufficient Condition.” Journal of Mathematical Analysis
and Applications 528, no. 1 (2023). https://doi.org/10.1016/j.jmaa.2023.127558.'
ieee: 'B. Hinrichs, D. W. Janssen, and J. Ziebell, “Super-Gaussian decay of exponentials:
A sufficient condition,” Journal of Mathematical Analysis and Applications,
vol. 528, no. 1, Art. no. 127558, 2023, doi: 10.1016/j.jmaa.2023.127558.'
mla: 'Hinrichs, Benjamin, et al. “Super-Gaussian Decay of Exponentials: A Sufficient
Condition.” Journal of Mathematical Analysis and Applications, vol. 528,
no. 1, 127558, Elsevier BV, 2023, doi:10.1016/j.jmaa.2023.127558.'
short: B. Hinrichs, D.W. Janssen, J. Ziebell, Journal of Mathematical Analysis and
Applications 528 (2023).
date_created: 2023-07-20T05:08:49Z
date_updated: 2026-01-16T09:04:39Z
department:
- _id: '799'
doi: 10.1016/j.jmaa.2023.127558
external_id:
arxiv:
- '2205.09189'
intvolume: ' 528'
issue: '1'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication: Journal of Mathematical Analysis and Applications
publication_identifier:
issn:
- 0022-247X
publication_status: published
publisher: Elsevier BV
status: public
title: 'Super-Gaussian decay of exponentials: A sufficient condition'
type: journal_article
user_id: '99427'
volume: 528
year: '2023'
...
---
_id: '31190'
abstract:
- lang: eng
text: "For a compact Riemannian locally symmetric space $\\Gamma\\backslash G/K$
of\r\narbitrary rank we determine the location of certain Ruelle-Taylor resonances\r\nfor
the Weyl chamber action. We provide a Weyl-lower bound on an appropriate\r\ncounting
function for the Ruelle-Taylor resonances and establish a spectral gap\r\nwhich
is uniform in $\\Gamma$ if $G/K$ is irreducible of higher rank. This is\r\nachieved
by proving a quantum-classical correspondence, i.e. a\r\n1:1-correspondence between
horocyclically invariant Ruelle-Taylor resonant\r\nstates and joint eigenfunctions
of the algebra of invariant differential\r\noperators on $G/K$."
author:
- 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
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
orcid: 0000-0001-8893-2045
citation:
ama: Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence.
Analysis & PDE. 2023;16(10):2241–2265. doi:https://doi.org/10.2140/apde.2023.16.2241
apa: Hilgert, J., Weich, T., & Wolf, L. L. (2023). Higher rank quantum-classical
correspondence. Analysis & PDE, 16(10), 2241–2265. https://doi.org/10.2140/apde.2023.16.2241
bibtex: '@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical
correspondence}, volume={16}, DOI={https://doi.org/10.2140/apde.2023.16.2241},
number={10}, journal={Analysis & PDE}, publisher={MSP}, author={Hilgert, Joachim
and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }'
chicago: 'Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical
Correspondence.” Analysis & PDE 16, no. 10 (2023): 2241–2265. https://doi.org/10.2140/apde.2023.16.2241.'
ieee: 'J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,”
Analysis & PDE, vol. 16, no. 10, pp. 2241–2265, 2023, doi: https://doi.org/10.2140/apde.2023.16.2241.'
mla: Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” Analysis
& PDE, vol. 16, no. 10, MSP, 2023, pp. 2241–2265, doi:https://doi.org/10.2140/apde.2023.16.2241.
short: J. Hilgert, T. Weich, L.L. Wolf, Analysis & PDE 16 (2023) 2241–2265.
date_created: 2022-05-11T10:41:35Z
date_updated: 2026-02-18T10:39:36Z
department:
- _id: '10'
- _id: '548'
- _id: '91'
doi: https://doi.org/10.2140/apde.2023.16.2241
external_id:
arxiv:
- '2103.05667'
intvolume: ' 16'
issue: '10'
language:
- iso: eng
page: 2241–2265
publication: Analysis & PDE
publisher: MSP
status: public
title: Higher rank quantum-classical correspondence
type: journal_article
user_id: '49178'
volume: 16
year: '2023'
...
---
_id: '31059'
abstract:
- lang: eng
text: In this article we prove meromorphic continuation of weighted zeta functions
in the framework of open hyperbolic systems by using the meromorphically continued
restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula
proving equality between residues of weighted zetas and invariant Ruelle distributions.
We combine this equality with results of Guillarmou, Hilgert and Weich (2021)
in order to relate the residues to Patterson-Sullivan distributions. Finally we
provide proof-of-principle results concerning the numerical calculation of invariant
Ruelle distributions for 3-disc scattering systems.
author:
- first_name: Philipp
full_name: Schütte, Philipp
id: '50168'
last_name: Schütte
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Sonja
full_name: Barkhofen, Sonja
id: '48188'
last_name: Barkhofen
citation:
ama: Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta
Functions on Open Hyperbolic Systems. Communications in Mathematical Physics.
2023;398:655-678. doi:https://doi.org/10.1007/s00220-022-04538-z
apa: Schütte, P., Weich, T., & Barkhofen, S. (2023). Meromorphic Continuation
of Weighted Zeta Functions on Open Hyperbolic Systems. Communications in Mathematical
Physics, 398, 655–678. https://doi.org/10.1007/s00220-022-04538-z
bibtex: '@article{Schütte_Weich_Barkhofen_2023, title={Meromorphic Continuation
of Weighted Zeta Functions on Open Hyperbolic Systems}, volume={398}, DOI={https://doi.org/10.1007/s00220-022-04538-z},
journal={Communications in Mathematical Physics}, author={Schütte, Philipp and
Weich, Tobias and Barkhofen, Sonja}, year={2023}, pages={655–678} }'
chicago: 'Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation
of Weighted Zeta Functions on Open Hyperbolic Systems.” Communications in Mathematical
Physics 398 (2023): 655–78. https://doi.org/10.1007/s00220-022-04538-z.'
ieee: 'P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted
Zeta Functions on Open Hyperbolic Systems,” Communications in Mathematical
Physics, vol. 398, pp. 655–678, 2023, doi: https://doi.org/10.1007/s00220-022-04538-z.'
mla: Schütte, Philipp, et al. “Meromorphic Continuation of Weighted Zeta Functions
on Open Hyperbolic Systems.” Communications in Mathematical Physics, vol.
398, 2023, pp. 655–78, doi:https://doi.org/10.1007/s00220-022-04538-z.
short: P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics
398 (2023) 655–678.
date_created: 2022-05-04T12:27:46Z
date_updated: 2026-02-18T10:41:07Z
department:
- _id: '10'
- _id: '548'
- _id: '623'
- _id: '15'
doi: https://doi.org/10.1007/s00220-022-04538-z
external_id:
arxiv:
- '2112.05791'
intvolume: ' 398'
language:
- iso: eng
page: 655-678
publication: Communications in Mathematical Physics
status: public
title: Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems
type: journal_article
user_id: '49178'
volume: 398
year: '2023'
...
---
_id: '58097'
author:
- first_name: Tobias
full_name: Mai, Tobias
last_name: Mai
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Mai T, Biehler R. Einblicke in ein Referenzmodell zur Analyse der Einführung
von Vektoren in Schulbüchern. In: IDMI-Primar Goethe-Universität Frankfurt, ed.
Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für
Didaktik der Mathematik. WTM-Verlag; 2023.'
apa: Mai, T., & Biehler, R. (2023). Einblicke in ein Referenzmodell zur Analyse
der Einführung von Vektoren in Schulbüchern. In IDMI-Primar Goethe-Universität
Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der
Gesellschaft für Didaktik der Mathematik. WTM-Verlag.
bibtex: '@inbook{Mai_Biehler_2023, place={Münster}, title={Einblicke in ein Referenzmodell
zur Analyse der Einführung von Vektoren in Schulbüchern}, booktitle={Beiträge
zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik
der Mathematik}, publisher={WTM-Verlag}, author={Mai, Tobias and Biehler, Rolf},
editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2023} }'
chicago: 'Mai, Tobias, and Rolf Biehler. “Einblicke in ein Referenzmodell zur Analyse
der Einführung von Vektoren in Schulbüchern.” In Beiträge zum Mathematikunterricht
2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, edited
by IDMI-Primar Goethe-Universität Frankfurt. Münster: WTM-Verlag, 2023.'
ieee: 'T. Mai and R. Biehler, “Einblicke in ein Referenzmodell zur Analyse der Einführung
von Vektoren in Schulbüchern,” in Beiträge zum Mathematikunterricht 2022. 56.
Jahrestagung der Gesellschaft für Didaktik der Mathematik, IDMI-Primar Goethe-Universität
Frankfurt, Ed. Münster: WTM-Verlag, 2023.'
mla: Mai, Tobias, and Rolf Biehler. “Einblicke in ein Referenzmodell zur Analyse
der Einführung von Vektoren in Schulbüchern.” Beiträge zum Mathematikunterricht
2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, edited
by IDMI-Primar Goethe-Universität Frankfurt, WTM-Verlag, 2023.
short: 'T. Mai, R. Biehler, in: IDMI-Primar Goethe-Universität Frankfurt (Ed.),
Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für
Didaktik der Mathematik, WTM-Verlag, Münster, 2023.'
corporate_editor:
- IDMI-Primar Goethe-Universität Frankfurt
date_created: 2025-01-08T08:17:35Z
date_updated: 2025-01-08T08:17:40Z
ddc:
- '510'
department:
- _id: '363'
file:
- access_level: closed
content_type: application/pdf
creator: krueter
date_created: 2025-01-08T08:17:16Z
date_updated: 2025-01-08T08:17:16Z
file_id: '58098'
file_name: Mai aus Beitraege_2022___ISBN9783959872089-3.pdf
file_size: 546218
relation: main_file
success: 1
file_date_updated: 2025-01-08T08:17:16Z
has_accepted_license: '1'
language:
- iso: ger
place: Münster
publication: Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik
publisher: WTM-Verlag
status: public
title: Einblicke in ein Referenzmodell zur Analyse der Einführung von Vektoren in
Schulbüchern
type: book_chapter
user_id: '37888'
year: '2023'
...
---
_id: '58101'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Dominik
full_name: Guntermann, Dominik
last_name: Guntermann
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: Sandra
full_name: Krämer, Sandra
last_name: Krämer
- first_name: Sarah
full_name: Schlüter, Sarah
last_name: Schlüter
citation:
ama: 'Biehler R, Guntermann D, Liebendörfer M, Krämer S, Schlüter S. Fachdidaktisches
Design von Begründungsvideos im Projekt studiVEMINTvideos. In: IDMI-Primar Goethe-Universität
Frankfurt, ed. Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der
Gesellschaft für Didaktik der Mathematik. WTM-Verlag; 2023.'
apa: Biehler, R., Guntermann, D., Liebendörfer, M., Krämer, S., & Schlüter,
S. (2023). Fachdidaktisches Design von Begründungsvideos im Projekt studiVEMINTvideos.
In IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht
2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik. WTM-Verlag.
bibtex: '@inbook{Biehler_Guntermann_Liebendörfer_Krämer_Schlüter_2023, place={Münster},
title={Fachdidaktisches Design von Begründungsvideos im Projekt studiVEMINTvideos},
booktitle={Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik}, publisher={WTM-Verlag}, author={Biehler, Rolf and
Guntermann, Dominik and Liebendörfer, Michael and Krämer, Sandra and Schlüter,
Sarah}, editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2023} }'
chicago: 'Biehler, Rolf, Dominik Guntermann, Michael Liebendörfer, Sandra Krämer,
and Sarah Schlüter. “Fachdidaktisches Design von Begründungsvideos im Projekt
studiVEMINTvideos.” In Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung
der Gesellschaft für Didaktik der Mathematik, edited by IDMI-Primar Goethe-Universität
Frankfurt. Münster: WTM-Verlag, 2023.'
ieee: 'R. Biehler, D. Guntermann, M. Liebendörfer, S. Krämer, and S. Schlüter, “Fachdidaktisches
Design von Begründungsvideos im Projekt studiVEMINTvideos,” in Beiträge zum
Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der
Mathematik, IDMI-Primar Goethe-Universität Frankfurt, Ed. Münster: WTM-Verlag,
2023.'
mla: Biehler, Rolf, et al. “Fachdidaktisches Design von Begründungsvideos im Projekt
studiVEMINTvideos.” Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung
der Gesellschaft für Didaktik der Mathematik, edited by IDMI-Primar Goethe-Universität
Frankfurt, WTM-Verlag, 2023.
short: 'R. Biehler, D. Guntermann, M. Liebendörfer, S. Krämer, S. Schlüter, in:
IDMI-Primar Goethe-Universität Frankfurt (Ed.), Beiträge zum Mathematikunterricht
2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, WTM-Verlag,
Münster, 2023.'
corporate_editor:
- IDMI-Primar Goethe-Universität Frankfurt
date_created: 2025-01-08T08:22:10Z
date_updated: 2025-01-08T08:22:14Z
ddc:
- '510'
department:
- _id: '363'
- _id: '625'
file:
- access_level: closed
content_type: application/pdf
creator: krueter
date_created: 2025-01-08T08:21:52Z
date_updated: 2025-01-08T08:21:52Z
file_id: '58102'
file_name: Biehler_studiVEMINT aus Beitraege_2022___ISBN9783959872089.pdf
file_size: 528531
relation: main_file
success: 1
file_date_updated: 2025-01-08T08:21:52Z
has_accepted_license: '1'
language:
- iso: ger
place: Münster
publication: Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik
publisher: WTM-Verlag
status: public
title: Fachdidaktisches Design von Begründungsvideos im Projekt studiVEMINTvideos
type: book_chapter
user_id: '37888'
year: '2023'
...
---
_id: '58099'
author:
- first_name: Elisa
full_name: Lankeit, Elisa
last_name: Lankeit
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Lankeit E, Biehler R. Das totale Differential und die Richtungsableitung –
Eine Analyse mit Blick in ausgewählte Lehrbücher. In: IDMI-Primar Goethe-Universität
Frankfurt, ed. Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der
Gesellschaft für Didaktik der Mathematik. WTM-Verlag; 2023.'
apa: Lankeit, E., & Biehler, R. (2023). Das totale Differential und die Richtungsableitung
– Eine Analyse mit Blick in ausgewählte Lehrbücher. In IDMI-Primar Goethe-Universität
Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der
Gesellschaft für Didaktik der Mathematik. WTM-Verlag.
bibtex: '@inbook{Lankeit_Biehler_2023, place={Münster}, title={Das totale Differential
und die Richtungsableitung – Eine Analyse mit Blick in ausgewählte Lehrbücher},
booktitle={Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik}, publisher={WTM-Verlag}, author={Lankeit, Elisa and
Biehler, Rolf}, editor={IDMI-Primar Goethe-Universität Frankfurt}, year={2023}
}'
chicago: 'Lankeit, Elisa, and Rolf Biehler. “Das totale Differential und die Richtungsableitung
– Eine Analyse mit Blick in ausgewählte Lehrbücher.” In Beiträge zum Mathematikunterricht
2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, edited
by IDMI-Primar Goethe-Universität Frankfurt. Münster: WTM-Verlag, 2023.'
ieee: 'E. Lankeit and R. Biehler, “Das totale Differential und die Richtungsableitung
– Eine Analyse mit Blick in ausgewählte Lehrbücher,” in Beiträge zum Mathematikunterricht
2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, IDMI-Primar
Goethe-Universität Frankfurt, Ed. Münster: WTM-Verlag, 2023.'
mla: Lankeit, Elisa, and Rolf Biehler. “Das totale Differential und die Richtungsableitung
– Eine Analyse mit Blick in ausgewählte Lehrbücher.” Beiträge zum Mathematikunterricht
2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik, edited
by IDMI-Primar Goethe-Universität Frankfurt, WTM-Verlag, 2023.
short: 'E. Lankeit, R. Biehler, in: IDMI-Primar Goethe-Universität Frankfurt (Ed.),
Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für
Didaktik der Mathematik, WTM-Verlag, Münster, 2023.'
corporate_editor:
- IDMI-Primar Goethe-Universität Frankfurt
date_created: 2025-01-08T08:19:59Z
date_updated: 2025-01-08T08:20:05Z
ddc:
- '510'
department:
- _id: '363'
file:
- access_level: closed
content_type: application/pdf
creator: krueter
date_created: 2025-01-08T08:19:33Z
date_updated: 2025-01-08T08:19:33Z
file_id: '58100'
file_name: Lankeit aus Beitraege_2022___ISBN9783959872089-2.pdf
file_size: 536630
relation: main_file
success: 1
file_date_updated: 2025-01-08T08:19:33Z
has_accepted_license: '1'
language:
- iso: ger
place: Münster
publication: Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft
für Didaktik der Mathematik
publisher: WTM-Verlag
status: public
title: Das totale Differential und die Richtungsableitung – Eine Analyse mit Blick
in ausgewählte Lehrbücher
type: book_chapter
user_id: '37888'
year: '2023'
...
---
_id: '51383'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: C.
full_name: Arends, C.
last_name: Arends
citation:
ama: Hilgert J, Arends C. Spectral correspondences for rank one locally symmetric
spaces - The case of exceptional parameters. J de l’École polytechnique — Mathématiques.
2023;10:335-403.
apa: Hilgert, J., & Arends, C. (2023). Spectral correspondences for rank one
locally symmetric spaces - The case of exceptional parameters. J. de l’École
Polytechnique — Mathématiques, 10, 335–403.
bibtex: '@article{Hilgert_Arends_2023, title={Spectral correspondences for rank
one locally symmetric spaces - The case of exceptional parameters}, volume={10},
journal={J. de l’École polytechnique — Mathématiques}, author={Hilgert, Joachim
and Arends, C.}, year={2023}, pages={335–403} }'
chicago: 'Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One
Locally Symmetric Spaces - The Case of Exceptional Parameters.” J. de l’École
Polytechnique — Mathématiques 10 (2023): 335–403.'
ieee: J. Hilgert and C. Arends, “Spectral correspondences for rank one locally symmetric
spaces - The case of exceptional parameters,” J. de l’École polytechnique —
Mathématiques, vol. 10, pp. 335–403, 2023.
mla: Hilgert, Joachim, and C. Arends. “Spectral Correspondences for Rank One Locally
Symmetric Spaces - The Case of Exceptional Parameters.” J. de l’École Polytechnique
— Mathématiques, vol. 10, 2023, pp. 335–403.
short: J. Hilgert, C. Arends, J. de l’École Polytechnique — Mathématiques 10 (2023)
335–403.
date_created: 2024-02-19T06:34:11Z
date_updated: 2026-03-31T08:26:09Z
department:
- _id: '91'
intvolume: ' 10'
language:
- iso: eng
page: 335-403
publication: J. de l'École polytechnique — Mathématiques
publication_status: published
status: public
title: Spectral correspondences for rank one locally symmetric spaces - The case of
exceptional parameters
type: journal_article
user_id: '220'
volume: 10
year: '2023'
...
---
_id: '51384'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
- first_name: H.
full_name: Glöckner, H.
last_name: Glöckner
citation:
ama: Hilgert J, Glöckner H. Aspects of control theory on infinite-dimensional Lie
groups and G-manifolds. J Diff Equations. 2023;343:186-232.
apa: Hilgert, J., & Glöckner, H. (2023). Aspects of control theory on infinite-dimensional
Lie groups and G-manifolds. J. Diff. Equations, 343, 186–232.
bibtex: '@article{Hilgert_Glöckner_2023, title={Aspects of control theory on infinite-dimensional
Lie groups and G-manifolds}, volume={343}, journal={J. Diff. Equations}, author={Hilgert,
Joachim and Glöckner, H.}, year={2023}, pages={186–232} }'
chicago: 'Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional
Lie Groups and G-Manifolds.” J. Diff. Equations 343 (2023): 186–232.'
ieee: J. Hilgert and H. Glöckner, “Aspects of control theory on infinite-dimensional
Lie groups and G-manifolds,” J. Diff. Equations, vol. 343, pp. 186–232,
2023.
mla: Hilgert, Joachim, and H. Glöckner. “Aspects of Control Theory on Infinite-Dimensional
Lie Groups and G-Manifolds.” J. Diff. Equations, vol. 343, 2023, pp. 186–232.
short: J. Hilgert, H. Glöckner, J. Diff. Equations 343 (2023) 186–232.
date_created: 2024-02-19T06:35:08Z
date_updated: 2026-03-31T08:25:53Z
department:
- _id: '91'
intvolume: ' 343'
language:
- iso: eng
page: 186-232
publication: J. Diff. Equations
publication_status: published
status: public
title: Aspects of control theory on infinite-dimensional Lie groups and G-manifolds
type: journal_article
user_id: '220'
volume: 343
year: '2023'
...
---
_id: '53540'
abstract:
- lang: eng
text: "AbstractThis note is concerned with two
families of operators related to the fractional Laplacian, the first arising from
the Caffarelli-Silvestre extension problem and the second from the fractional
heat equation. They both include the Poisson semigroup. We show that on a complete,
connected, and non-compact Riemannian manifold of non-negative Ricci curvature,
in both cases, the solution with $$L^1$$\r\n \r\n
\ L\r\n 1\r\n
\ \r\n
initial data behaves asymptotically as the mass times the fundamental solution.
Similar long-time convergence results remain valid on more general manifolds satisfying
the Li-Yau two-sided estimate of the heat kernel. The situation changes drastically
on hyperbolic space, and more generally on rank one non-compact symmetric spaces:
we show that for the Poisson semigroup, the convergence to the Poisson kernel
fails -but remains true under the additional assumption of radial initial data."
author:
- first_name: Efthymia
full_name: Papageorgiou, Efthymia
id: '100325'
last_name: Papageorgiou
citation:
ama: Papageorgiou E. Large-Time Behavior of Two Families of Operators Related to
the Fractional Laplacian on Certain Riemannian Manifolds. Potential Analysis.
Published online 2023. doi:10.1007/s11118-023-10109-1
apa: Papageorgiou, E. (2023). Large-Time Behavior of Two Families of Operators Related
to the Fractional Laplacian on Certain Riemannian Manifolds. Potential Analysis.
https://doi.org/10.1007/s11118-023-10109-1
bibtex: '@article{Papageorgiou_2023, title={Large-Time Behavior of Two Families
of Operators Related to the Fractional Laplacian on Certain Riemannian Manifolds},
DOI={10.1007/s11118-023-10109-1},
journal={Potential Analysis}, publisher={Springer Science and Business Media LLC},
author={Papageorgiou, Efthymia}, year={2023} }'
chicago: Papageorgiou, Efthymia. “Large-Time Behavior of Two Families of Operators
Related to the Fractional Laplacian on Certain Riemannian Manifolds.” Potential
Analysis, 2023. https://doi.org/10.1007/s11118-023-10109-1.
ieee: 'E. Papageorgiou, “Large-Time Behavior of Two Families of Operators Related
to the Fractional Laplacian on Certain Riemannian Manifolds,” Potential Analysis,
2023, doi: 10.1007/s11118-023-10109-1.'
mla: Papageorgiou, Efthymia. “Large-Time Behavior of Two Families of Operators Related
to the Fractional Laplacian on Certain Riemannian Manifolds.” Potential Analysis,
Springer Science and Business Media LLC, 2023, doi:10.1007/s11118-023-10109-1.
short: E. Papageorgiou, Potential Analysis (2023).
date_created: 2024-04-17T13:17:37Z
date_updated: 2026-07-03T12:37:31Z
department:
- _id: '555'
doi: 10.1007/s11118-023-10109-1
keyword:
- Analysis
language:
- iso: eng
publication: Potential Analysis
publication_identifier:
issn:
- 0926-2601
- 1572-929X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Large-Time Behavior of Two Families of Operators Related to the Fractional
Laplacian on Certain Riemannian Manifolds
type: journal_article
user_id: '100325'
year: '2023'
...