---
_id: '34817'
article_type: original
author:
- first_name: Maximilian
full_name: Hanusch, Maximilian
id: '30905'
last_name: Hanusch
citation:
ama: Hanusch M. Regularity of Lie groups. Communications in Analysis and Geometry.
2022;30(1):53-152. doi:10.4310/cag.2022.v30.n1.a2
apa: Hanusch, M. (2022). Regularity of Lie groups. Communications in Analysis
and Geometry, 30(1), 53–152. https://doi.org/10.4310/cag.2022.v30.n1.a2
bibtex: '@article{Hanusch_2022, title={Regularity of Lie groups}, volume={30}, DOI={10.4310/cag.2022.v30.n1.a2},
number={1}, journal={Communications in Analysis and Geometry}, publisher={International
Press of Boston}, author={Hanusch, Maximilian}, year={2022}, pages={53–152} }'
chicago: 'Hanusch, Maximilian. “Regularity of Lie Groups.” Communications in
Analysis and Geometry 30, no. 1 (2022): 53–152. https://doi.org/10.4310/cag.2022.v30.n1.a2.'
ieee: 'M. Hanusch, “Regularity of Lie groups,” Communications in Analysis and
Geometry, vol. 30, no. 1, pp. 53–152, 2022, doi: 10.4310/cag.2022.v30.n1.a2.'
mla: Hanusch, Maximilian. “Regularity of Lie Groups.” Communications in Analysis
and Geometry, vol. 30, no. 1, International Press of Boston, 2022, pp. 53–152,
doi:10.4310/cag.2022.v30.n1.a2.
short: M. Hanusch, Communications in Analysis and Geometry 30 (2022) 53–152.
date_created: 2022-12-22T09:19:43Z
date_updated: 2023-01-09T18:07:30Z
department:
- _id: '93'
doi: 10.4310/cag.2022.v30.n1.a2
extern: '1'
intvolume: ' 30'
issue: '1'
keyword:
- regularity of Lie groups
language:
- iso: eng
page: 53-152
publication: Communications in Analysis and Geometry
publication_identifier:
issn:
- 1019-8385
- 1944-9992
publication_status: published
publisher: International Press of Boston
status: public
title: Regularity of Lie groups
type: journal_article
user_id: '30905'
volume: 30
year: '2022'
...
---
_id: '34856'
author:
- first_name: Maximilian
full_name: Hanusch, Maximilian
id: '30905'
last_name: Hanusch
citation:
ama: Hanusch M. Analysis 1 und 2 Skript/Buch. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching
apa: Hanusch, M. (n.d.). Analysis 1 und 2 Skript/Buch. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
bibtex: '@book{Hanusch, title={Analysis 1 und 2 Skript/Buch}, publisher={https://maximilianhanusch.wixsite.com/my-site/lehre-teaching},
author={Hanusch, Maximilian} }'
chicago: Hanusch, Maximilian. Analysis 1 und 2 Skript/Buch. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching,
n.d.
ieee: M. Hanusch, Analysis 1 und 2 Skript/Buch. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
mla: Hanusch, Maximilian. Analysis 1 und 2 Skript/Buch. https://maximilianhanusch.wixsite.com/my-site/lehre-teaching.
short: M. Hanusch, Analysis 1 und 2 Skript/Buch, https://maximilianhanusch.wixsite.com/my-site/lehre-teaching,
n.d.
date_created: 2022-12-22T17:06:02Z
date_updated: 2023-01-09T18:07:00Z
department:
- _id: '93'
language:
- iso: ger
page: '385'
publication_status: draft
publisher: https://maximilianhanusch.wixsite.com/my-site/lehre-teaching
status: public
title: Analysis 1 und 2 Skript/Buch
type: working_paper
user_id: '30905'
year: '2022'
...
---
_id: '35644'
author:
- first_name: Martin
full_name: Kolb, Martin
id: '48880'
last_name: Kolb
- first_name: Alexander
full_name: Klump, Alexander
id: '45067'
last_name: Klump
citation:
ama: Kolb M, Klump A. Uniqueness of the Inverse First Passage Time Problem and the
Shape of the Shiryaev boundary. Theory of Probability and its Applications.
2022;67(4):717-744.
apa: Kolb, M., & Klump, A. (2022). Uniqueness of the Inverse First Passage Time
Problem and the Shape of the Shiryaev boundary. Theory of Probability and Its
Applications, 67(4), 717–744.
bibtex: '@article{Kolb_Klump_2022, title={Uniqueness of the Inverse First Passage
Time Problem and the Shape of the Shiryaev boundary}, volume={67}, number={4},
journal={Theory of Probability and its Applications}, publisher={Society for Industrial
and Applied Mathematics}, author={Kolb, Martin and Klump, Alexander}, year={2022},
pages={717–744} }'
chicago: 'Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage
Time Problem and the Shape of the Shiryaev Boundary.” Theory of Probability
and Its Applications 67, no. 4 (2022): 717–44.'
ieee: M. Kolb and A. Klump, “Uniqueness of the Inverse First Passage Time Problem
and the Shape of the Shiryaev boundary,” Theory of Probability and its Applications,
vol. 67, no. 4, pp. 717–744, 2022.
mla: Kolb, Martin, and Alexander Klump. “Uniqueness of the Inverse First Passage
Time Problem and the Shape of the Shiryaev Boundary.” Theory of Probability
and Its Applications, vol. 67, no. 4, Society for Industrial and Applied Mathematics,
2022, pp. 717–44.
short: M. Kolb, A. Klump, Theory of Probability and Its Applications 67 (2022) 717–744.
date_created: 2023-01-10T08:13:17Z
date_updated: 2023-01-10T08:13:30Z
department:
- _id: '96'
intvolume: ' 67'
issue: '4'
language:
- iso: eng
page: 717-744
publication: Theory of Probability and its Applications
publication_status: published
publisher: Society for Industrial and Applied Mathematics
status: public
title: Uniqueness of the Inverse First Passage Time Problem and the Shape of the Shiryaev
boundary
type: journal_article
user_id: '85821'
volume: 67
year: '2022'
...
---
_id: '35649'
abstract:
- lang: eng
text: Motivated by the work [6] of Mariusz Bieniek, Krzysztof Burdzy and Soumik
Pal we study a Fleming-Viot-type particle system consisting of independently moving
particles each driven by generalized Bessel processes on the positive real line.
Upon hitting the boundary {0} this particle is killed and an uniformly chosen
different one branches into two particles. Using the symmetry of the model and
the self similarity property of Bessel processes, we obtain a criterion to decide
whether the particles converge to the origin at a finite time. This addresses
open problem 1.4 in [6]. Specifically, inspired by [6, Open Problem 1.5], we investigate
the case of three moving particles and refine the general result of [6, Theorem
1.1(ii)] extending the regime of drift parameters, where convergence does not
occur – even to values, where it does occur when considering the case of only
two particles.
author:
- first_name: Martin
full_name: Kolb, Martin
id: '48880'
last_name: Kolb
- first_name: Matthias
full_name: Liesenfeld, Matthias
last_name: Liesenfeld
citation:
ama: Kolb M, Liesenfeld M. On non-extinction in a Fleming-Viot-type particle model
with Bessel drift. Electronic Journal of Probability. 2022;(27):1-28. doi:https://doi.org/10.1214/22-EJP866
apa: Kolb, M., & Liesenfeld, M. (2022). On non-extinction in a Fleming-Viot-type
particle model with Bessel drift. Electronic Journal of Probability, 27,
1–28. https://doi.org/10.1214/22-EJP866
bibtex: '@article{Kolb_Liesenfeld_2022, title={On non-extinction in a Fleming-Viot-type
particle model with Bessel drift}, DOI={https://doi.org/10.1214/22-EJP866},
number={27}, journal={Electronic Journal of Probability}, publisher={Institute
of Mathematical Statistics}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2022},
pages={1–28} }'
chicago: 'Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type
Particle Model with Bessel Drift.” Electronic Journal of Probability, no.
27 (2022): 1–28. https://doi.org/10.1214/22-EJP866.'
ieee: 'M. Kolb and M. Liesenfeld, “On non-extinction in a Fleming-Viot-type particle
model with Bessel drift,” Electronic Journal of Probability, no. 27, pp.
1–28, 2022, doi: https://doi.org/10.1214/22-EJP866.'
mla: Kolb, Martin, and Matthias Liesenfeld. “On Non-Extinction in a Fleming-Viot-Type
Particle Model with Bessel Drift.” Electronic Journal of Probability, no.
27, Institute of Mathematical Statistics, 2022, pp. 1–28, doi:https://doi.org/10.1214/22-EJP866.
short: M. Kolb, M. Liesenfeld, Electronic Journal of Probability (2022) 1–28.
date_created: 2023-01-10T08:19:25Z
date_updated: 2023-01-10T08:19:38Z
department:
- _id: '96'
doi: https://doi.org/10.1214/22-EJP866
issue: '27'
language:
- iso: eng
page: 1-28
publication: Electronic Journal of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: On non-extinction in a Fleming-Viot-type particle model with Bessel drift
type: journal_article
user_id: '85821'
year: '2022'
...
---
_id: '35650'
abstract:
- lang: eng
text: "We consider autoregressive sequences Xn = aXn−1 + ξn and\r\nMn = max{aMn−1
, ξn} with a constant a ∈ (0, 1) and with positive, in-\r\ndependent and identically
distributed innovations {ξk }. It is known that if\r\nP(ξ1 > x) ∼ d\r\nlog x with
some d ∈ (0, − log a) then the chains {Xn} and {Mn}\r\nare null recurrent. We
investigate the tail behaviour of recurrence times in this\r\ncase of logarithmically
decaying tails. More precisely, we show that the tails\r\nof recurrence times
are regularly varying of index −1 − d/ log a. We also prove\r\nlimit theorems
for {Xn} and {Mn} conditioned to stay over a fixed level x0.\r\nFurthermore, we
study tail asymptotics for recurrence times of {Xn} and {Mn}\r\nin the case when
these chains are positive recurrent and the tail of log ξ1 is\r\nsubexponential."
author:
- first_name: Denis
full_name: Denisov, Denis
last_name: Denisov
- first_name: Günter
full_name: Hinrichs, Günter
last_name: Hinrichs
- first_name: Martin
full_name: Kolb, Martin
id: '48880'
last_name: Kolb
- first_name: Vitali
full_name: Wachtel, Vitali
last_name: Wachtel
citation:
ama: Denisov D, Hinrichs G, Kolb M, Wachtel V. Persistence of autoregressive sequences
with logarithmic tails. Electronic Journal of Probability. 2022;27:1-43.
doi:https://doi.org/10.48550/arXiv.2203.14772
apa: Denisov, D., Hinrichs, G., Kolb, M., & Wachtel, V. (2022). Persistence
of autoregressive sequences with logarithmic tails. Electronic Journal of Probability,
27, 1–43. https://doi.org/10.48550/arXiv.2203.14772
bibtex: '@article{Denisov_Hinrichs_Kolb_Wachtel_2022, title={Persistence of autoregressive
sequences with logarithmic tails}, volume={27}, DOI={https://doi.org/10.48550/arXiv.2203.14772},
journal={Electronic Journal of Probability}, publisher={Institute of Mathematical
Statistics}, author={Denisov, Denis and Hinrichs, Günter and Kolb, Martin and
Wachtel, Vitali}, year={2022}, pages={1–43} }'
chicago: 'Denisov, Denis, Günter Hinrichs, Martin Kolb, and Vitali Wachtel. “Persistence
of Autoregressive Sequences with Logarithmic Tails.” Electronic Journal of
Probability 27 (2022): 1–43. https://doi.org/10.48550/arXiv.2203.14772.'
ieee: 'D. Denisov, G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of autoregressive
sequences with logarithmic tails,” Electronic Journal of Probability, vol.
27, pp. 1–43, 2022, doi: https://doi.org/10.48550/arXiv.2203.14772.'
mla: Denisov, Denis, et al. “Persistence of Autoregressive Sequences with Logarithmic
Tails.” Electronic Journal of Probability, vol. 27, Institute of Mathematical
Statistics, 2022, pp. 1–43, doi:https://doi.org/10.48550/arXiv.2203.14772.
short: D. Denisov, G. Hinrichs, M. Kolb, V. Wachtel, Electronic Journal of Probability
27 (2022) 1–43.
date_created: 2023-01-10T08:28:12Z
date_updated: 2023-01-10T08:29:02Z
department:
- _id: '96'
doi: https://doi.org/10.48550/arXiv.2203.14772
intvolume: ' 27'
language:
- iso: eng
page: 1-43
publication: Electronic Journal of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: Persistence of autoregressive sequences with logarithmic tails
type: journal_article
user_id: '85821'
volume: 27
year: '2022'
...
---
_id: '31367'
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. Schnittstellenaufgaben in der Analysis I zur Verknüpfung
von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.
In: Halverscheid S, Kersten I, Schmidt-Thieme B, eds. Bedarfsgerechte fachmathematische
Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen
. Springer Spektrum; 2022:351-368.'
apa: Hoffmann, M., & Biehler, R. (2022). Schnittstellenaufgaben in der Analysis
I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse
einer Evaluationsstudie. In S. Halverscheid, I. Kersten, & B. Schmidt-Thieme
(Eds.), Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen
und Konzepte unter heterogenen Voraussetzungen (pp. 351–368). Springer Spektrum.
bibtex: '@inproceedings{Hoffmann_Biehler_2022, place={Wiesbaden}, title={Schnittstellenaufgaben
in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele
und Ergebnisse einer Evaluationsstudie.}, booktitle={ Bedarfsgerechte fachmathematische
Lehramtsausbildung. Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen
}, publisher={Springer Spektrum}, author={Hoffmann, Max and Biehler, Rolf}, editor={Halverscheid,
Stefan and Kersten, Ina and Schmidt-Thieme, Barbara}, year={2022}, pages={351–368}
}'
chicago: 'Hoffmann, Max, and Rolf Biehler. “Schnittstellenaufgaben in der Analysis
I zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse
einer Evaluationsstudie.” In Bedarfsgerechte fachmathematische Lehramtsausbildung.
Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen , edited
by Stefan Halverscheid, Ina Kersten, and Barbara Schmidt-Thieme, 351–68. Wiesbaden:
Springer Spektrum, 2022.'
ieee: M. Hoffmann and R. Biehler, “Schnittstellenaufgaben in der Analysis I zur
Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse
einer Evaluationsstudie.,” in Bedarfsgerechte fachmathematische Lehramtsausbildung.
Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen , 2022,
pp. 351–368.
mla: Hoffmann, Max, and Rolf Biehler. “Schnittstellenaufgaben in der Analysis I
zur Verknüpfung von Schul- und Hochschulmathematik - Aufgabenbeispiele und Ergebnisse
einer Evaluationsstudie.” Bedarfsgerechte fachmathematische Lehramtsausbildung.
Analyse, Zielsetzungen und Konzepte unter heterogenen Voraussetzungen , edited
by Stefan Halverscheid et al., Springer Spektrum, 2022, pp. 351–68.
short: 'M. Hoffmann, R. Biehler, in: S. Halverscheid, I. Kersten, B. Schmidt-Thieme
(Eds.), Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen
und Konzepte unter heterogenen Voraussetzungen , Springer Spektrum, Wiesbaden,
2022, pp. 351–368.'
date_created: 2022-05-22T14:16:52Z
date_updated: 2023-01-11T15:28:21Z
department:
- _id: '97'
editor:
- first_name: Stefan
full_name: Halverscheid, Stefan
last_name: Halverscheid
- first_name: Ina
full_name: Kersten, Ina
last_name: Kersten
- first_name: Barbara
full_name: Schmidt-Thieme, Barbara
last_name: Schmidt-Thieme
language:
- iso: ger
page: 351-368
place: Wiesbaden
publication: ' Bedarfsgerechte fachmathematische Lehramtsausbildung. Analyse, Zielsetzungen
und Konzepte unter heterogenen Voraussetzungen '
publication_status: published
publisher: Springer Spektrum
quality_controlled: '1'
status: public
title: Schnittstellenaufgaben in der Analysis I zur Verknüpfung von Schul- und Hochschulmathematik
- Aufgabenbeispiele und Ergebnisse einer Evaluationsstudie.
type: conference
user_id: '32202'
year: '2022'
...
---
_id: '31365'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
citation:
ama: 'Biehler R, Hoffmann M. Fachwissen als Grundlage fachdidaktischer Urteilskompetenz
– Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher
und fachdidaktischer Lehre im gymnasialen Lehramtsstudium. In: Isaev V, Eichler
A, Loose F, eds. Professionsorientierte Fachwissenschaft. Kohärenzstiftende
Lerngelegenheiten für das Lehramtsstudium Mathematik. Springer; 2022:49–72.
doi:10.1007/978-3-662-63948-1_4'
apa: Biehler, R., & Hoffmann, M. (2022). Fachwissen als Grundlage fachdidaktischer
Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen
fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium.
In V. Isaev, A. Eichler, & F. Loose (Eds.), Professionsorientierte Fachwissenschaft.
Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium Mathematik (pp.
49–72). Springer. https://doi.org/10.1007/978-3-662-63948-1_4
bibtex: '@inproceedings{Biehler_Hoffmann_2022, place={Berlin, Heidelberg}, title={Fachwissen
als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für die Herstellung
konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer Lehre
im gymnasialen Lehramtsstudium}, DOI={10.1007/978-3-662-63948-1_4},
booktitle={ Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten
für das Lehramtsstudium Mathematik}, publisher={Springer}, author={Biehler, Rolf
and Hoffmann, Max}, editor={Isaev, Viktor and Eichler, Andreas and Loose, Frank},
year={2022}, pages={49–72} }'
chicago: 'Biehler, Rolf, and Max Hoffmann. “Fachwissen als Grundlage fachdidaktischer
Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen
fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium.”
In Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten
für das Lehramtsstudium Mathematik, edited by Viktor Isaev, Andreas Eichler,
and Frank Loose, 49–72. Berlin, Heidelberg: Springer, 2022. https://doi.org/10.1007/978-3-662-63948-1_4.'
ieee: 'R. Biehler and M. Hoffmann, “Fachwissen als Grundlage fachdidaktischer Urteilskompetenz
– Beispiele für die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher
und fachdidaktischer Lehre im gymnasialen Lehramtsstudium,” in Professionsorientierte
Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium
Mathematik, 2022, pp. 49–72, doi: 10.1007/978-3-662-63948-1_4.'
mla: Biehler, Rolf, and Max Hoffmann. “Fachwissen als Grundlage fachdidaktischer
Urteilskompetenz – Beispiele für die Herstellung konzeptueller Bezüge zwischen
fachwissenschaftlicher und fachdidaktischer Lehre im gymnasialen Lehramtsstudium.”
Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten
für das Lehramtsstudium Mathematik, edited by Viktor Isaev et al., Springer,
2022, pp. 49–72, doi:10.1007/978-3-662-63948-1_4.
short: 'R. Biehler, M. Hoffmann, in: V. Isaev, A. Eichler, F. Loose (Eds.), Professionsorientierte
Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten für das Lehramtsstudium
Mathematik, Springer, Berlin, Heidelberg, 2022, pp. 49–72.'
date_created: 2022-05-22T14:03:58Z
date_updated: 2023-01-11T15:29:09Z
department:
- _id: '97'
doi: 10.1007/978-3-662-63948-1_4
editor:
- first_name: Viktor
full_name: Isaev, Viktor
last_name: Isaev
- first_name: Andreas
full_name: Eichler, Andreas
last_name: Eichler
- first_name: Frank
full_name: Loose, Frank
last_name: Loose
language:
- iso: ger
main_file_link:
- url: https://link.springer.com/chapter/10.1007/978-3-662-63948-1_4
page: ' 49–72'
place: Berlin, Heidelberg
publication: ' Professionsorientierte Fachwissenschaft. Kohärenzstiftende Lerngelegenheiten
für das Lehramtsstudium Mathematik'
publication_identifier:
isbn:
- '9783662639474'
- '9783662639481'
issn:
- 2197-8751
- 2197-876X
publication_status: published
publisher: Springer
quality_controlled: '1'
status: public
title: Fachwissen als Grundlage fachdidaktischer Urteilskompetenz – Beispiele für
die Herstellung konzeptueller Bezüge zwischen fachwissenschaftlicher und fachdidaktischer
Lehre im gymnasialen Lehramtsstudium
type: conference
user_id: '32202'
year: '2022'
...
---
_id: '45373'
author:
- first_name: Jennifer
full_name: Dröse, Jennifer
id: '85820'
last_name: Dröse
- first_name: P.
full_name: Neugebauer, P.
last_name: Neugebauer
- first_name: R.
full_name: Delucchi Danhier, R.
last_name: Delucchi Danhier
- first_name: B.
full_name: Mertins, B.
last_name: Mertins
citation:
ama: 'Dröse J, Neugebauer P, Delucchi Danhier R, Mertins B. Eye-Tracking Studie
zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer Strukturen.
In: Kleine P, Graulich N, Kuhn J, Schindler M, eds. Eye-Tracking in der Mathematik-
und Naturwissenschaftsdidaktik. Forschung und Praxis. ; 2022:209-225. doi:https://doi.org/10.1007/978-3-662-63214-7'
apa: 'Dröse, J., Neugebauer, P., Delucchi Danhier, R., & Mertins, B. (2022).
Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer
Strukturen. In P. Kleine, N. Graulich, J. Kuhn, & M. Schindler (Eds.), Eye-Tracking
in der Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis (pp.
209–225). https://doi.org/10.1007/978-3-662-63214-7'
bibtex: '@inbook{Dröse_Neugebauer_Delucchi Danhier_Mertins_2022, title={Eye-Tracking
Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer
Strukturen}, DOI={https://doi.org/10.1007/978-3-662-63214-7},
booktitle={Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung
und Praxis}, author={Dröse, Jennifer and Neugebauer, P. and Delucchi Danhier,
R. and Mertins, B.}, editor={Kleine, P. and Graulich, N. and Kuhn, J. and Schindler,
M.}, year={2022}, pages={209–225} }'
chicago: 'Dröse, Jennifer, P. Neugebauer, R. Delucchi Danhier, and B. Mertins. “Eye-Tracking
Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer
Strukturen.” In Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik.
Forschung und Praxis, edited by P. Kleine, N. Graulich, J. Kuhn, and M. Schindler,
209–25, 2022. https://doi.org/10.1007/978-3-662-63214-7.'
ieee: 'J. Dröse, P. Neugebauer, R. Delucchi Danhier, and B. Mertins, “Eye-Tracking
Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren syntaktischer
Strukturen,” in Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik.
Forschung und Praxis, P. Kleine, N. Graulich, J. Kuhn, and M. Schindler, Eds.
2022, pp. 209–225.'
mla: 'Dröse, Jennifer, et al. “Eye-Tracking Studie zu Textaufgaben in Klasse 5:
Bemerken und Interpretieren syntaktischer Strukturen.” Eye-Tracking in der
Mathematik- und Naturwissenschaftsdidaktik. Forschung und Praxis, edited by
P. Kleine et al., 2022, pp. 209–25, doi:https://doi.org/10.1007/978-3-662-63214-7.'
short: 'J. Dröse, P. Neugebauer, R. Delucchi Danhier, B. Mertins, in: P. Kleine,
N. Graulich, J. Kuhn, M. Schindler (Eds.), Eye-Tracking in der Mathematik- und
Naturwissenschaftsdidaktik. Forschung und Praxis, 2022, pp. 209–225.'
date_created: 2023-05-31T06:22:21Z
date_updated: 2023-11-02T08:07:31Z
department:
- _id: '98'
doi: https://doi.org/10.1007/978-3-662-63214-7
editor:
- first_name: P.
full_name: Kleine, P.
last_name: Kleine
- first_name: N.
full_name: Graulich, N.
last_name: Graulich
- first_name: J.
full_name: Kuhn, J.
last_name: Kuhn
- first_name: M.
full_name: Schindler, M.
last_name: Schindler
language:
- iso: ger
page: 209-225
publication: Eye-Tracking in der Mathematik- und Naturwissenschaftsdidaktik. Forschung
und Praxis
quality_controlled: '1'
status: public
title: 'Eye-Tracking Studie zu Textaufgaben in Klasse 5: Bemerken und Interpretieren
syntaktischer Strukturen'
type: book_chapter
user_id: '85820'
year: '2022'
...
---
_id: '30733'
abstract:
- lang: eng
text: Hamilton-Jacobi reachability methods for safety-critical control have been
well studied, but the safety guarantees derived rely on the accuracy of the numerical
computation. Thus, it is crucial to understand and account for any inaccuracies
that occur due to uncertainty in the underlying dynamics and environment as well
as the induced numerical errors. To this end, we propose a framework for modeling
the error of the value function inherent in Hamilton-Jacobi reachability using
a Gaussian process. The derived safety controller can be used in conjuncture with
arbitrary controllers to provide a safe hybrid control law. The marginal likelihood
of the Gaussian process then provides a confidence metric used to determine switches
between a least restrictive controller and a safety controller. We test both the
prediction as well as the correction capabilities of the presented method in a
classical pursuit-evasion example.
author:
- first_name: Nikolaus
full_name: Vertovec, Nikolaus
id: '93930'
last_name: Vertovec
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kostas
full_name: Margellos, Kostas
last_name: Margellos
citation:
ama: 'Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control
policies using kernel methods. In: ; 2022:1870-1875.'
apa: Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (2022). Verification
of safety critical control policies using kernel methods. 1870–1875.
bibtex: '@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification
of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus
and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875}
}'
chicago: Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification
of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.
ieee: N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical
control policies using kernel methods,” London, 2022, pp. 1870–1875.
mla: Vertovec, Nikolaus, et al. Verification of Safety Critical Control Policies
Using Kernel Methods. 2022, pp. 1870–75.
short: 'N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.'
conference:
end_date: 2022-07-15
location: London
name: 2022 European Control Conference (ECC)
start_date: 2022-07-12
date_created: 2022-03-31T11:14:13Z
date_updated: 2023-11-29T10:00:18Z
ddc:
- '510'
department:
- _id: '636'
has_accepted_license: '1'
language:
- iso: eng
page: 1870-1875
status: public
title: Verification of safety critical control policies using kernel methods
type: conference
user_id: '15694'
year: '2022'
...
---
_id: '45378'
author:
- first_name: Jennifer
full_name: Dröse, Jennifer
id: '85820'
last_name: Dröse
- first_name: Lena
full_name: Wessel, Lena
id: '85190'
last_name: Wessel
citation:
ama: 'Dröse J, Wessel L. Prospective Teachers‘ Competence of Fostering Students’
Understanding in Script Writing Task. In: Fernandez C, Llinares S, Gutiérrez A,
Planas N, eds. Proceedings of the 45th Conference of the International Group
for the Psychology of Mathematics Education. PME. ; 2022.'
apa: Dröse, J., & Wessel, L. (2022). Prospective Teachers‘ Competence of Fostering
Students’ Understanding in Script Writing Task. In C. Fernandez, S. Llinares,
A. Gutiérrez, & N. Planas (Eds.), Proceedings of the 45th Conference of
the International Group for the Psychology of Mathematics Education. PME.
bibtex: '@inproceedings{Dröse_Wessel_2022, title={Prospective Teachers‘ Competence
of Fostering Students’ Understanding in Script Writing Task}, booktitle={Proceedings
of the 45th Conference of the International Group for the Psychology of Mathematics
Education. PME}, author={Dröse, Jennifer and Wessel, Lena}, editor={Fernandez,
C. and Llinares, S. and Gutiérrez, A. and Planas, N.}, year={2022} }'
chicago: Dröse, Jennifer, and Lena Wessel. “Prospective Teachers‘ Competence of
Fostering Students’ Understanding in Script Writing Task.” In Proceedings of
the 45th Conference of the International Group for the Psychology of Mathematics
Education. PME, edited by C. Fernandez, S. Llinares, A. Gutiérrez, and N.
Planas, 2022.
ieee: J. Dröse and L. Wessel, “Prospective Teachers‘ Competence of Fostering Students’
Understanding in Script Writing Task,” in Proceedings of the 45th Conference
of the International Group for the Psychology of Mathematics Education. PME,
2022.
mla: Dröse, Jennifer, and Lena Wessel. “Prospective Teachers‘ Competence of Fostering
Students’ Understanding in Script Writing Task.” Proceedings of the 45th Conference
of the International Group for the Psychology of Mathematics Education. PME,
edited by C. Fernandez et al., 2022.
short: 'J. Dröse, L. Wessel, in: C. Fernandez, S. Llinares, A. Gutiérrez, N. Planas
(Eds.), Proceedings of the 45th Conference of the International Group for the
Psychology of Mathematics Education. PME, 2022.'
date_created: 2023-05-31T06:54:24Z
date_updated: 2023-11-02T08:05:31Z
department:
- _id: '98'
editor:
- first_name: C.
full_name: Fernandez, C.
last_name: Fernandez
- first_name: S.
full_name: Llinares, S.
last_name: Llinares
- first_name: A.
full_name: Gutiérrez, A.
last_name: Gutiérrez
- first_name: N.
full_name: Planas, N.
last_name: Planas
language:
- iso: eng
publication: Proceedings of the 45th Conference of the International Group for the
Psychology of Mathematics Education. PME
quality_controlled: '1'
status: public
title: Prospective Teachers‘ Competence of Fostering Students’ Understanding in Script
Writing Task
type: conference
user_id: '85820'
year: '2022'
...
---
_id: '31057'
abstract:
- lang: eng
text: In this paper we give an overview over some aspects of the modern mathematical
theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical
systems and their implications in physics. First we recall recent developments
in the mathematical theory of resonances, in particular how invariant Ruelle distributions
arise as residues of weighted zeta functions. Then we derive a correspondence
between weighted and semiclassical zeta functions in the setting of negatively
curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich
yields a high frequency interpretation of invariant Ruelle distributions as quantum
mechanical matrix coefficients in constant negative curvature. We finish by presenting
numerical calculations of phase space distributions in the more physical setting
of 3-disk scattering systems.
article_number: '244007'
article_type: review
author:
- first_name: Sonja
full_name: Barkhofen, Sonja
id: '48188'
last_name: Barkhofen
- 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
citation:
ama: 'Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions.
Journal of Physics A: Mathematical and Theoretical. 2022;55(24). doi:10.1088/1751-8121/ac6d2b'
apa: 'Barkhofen, S., Schütte, P., & Weich, T. (2022). Semiclassical formulae
For Wigner distributions. Journal of Physics A: Mathematical and Theoretical,
55(24), Article 244007. https://doi.org/10.1088/1751-8121/ac6d2b'
bibtex: '@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For
Wigner distributions}, volume={55}, DOI={10.1088/1751-8121/ac6d2b},
number={24244007}, journal={Journal of Physics A: Mathematical and Theoretical},
publisher={IOP Publishing Ltd}, author={Barkhofen, Sonja and Schütte, Philipp
and Weich, Tobias}, year={2022} }'
chicago: 'Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae
For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical
55, no. 24 (2022). https://doi.org/10.1088/1751-8121/ac6d2b.'
ieee: 'S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner
distributions,” Journal of Physics A: Mathematical and Theoretical, vol.
55, no. 24, Art. no. 244007, 2022, doi: 10.1088/1751-8121/ac6d2b.'
mla: 'Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.”
Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, 244007,
IOP Publishing Ltd, 2022, doi:10.1088/1751-8121/ac6d2b.'
short: 'S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and
Theoretical 55 (2022).'
date_created: 2022-05-04T12:23:11Z
date_updated: 2024-02-06T20:40:45Z
department:
- _id: '623'
- _id: '548'
- _id: '10'
doi: 10.1088/1751-8121/ac6d2b
external_id:
arxiv:
- '2201.04892'
intvolume: ' 55'
issue: '24'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publisher: IOP Publishing Ltd
status: public
title: Semiclassical formulae For Wigner distributions
type: journal_article
user_id: '49178'
volume: 55
year: '2022'
...
---
_id: '31363'
abstract:
- lang: eng
text: Vorgestellt wird ein Entwicklungsforschungsprojekt zur Konzeption und Durchführung
einer Veranstaltung "Geometrie für Lehramtsstudierende". Die Schwerpunkte des
Projekts sind zum einen die inhaltliche Gestaltung der Veranstaltung und zum anderen
die Umsetzung von Professionsorientierung. Bezogen auf den inhaltlichen Aufbau
wird das auf metrischen Räumen aufbauende Axiomensystem der "Saccheri-Ebene" vorgestellt
und mit alternativen axiomatischen Zugängen zur ebenen Geometrie verglichen. Die
Frage nach der Umsetzung von Professionsorientierung in Fachveranstaltungen ist
eng mit der Problematik der zweiten Diskontinuität verbunden. In der Arbeit wird
dieses Problem auf Grundlage der Synthese von theoretischen Hintergründen zur
Bedeutung von mathematischem Wissen und Können für professionelle Handlungskompetenz
von Mathematiklehrkräften diskutiert und darauf aufbauend werden theoriebasierte
Entwurfsprinzipien für professionsorientierte Fachveranstaltungen entworfen. Zentrale
Elemente der methodischen Gestaltung sind die sogenannten "Schnittstellenwochen"
zu den Themen Kongruenz und Symmetrie sowie das begleitende Schnittstellen-ePortfolio.
Das zentrale Ergebnis der Arbeit ist ein theoretisch fundiertes und empirisch
evaluiertes ganzheitliches Veranstaltungskonzept für eine professionsorientierte
Geometrie-Veranstaltung für Lehramtsstudierende, dessen Konzeption auf andere
Fachveranstaltungen übertragbar ist. Darüber hinaus ergeben sich im Rahmen der
durchgeführten Entwicklungsforschung verschiedene neue Beiträge zur Geometriedidaktik
in Schule- und Hochschule.
- lang: eng
text: This thesis presents a design research project on the conception and implementation
of a course "Geometry for Student Teachers". The focal points of the project are,
on the one hand, the content structure of the course and, on the other hand, the
implementation of professional orientation. With regard to the content structure,
the axiom system of the "Saccheri plane", which is based on metric spaces, is
presented and compared with alternative axiomatic approaches to plane geometry.
The question of implementing professional orientation in mathematics courses is
closely connected to the problem of the second discontinuity. In the paper, this
problem is discussed on the basis of the synthesis of theoretical backgrounds
on the importance of mathematical knowledge and skills for professional competence
of mathematics teachers. Building on this, theory-based design principles for
profession-oriented subject courses are developed. Central elements of the methodological
design are the so-called "interface weeks" on the topics of congruence and symmetry
and an accompanying interface ePortfolio. The central result of the thesis is
a theoretically founded and empirically evaluated holistic course concept for
a profession-oriented geometry course for student teachers, the conception of
which is transferable to other subject events. In addition, various new contributions
to the didactics of geometry in schools and universities result from the desing
research.
author:
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
citation:
ama: 'Hoffmann M. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung
Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie
Für Lehramtsstudierende.; 2022. doi:10.17619/UNIPB/1-1313'
apa: 'Hoffmann, M. (2022). Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung
und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie
für Lehramtsstudierende. https://doi.org/10.17619/UNIPB/1-1313'
bibtex: '@book{Hoffmann_2022, title={Von der Axiomatik bis zur Schnittstellenaufgabe:
Entwicklung und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung
Geometrie für Lehramtsstudierende}, DOI={10.17619/UNIPB/1-1313},
author={Hoffmann, Max}, year={2022} }'
chicago: 'Hoffmann, Max. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung
Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie
Für Lehramtsstudierende, 2022. https://doi.org/10.17619/UNIPB/1-1313.'
ieee: 'M. Hoffmann, Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung
und Erforschung eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie
für Lehramtsstudierende. 2022.'
mla: 'Hoffmann, Max. Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung
Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie
Für Lehramtsstudierende. 2022, doi:10.17619/UNIPB/1-1313.'
short: 'M. Hoffmann, Von Der Axiomatik Bis Zur Schnittstellenaufgabe: Entwicklung
Und Erforschung Eines Ganzheitlichen Lehrkonzepts Für Eine Veranstaltung Geometrie
Für Lehramtsstudierende, 2022.'
date_created: 2022-05-22T10:56:47Z
date_updated: 2024-02-19T06:28:58Z
department:
- _id: '97'
doi: 10.17619/UNIPB/1-1313
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/content/titleinfo/6503170
oa: '1'
page: '410'
status: public
supervisor:
- first_name: Rolf
full_name: Biehler, Rolf
last_name: Biehler
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
title: 'Von der Axiomatik bis zur Schnittstellenaufgabe: Entwicklung und Erforschung
eines ganzheitlichen Lehrkonzepts für eine Veranstaltung Geometrie für Lehramtsstudierende'
type: dissertation
user_id: '49063'
year: '2022'
...
---
_id: '35322'
author:
- first_name: Kai-Uwe
full_name: Bux, Kai-Uwe
last_name: Bux
- 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: Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree.
Journal of Spectral Theory. 2022;12(2):659-681. doi:10.4171/jst/414
apa: Bux, K.-U., Hilgert, J., & Weich, T. (2022). Poisson transforms for trees
of bounded degree. Journal of Spectral Theory, 12(2), 659–681. https://doi.org/10.4171/jst/414
bibtex: '@article{Bux_Hilgert_Weich_2022, title={Poisson transforms for trees of
bounded degree}, volume={12}, DOI={10.4171/jst/414},
number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical
Society - EMS - Publishing House GmbH}, author={Bux, Kai-Uwe and Hilgert, Joachim
and Weich, Tobias}, year={2022}, pages={659–681} }'
chicago: 'Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Poisson Transforms for
Trees of Bounded Degree.” Journal of Spectral Theory 12, no. 2 (2022):
659–81. https://doi.org/10.4171/jst/414.'
ieee: 'K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded
degree,” Journal of Spectral Theory, vol. 12, no. 2, pp. 659–681, 2022,
doi: 10.4171/jst/414.'
mla: Bux, Kai-Uwe, et al. “Poisson Transforms for Trees of Bounded Degree.” Journal
of Spectral Theory, vol. 12, no. 2, European Mathematical Society - EMS -
Publishing House GmbH, 2022, pp. 659–81, doi:10.4171/jst/414.
short: K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681.
date_created: 2023-01-06T08:49:06Z
date_updated: 2024-02-19T06:28:12Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
- _id: '91'
doi: 10.4171/jst/414
intvolume: ' 12'
issue: '2'
keyword:
- Geometry and Topology
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
page: 659-681
publication: Journal of Spectral Theory
publication_identifier:
issn:
- 1664-039X
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
status: public
title: Poisson transforms for trees of bounded degree
type: journal_article
user_id: '49063'
volume: 12
year: '2022'
...
---
_id: '51554'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: 'Hilgert J. Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second
Edition. AMS/MAA Press 2021. Mathematische Semesterberichte. 2022;69:151–153.
doi:10.1007/s00591-021-00314-7'
apa: 'Hilgert, J. (2022). Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics,
Second Edition. AMS/MAA Press 2021. In Mathematische Semesterberichte (Vol.
69, pp. 151–153). https://doi.org/10.1007/s00591-021-00314-7'
bibtex: '@article{Hilgert_2022, title={Ethan D. Bolker und Maura B. Mast: Common
Sense Mathematics, Second Edition. AMS/MAA Press 2021}, volume={69}, DOI={10.1007/s00591-021-00314-7},
journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2022},
pages={151–153} }'
chicago: 'Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics,
Second Edition. AMS/MAA Press 2021.” Mathematische Semesterberichte, 2022.
https://doi.org/10.1007/s00591-021-00314-7.'
ieee: 'J. Hilgert, “Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics,
Second Edition. AMS/MAA Press 2021,” Mathematische Semesterberichte, vol.
69. pp. 151–153, 2022, doi: 10.1007/s00591-021-00314-7.'
mla: 'Hilgert, Joachim. “Ethan D. Bolker Und Maura B. Mast: Common Sense Mathematics,
Second Edition. AMS/MAA Press 2021.” Mathematische Semesterberichte, vol.
69, 2022, pp. 151–153, doi:10.1007/s00591-021-00314-7.'
short: J. Hilgert, Mathematische Semesterberichte 69 (2022) 151–153.
date_created: 2024-02-20T09:49:04Z
date_updated: 2024-02-20T09:52:53Z
department:
- _id: '91'
doi: 10.1007/s00591-021-00314-7
intvolume: ' 69'
language:
- iso: eng
page: 151–153
publication: Mathematische Semesterberichte
publication_status: published
status: public
title: 'Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics, Second Edition.
AMS/MAA Press 2021'
type: review
user_id: '49063'
volume: 69
year: '2022'
...
---
_id: '45970'
abstract:
- lang: eng
text: ' We introduce a new phase field model for tumor growth where viscoelastic
effects are taken into account. The model is derived from basic thermodynamical
principles and consists of a convected Cahn–Hilliard equation with source terms
for the tumor cells and a convected reaction–diffusion equation with boundary
supply for the nutrient. Chemotactic terms, which are essential for the invasive
behavior of tumors, are taken into account. The model is completed by a viscoelastic
system consisting of the Navier–Stokes equation for the hydrodynamic quantities,
and a general constitutive equation with stress relaxation for the left Cauchy–Green
tensor associated with the elastic part of the total mechanical response of the
viscoelastic material. For a specific choice of the elastic energy density and
with an additional dissipative term accounting for stress diffusion, we prove
existence of global-in-time weak solutions of the viscoelastic model for tumor
growth in two space dimensions [Formula: see text] by the passage to the limit
in a fully-discrete finite element scheme where a CFL condition, i.e. [Formula:
see text], is required. Moreover, in arbitrary dimensions [Formula:
see text], we show stability and existence of solutions for the fully-discrete
finite element scheme, where positive definiteness of the discrete Cauchy–Green
tensor is proved with a regularization technique that was first introduced by
Barrett and Boyaval [Existence and approximation of a (regularized) Oldroyd-B
model, Math. Models Methods Appl. Sci. 21 (2011) 1783–1837]. After that, we improve
the regularity results in arbitrary dimensions [Formula: see text] and in two
dimensions [Formula: see text], where a CFL condition is required. Then, in two
dimensions [Formula: see text], we pass to the limit in the discretization parameters
and show that subsequences of discrete solutions converge to a global-in-time
weak solution. Finally, we present numerical results in two dimensions [Formula:
see text]. '
author:
- first_name: Harald
full_name: Garcke, Harald
last_name: Garcke
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Dennis
full_name: Trautwein, Dennis
last_name: Trautwein
citation:
ama: Garcke H, Kovács B, Trautwein D. Viscoelastic Cahn–Hilliard models for tumor
growth. Mathematical Models and Methods in Applied Sciences. 2022;32(13):2673-2758.
doi:10.1142/s0218202522500634
apa: Garcke, H., Kovács, B., & Trautwein, D. (2022). Viscoelastic Cahn–Hilliard
models for tumor growth. Mathematical Models and Methods in Applied Sciences,
32(13), 2673–2758. https://doi.org/10.1142/s0218202522500634
bibtex: '@article{Garcke_Kovács_Trautwein_2022, title={Viscoelastic Cahn–Hilliard
models for tumor growth}, volume={32}, DOI={10.1142/s0218202522500634},
number={13}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
Scientific Pub Co Pte Ltd}, author={Garcke, Harald and Kovács, Balázs and Trautwein,
Dennis}, year={2022}, pages={2673–2758} }'
chicago: 'Garcke, Harald, Balázs Kovács, and Dennis Trautwein. “Viscoelastic Cahn–Hilliard
Models for Tumor Growth.” Mathematical Models and Methods in Applied Sciences
32, no. 13 (2022): 2673–2758. https://doi.org/10.1142/s0218202522500634.'
ieee: 'H. Garcke, B. Kovács, and D. Trautwein, “Viscoelastic Cahn–Hilliard models
for tumor growth,” Mathematical Models and Methods in Applied Sciences,
vol. 32, no. 13, pp. 2673–2758, 2022, doi: 10.1142/s0218202522500634.'
mla: Garcke, Harald, et al. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.”
Mathematical Models and Methods in Applied Sciences, vol. 32, no. 13, World
Scientific Pub Co Pte Ltd, 2022, pp. 2673–758, doi:10.1142/s0218202522500634.
short: H. Garcke, B. Kovács, D. Trautwein, Mathematical Models and Methods in Applied
Sciences 32 (2022) 2673–2758.
date_created: 2023-07-10T11:47:27Z
date_updated: 2024-04-03T09:15:35Z
department:
- _id: '841'
doi: 10.1142/s0218202522500634
intvolume: ' 32'
issue: '13'
keyword:
- Applied Mathematics
- Modeling and Simulation
language:
- iso: eng
page: 2673-2758
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
issn:
- 0218-2025
- 1793-6314
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Viscoelastic Cahn–Hilliard models for tumor growth
type: journal_article
user_id: '100441'
volume: 32
year: '2022'
...
---
_id: '45969'
abstract:
- lang: eng
text: 'AbstractAn evolving surface finite element
discretisation is analysed for the evolution of a closed two-dimensional surface
governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion
process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms
are proposed, both based on a system coupling the diffusion equation to evolution
equations for geometric quantities in the velocity law for the surface. One of
the numerical methods is proved to be convergent in the$$H^1$$H1norm
with optimal-order for finite elements of degree at least two. We present numerical
experiments illustrating the convergence behaviour and demonstrating the qualitative
properties of the flow: preservation of mean convexity, loss of convexity, weak
maximum principles, and the occurrence of self-intersections.'
author:
- first_name: Charles M.
full_name: Elliott, Charles M.
last_name: Elliott
- first_name: Harald
full_name: Garcke, Harald
last_name: Garcke
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean
curvature flow and diffusion on closed surfaces. Numerische Mathematik.
2022;151(4):873-925. doi:10.1007/s00211-022-01301-3
apa: Elliott, C. M., Garcke, H., & Kovács, B. (2022). Numerical analysis for
the interaction of mean curvature flow and diffusion on closed surfaces. Numerische
Mathematik, 151(4), 873–925. https://doi.org/10.1007/s00211-022-01301-3
bibtex: '@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the
interaction of mean curvature flow and diffusion on closed surfaces}, volume={151},
DOI={10.1007/s00211-022-01301-3},
number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs},
year={2022}, pages={873–925} }'
chicago: 'Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis
for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.”
Numerische Mathematik 151, no. 4 (2022): 873–925. https://doi.org/10.1007/s00211-022-01301-3.'
ieee: 'C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction
of mean curvature flow and diffusion on closed surfaces,” Numerische Mathematik,
vol. 151, no. 4, pp. 873–925, 2022, doi: 10.1007/s00211-022-01301-3.'
mla: Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean
Curvature Flow and Diffusion on Closed Surfaces.” Numerische Mathematik,
vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:10.1007/s00211-022-01301-3.
short: C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.
date_created: 2023-07-10T11:47:11Z
date_updated: 2024-04-03T09:15:44Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01301-3
intvolume: ' 151'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 873-925
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Numerical analysis for the interaction of mean curvature flow and diffusion
on closed surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45963'
abstract:
- lang: eng
text: AbstractThe scattering of electromagnetic
waves from obstacles with wave-material interaction in thin layers on the surface
is described by generalized impedance boundary conditions, which provide effective
approximate models. In particular, this includes a thin coating around a perfect
conductor and the skin effect of a highly conducting material. The approach taken
in this work is to derive, analyse and discretize a system of time-dependent boundary
integral equations that determines the tangential traces of the scattered electric
and magnetic fields. In a familiar second step, the fields are evaluated in the
exterior domain by a representation formula, which uses the time-dependent potential
operators of Maxwell’s equations. The time-dependent boundary integral equation
is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas
boundary elements in space. Using the frequency-explicit bounds from the well-posedness
analysis given here together with known approximation properties of the numerical
methods, the full discretization is proved to be stable and convergent, with explicitly
given rates in the case of sufficient regularity. Taking the same Runge–Kutta
based convolution quadrature for discretizing the time-dependent representation
formulas, the optimal order of convergence is obtained away from the scattering
boundary, whereas an order reduction occurs close to the boundary. The theoretical
results are illustrated by numerical experiments.
author:
- first_name: Jörg
full_name: Nick, Jörg
last_name: Nick
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christian
full_name: Lubich, Christian
last_name: Lubich
citation:
ama: Nick J, Kovács B, Lubich C. Time-dependent electromagnetic scattering from
thin layers. Numerische Mathematik. 2022;150(4):1123-1164. doi:10.1007/s00211-022-01277-0
apa: Nick, J., Kovács, B., & Lubich, C. (2022). Time-dependent electromagnetic
scattering from thin layers. Numerische Mathematik, 150(4), 1123–1164.
https://doi.org/10.1007/s00211-022-01277-0
bibtex: '@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic
scattering from thin layers}, volume={150}, DOI={10.1007/s00211-022-01277-0},
number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2022},
pages={1123–1164} }'
chicago: 'Nick, Jörg, Balázs Kovács, and Christian Lubich. “Time-Dependent Electromagnetic
Scattering from Thin Layers.” Numerische Mathematik 150, no. 4 (2022):
1123–64. https://doi.org/10.1007/s00211-022-01277-0.'
ieee: 'J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering
from thin layers,” Numerische Mathematik, vol. 150, no. 4, pp. 1123–1164,
2022, doi: 10.1007/s00211-022-01277-0.'
mla: Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.”
Numerische Mathematik, vol. 150, no. 4, Springer Science and Business Media
LLC, 2022, pp. 1123–64, doi:10.1007/s00211-022-01277-0.
short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164.
date_created: 2023-07-10T11:44:57Z
date_updated: 2024-04-03T09:18:23Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01277-0
intvolume: ' 150'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1123-1164
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Time-dependent electromagnetic scattering from thin layers
type: journal_article
user_id: '100441'
volume: 150
year: '2022'
...
---
_id: '45964'
abstract:
- lang: eng
text: "Abstract\r\n Maximal parabolic
$L^p$-regularity of linear parabolic equations on an evolving surface is shown
by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity
on a fixed surface. By freezing the coefficients in the parabolic equations at
a fixed time and utilizing a perturbation argument around the freezed time, it
is shown that backward difference time discretizations of linear parabolic equations
on an evolving surface along characteristic trajectories can preserve maximal
$L^p$-regularity in the discrete setting. The result is applied to prove the stability
and convergence of time discretizations of nonlinear parabolic equations on an
evolving surface, with linearly implicit backward differentiation formulae characteristic
trajectories of the surface, for general locally Lipschitz nonlinearities. The
discrete maximal $L^p$-regularity is used to prove the boundedness and stability
of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is
used to bound the nonlinear terms in the stability analysis. Optimal-order error
estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm
is obtained by combining the stability analysis with the consistency estimates."
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Buyang
full_name: Li, Buyang
last_name: Li
citation:
ama: Kovács B, Li B. Maximal regularity of backward difference time discretization
for evolving surface PDEs and its application to nonlinear problems. IMA Journal
of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac033
apa: Kovács, B., & Li, B. (2022). Maximal regularity of backward difference
time discretization for evolving surface PDEs and its application to nonlinear
problems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac033
bibtex: '@article{Kovács_Li_2022, title={Maximal regularity of backward difference
time discretization for evolving surface PDEs and its application to nonlinear
problems}, DOI={10.1093/imanum/drac033},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }'
chicago: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference
Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear
Problems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac033.
ieee: 'B. Kovács and B. Li, “Maximal regularity of backward difference time discretization
for evolving surface PDEs and its application to nonlinear problems,” IMA Journal
of Numerical Analysis, 2022, doi: 10.1093/imanum/drac033.'
mla: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time
Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.”
IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022,
doi:10.1093/imanum/drac033.
short: B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:45:14Z
date_updated: 2024-04-03T09:17:59Z
department:
- _id: '841'
doi: 10.1093/imanum/drac033
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Maximal regularity of backward difference time discretization for evolving
surface PDEs and its application to nonlinear problems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45966'
abstract:
- lang: eng
text: "Abstract\r\n This paper studies
bulk–surface splitting methods of first order for (semilinear) parabolic partial
differential equations with dynamic boundary conditions. The proposed Lie splitting
scheme is based on a reformulation of the problem as a coupled partial differential–algebraic
equation system, i.e., the boundary conditions are considered as a second dynamic
equation that is coupled to the bulk problem. The splitting approach is combined
with bulk–surface finite elements and an implicit Euler discretization of the
two subsystems. We prove first-order convergence of the resulting fully discrete
scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c
h$ for some constant $c>0$. The convergence is also illustrated numerically
using dynamic boundary conditions of Allen–Cahn type."
author:
- first_name: Robert
full_name: Altmann, Robert
last_name: Altmann
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christoph
full_name: Zimmer, Christoph
last_name: Zimmer
citation:
ama: Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems
with dynamic boundary conditions. IMA Journal of Numerical Analysis. 2022;43(2):950-975.
doi:10.1093/imanum/drac002
apa: Altmann, R., Kovács, B., & Zimmer, C. (2022). Bulk–surface Lie splitting
for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical
Analysis, 43(2), 950–975. https://doi.org/10.1093/imanum/drac002
bibtex: '@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting
for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={10.1093/imanum/drac002}, number={2},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022},
pages={950–975} }'
chicago: 'Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie
Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal
of Numerical Analysis 43, no. 2 (2022): 950–75. https://doi.org/10.1093/imanum/drac002.'
ieee: 'R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic
problems with dynamic boundary conditions,” IMA Journal of Numerical Analysis,
vol. 43, no. 2, pp. 950–975, 2022, doi: 10.1093/imanum/drac002.'
mla: Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems
with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol.
43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:10.1093/imanum/drac002.
short: R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022)
950–975.
date_created: 2023-07-10T11:45:49Z
date_updated: 2024-04-03T09:16:47Z
department:
- _id: '841'
doi: 10.1093/imanum/drac002
intvolume: ' 43'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 950-975
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 43
year: '2022'
...
---
_id: '45968'
abstract:
- lang: eng
text: "Abstract\r\n We derive a numerical
method, based on operator splitting, to abstract parabolic semilinear boundary
coupled systems. The method decouples the linear components that describe the
coupling and the dynamics in the abstract bulk- and surface-spaces, and treats
the nonlinear terms similarly to an exponential integrator. The convergence proof
is based on estimates for a recursive formulation of the error, using the parabolic
smoothing property of analytic semigroups, and a careful comparison of the exact
and approximate flows. This analysis also requires a deep understanding of the
effects of the Dirichlet operator (the abstract version of the harmonic extension
operator), which is essential for the stable coupling in our method. Numerical
experiments, including problems with dynamic boundary conditions, reporting on
convergence rates are presented."
author:
- first_name: Petra
full_name: Csomós, Petra
last_name: Csomós
- first_name: Bálint
full_name: Farkas, Bálint
last_name: Farkas
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for
abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis.
Published online 2022. doi:10.1093/imanum/drac079
apa: Csomós, P., Farkas, B., & Kovács, B. (2022). Error estimates for a splitting
integrator for abstract semilinear boundary coupled systems. IMA Journal of
Numerical Analysis. https://doi.org/10.1093/imanum/drac079
bibtex: '@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting
integrator for abstract semilinear boundary coupled systems}, DOI={10.1093/imanum/drac079},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022}
}'
chicago: Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a
Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA
Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac079.
ieee: 'P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator
for abstract semilinear boundary coupled systems,” IMA Journal of Numerical
Analysis, 2022, doi: 10.1093/imanum/drac079.'
mla: Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract
Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis,
Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac079.
short: P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:46:54Z
date_updated: 2024-04-03T09:15:52Z
department:
- _id: '841'
doi: 10.1093/imanum/drac079
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error estimates for a splitting integrator for abstract semilinear boundary
coupled systems
type: journal_article
user_id: '100441'
year: '2022'
...