---
_id: '53316'
abstract:
- lang: eng
text: "AbstractThe quasilinear Keller–Segel system
$$\\begin{aligned} \\left\\{
\\begin{array}{l} u_t=\\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (S(u)\\nabla
v), \\\\ v_t=\\Delta v-v+u, \\end{array}\\right. \\end{aligned}$$\r\n \r\n
\ \r\n \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n u\r\n
\ t\r\n \r\n
\ =\r\n ∇\r\n
\ ·\r\n \r\n
\ (\r\n D\r\n
\ \r\n (\r\n
\ u\r\n )\r\n
\ \r\n ∇\r\n
\ u\r\n )\r\n
\ \r\n -\r\n
\ ∇\r\n ·\r\n
\ \r\n (\r\n
\ S\r\n \r\n
\ (\r\n u\r\n
\ )\r\n \r\n
\ ∇\r\n v\r\n
\ )\r\n \r\n
\ ,\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n \r\n v\r\n
\ t\r\n \r\n
\ =\r\n Δ\r\n
\ v\r\n -\r\n
\ v\r\n +\r\n
\ u\r\n ,\r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n
\ \r\n \r\n \r\n
\ \r\n endowed
with homogeneous Neumann boundary conditions is considered in a bounded domain
$$\\Omega \\subset {\\mathbb
{R}}^n$$\r\n
\ \r\n Ω\r\n ⊂\r\n
\ \r\n \r\n R\r\n
\ \r\n n\r\n
\ \r\n \r\n ,
$$n \\ge 3$$\r\n \r\n
\ n\r\n ≥\r\n
\ 3\r\n \r\n ,
with smooth boundary for sufficiently regular functions D
and S satisfying $$D>0$$\r\n \r\n
\ D\r\n >\r\n
\ 0\r\n \r\n
on $$[0,\\infty )$$\r\n \r\n
\ [\r\n 0\r\n
\ ,\r\n ∞\r\n
\ )\r\n \r\n ,
$$S>0$$\r\n \r\n
\ S\r\n >\r\n
\ 0\r\n \r\n
on $$(0,\\infty )$$\r\n \r\n
\ (\r\n 0\r\n
\ ,\r\n ∞\r\n
\ )\r\n \r\n
and $$S(0)=0$$\r\n \r\n
\ S\r\n (\r\n
\ 0\r\n )\r\n
\ =\r\n 0\r\n
\ \r\n .
On the one hand, it is shown that if $$\\frac{S}{D}$$\r\n \r\n
\ S\r\n D\r\n
\ \r\n
satisfies the subcritical growth condition $$\\begin{aligned}
\\frac{S(s)}{D(s)} \\le C s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge
1 \\qquad \\text{ with } \\text{ some } \\alpha < \\frac{2}{n} \\end{aligned}$$\r\n \r\n
\ \r\n \r\n \r\n
\ \r\n \r\n
\ \r\n S\r\n
\ (\r\n s\r\n
\ )\r\n \r\n
\ \r\n D\r\n
\ (\r\n s\r\n
\ )\r\n \r\n
\ \r\n ≤\r\n
\ C\r\n \r\n
\ s\r\n α\r\n
\ \r\n \r\n \r\n for\r\n
\ \r\n \r\n all\r\n \r\n s\r\n ≥\r\n
\ 1\r\n \r\n \r\n with\r\n
\ \r\n \r\n some\r\n \r\n α\r\n <\r\n
\ \r\n 2\r\n
\ n\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n \r\n
\ and $$C>0$$\r\n \r\n
\ C\r\n >\r\n
\ 0\r\n \r\n ,
then for any sufficiently regular initial data there exists a global weak energy
solution such that $${
\\mathrm{{ess}}} \\sup _{t>0} \\Vert u(t) \\Vert _{L^p(\\Omega )}<\\infty
$$\r\n
\ \r\n ess\r\n \r\n
\ sup\r\n \r\n
\ t\r\n >\r\n
\ 0\r\n \r\n
\ \r\n \r\n \r\n
\ ‖\r\n u\r\n
\ \r\n (\r\n
\ t\r\n )\r\n
\ \r\n ‖\r\n
\ \r\n \r\n \r\n
\ L\r\n p\r\n
\ \r\n \r\n
\ (\r\n Ω\r\n
\ )\r\n \r\n
\ \r\n \r\n <\r\n
\ ∞\r\n \r\n
for some $$p > \\frac{2n}{n+2}$$\r\n \r\n
\ p\r\n >\r\n
\ \r\n \r\n 2\r\n
\ n\r\n \r\n
\ \r\n n\r\n
\ +\r\n 2\r\n
\ \r\n \r\n \r\n
\ . On the
other hand, if $$\\frac{S}{D}$$\r\n \r\n
\ S\r\n D\r\n
\ \r\n
satisfies the supercritical growth condition $$\\begin{aligned}
\\frac{S(s)}{D(s)} \\ge c s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge
1 \\qquad \\text{ with } \\text{ some } \\alpha > \\frac{2}{n} \\end{aligned}$$\r\n \r\n
\ \r\n \r\n \r\n
\ \r\n \r\n
\ \r\n S\r\n
\ (\r\n s\r\n
\ )\r\n \r\n
\ \r\n D\r\n
\ (\r\n s\r\n
\ )\r\n \r\n
\ \r\n ≥\r\n
\ c\r\n \r\n
\ s\r\n α\r\n
\ \r\n \r\n \r\n for\r\n
\ \r\n \r\n all\r\n \r\n s\r\n ≥\r\n
\ 1\r\n \r\n \r\n with\r\n
\ \r\n \r\n some\r\n \r\n α\r\n >\r\n
\ \r\n 2\r\n
\ n\r\n \r\n
\ \r\n \r\n
\ \r\n \r\n \r\n
\ and $$c>0$$\r\n \r\n
\ c\r\n >\r\n
\ 0\r\n \r\n ,
then the nonexistence of a global weak energy solution having the boundedness
property stated above is shown for some initial data in the radial setting. This
establishes some criticality of the value $$\\alpha
= \\frac{2}{n}$$\r\n
\ \r\n α\r\n =\r\n
\ \r\n 2\r\n
\ n\r\n \r\n
\ \r\n
for $$n \\ge 3$$\r\n \r\n
\ n\r\n ≥\r\n
\ 3\r\n \r\n ,
without any additional assumption on the behavior of D(s)
as $$s \\rightarrow \\infty
$$\r\n
\ \r\n s\r\n →\r\n
\ ∞\r\n \r\n ,
in particular without requiring any algebraic lower bound for D.
When applied to the Keller–Segel system with volume-filling effect for probability
distribution functions of the type $$Q(s)
= \\exp (-s^\\beta )$$\r\n
\ \r\n Q\r\n \r\n
\ (\r\n s\r\n
\ )\r\n \r\n
\ =\r\n exp\r\n
\ \r\n (\r\n
\ -\r\n \r\n
\ s\r\n β\r\n
\ \r\n )\r\n
\ \r\n \r\n ,
$$s \\ge 0$$\r\n \r\n
\ s\r\n ≥\r\n
\ 0\r\n \r\n ,
for global solvability the exponent $$\\beta
= \\frac{n-2}{n}$$\r\n
\ \r\n β\r\n =\r\n
\ \r\n \r\n n\r\n
\ -\r\n 2\r\n
\ \r\n n\r\n
\ \r\n \r\n
is seen to be critical.\r\n"
article_number: '26'
author:
- first_name: Christian
full_name: Stinner, Christian
last_name: Stinner
- first_name: Michael
full_name: Winkler, Michael
last_name: Winkler
citation:
ama: Stinner C, Winkler M. A critical exponent in a quasilinear Keller–Segel system
with arbitrarily fast decaying diffusivities accounting for volume-filling effects.
Journal of Evolution Equations. 2024;24(2). doi:10.1007/s00028-024-00954-x
apa: Stinner, C., & Winkler, M. (2024). A critical exponent in a quasilinear
Keller–Segel system with arbitrarily fast decaying diffusivities accounting for
volume-filling effects. Journal of Evolution Equations, 24(2), Article
26. https://doi.org/10.1007/s00028-024-00954-x
bibtex: '@article{Stinner_Winkler_2024, title={A critical exponent in a quasilinear
Keller–Segel system with arbitrarily fast decaying diffusivities accounting for
volume-filling effects}, volume={24}, DOI={10.1007/s00028-024-00954-x},
number={226}, journal={Journal of Evolution Equations}, publisher={Springer Science
and Business Media LLC}, author={Stinner, Christian and Winkler, Michael}, year={2024}
}'
chicago: Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear
Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for
Volume-Filling Effects.” Journal of Evolution Equations 24, no. 2 (2024).
https://doi.org/10.1007/s00028-024-00954-x.
ieee: 'C. Stinner and M. Winkler, “A critical exponent in a quasilinear Keller–Segel
system with arbitrarily fast decaying diffusivities accounting for volume-filling
effects,” Journal of Evolution Equations, vol. 24, no. 2, Art. no. 26,
2024, doi: 10.1007/s00028-024-00954-x.'
mla: Stinner, Christian, and Michael Winkler. “A Critical Exponent in a Quasilinear
Keller–Segel System with Arbitrarily Fast Decaying Diffusivities Accounting for
Volume-Filling Effects.” Journal of Evolution Equations, vol. 24, no. 2,
26, Springer Science and Business Media LLC, 2024, doi:10.1007/s00028-024-00954-x.
short: C. Stinner, M. Winkler, Journal of Evolution Equations 24 (2024).
date_created: 2024-04-07T12:29:25Z
date_updated: 2024-04-07T12:36:21Z
doi: 10.1007/s00028-024-00954-x
intvolume: ' 24'
issue: '2'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
publication: Journal of Evolution Equations
publication_identifier:
issn:
- 1424-3199
- 1424-3202
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast
decaying diffusivities accounting for volume-filling effects
type: journal_article
user_id: '31496'
volume: 24
year: '2024'
...
---
_id: '53542'
abstract:
- lang: eng
text: "AbstractThis work deals with the extension
problem for the fractional Laplacian on Riemannian symmetric spaces G/K
of noncompact type and of general rank, which gives rise to a family of convolution
operators, including the Poisson operator. More precisely, motivated by Euclidean
results for the Poisson semigroup, we study the long-time asymptotic behavior
of solutions to the extension problem for $$L^1$$\r\n \r\n
\ L\r\n 1\r\n
\ \r\n
initial data. In the case of the Laplace–Beltrami operator, we show that if the
initial data are bi-K-invariant, then the solution
to the extension problem behaves asymptotically as the mass times the fundamental
solution, but this convergence may break down in the non-bi-K-invariant
case. In the second part, we investigate the long-time asymptotic behavior of
the extension problem associated with the so-called distinguished Laplacian on
G/K. In this case, we observe
phenomena which are similar to the Euclidean setting for the Poisson semigroup,
such as $$L^1$$\r\n \r\n
\ L\r\n 1\r\n
\ \r\n
asymptotic convergence without the assumption of bi-K-invariance."
article_number: '34'
author:
- first_name: Efthymia
full_name: Papageorgiou, Efthymia
id: '100325'
last_name: Papageorgiou
citation:
ama: Papageorgiou E. Asymptotic behavior of solutions to the extension problem for
the fractional Laplacian on noncompact symmetric spaces. Journal of Evolution
Equations. 2024;24(2). doi:10.1007/s00028-024-00959-6
apa: Papageorgiou, E. (2024). Asymptotic behavior of solutions to the extension
problem for the fractional Laplacian on noncompact symmetric spaces. Journal
of Evolution Equations, 24(2), Article 34. https://doi.org/10.1007/s00028-024-00959-6
bibtex: '@article{Papageorgiou_2024, title={Asymptotic behavior of solutions to
the extension problem for the fractional Laplacian on noncompact symmetric spaces},
volume={24}, DOI={10.1007/s00028-024-00959-6},
number={234}, journal={Journal of Evolution Equations}, publisher={Springer Science
and Business Media LLC}, author={Papageorgiou, Efthymia}, year={2024} }'
chicago: Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension
Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” Journal
of Evolution Equations 24, no. 2 (2024). https://doi.org/10.1007/s00028-024-00959-6.
ieee: 'E. Papageorgiou, “Asymptotic behavior of solutions to the extension problem
for the fractional Laplacian on noncompact symmetric spaces,” Journal of Evolution
Equations, vol. 24, no. 2, Art. no. 34, 2024, doi: 10.1007/s00028-024-00959-6.'
mla: Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension
Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” Journal
of Evolution Equations, vol. 24, no. 2, 34, Springer Science and Business
Media LLC, 2024, doi:10.1007/s00028-024-00959-6.
short: E. Papageorgiou, Journal of Evolution Equations 24 (2024).
date_created: 2024-04-17T13:18:30Z
date_updated: 2024-04-17T13:20:29Z
department:
- _id: '555'
doi: 10.1007/s00028-024-00959-6
intvolume: ' 24'
issue: '2'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
publication: Journal of Evolution Equations
publication_identifier:
issn:
- 1424-3199
- 1424-3202
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Asymptotic behavior of solutions to the extension problem for the fractional
Laplacian on noncompact symmetric spaces
type: journal_article
user_id: '100325'
volume: 24
year: '2024'
...
---
_id: '52806'
author:
- first_name: H.
full_name: Gilbert, H.
last_name: Gilbert
- first_name: M.
full_name: Schürmann, M.
last_name: Schürmann
- first_name: M.
full_name: Liebendörfer, M.
last_name: Liebendörfer
- first_name: D.
full_name: Lawson, D.
last_name: Lawson
- first_name: M.
full_name: Hodds, M.
last_name: Hodds
citation:
ama: 'Gilbert H, Schürmann M, Liebendörfer M, Lawson D, Hodds M. Post-pandemic online
mathematics and statistics support: Practitioners’ opinions in Germany and Great
Britain & Ireland. International Journal of Mathematical Education
in Science and Technology. Published online 2023:1-26. doi:10.1080/0020739x.2023.2184282'
apa: 'Gilbert, H., Schürmann, M., Liebendörfer, M., Lawson, D., & Hodds, M.
(2023). Post-pandemic online mathematics and statistics support: Practitioners’
opinions in Germany and Great Britain & Ireland. International Journal
of Mathematical Education in Science and Technology, 1–26. https://doi.org/10.1080/0020739x.2023.2184282'
bibtex: '@article{Gilbert_Schürmann_Liebendörfer_Lawson_Hodds_2023, title={Post-pandemic
online mathematics and statistics support: Practitioners’ opinions in Germany
and Great Britain & Ireland}, DOI={10.1080/0020739x.2023.2184282},
journal={International Journal of Mathematical Education in Science and Technology},
publisher={Informa UK Limited}, author={Gilbert, H. and Schürmann, M. and Liebendörfer,
M. and Lawson, D. and Hodds, M.}, year={2023}, pages={1–26} }'
chicago: 'Gilbert, H., M. Schürmann, M. Liebendörfer, D. Lawson, and M. Hodds. “Post-Pandemic
Online Mathematics and Statistics Support: Practitioners’ Opinions in Germany
and Great Britain & Ireland.” International Journal of Mathematical
Education in Science and Technology, 2023, 1–26. https://doi.org/10.1080/0020739x.2023.2184282.'
ieee: 'H. Gilbert, M. Schürmann, M. Liebendörfer, D. Lawson, and M. Hodds, “Post-pandemic
online mathematics and statistics support: Practitioners’ opinions in Germany
and Great Britain & Ireland,” International Journal of Mathematical
Education in Science and Technology, pp. 1–26, 2023, doi: 10.1080/0020739x.2023.2184282.'
mla: 'Gilbert, H., et al. “Post-Pandemic Online Mathematics and Statistics Support:
Practitioners’ Opinions in Germany and Great Britain & Ireland.” International
Journal of Mathematical Education in Science and Technology, Informa UK Limited,
2023, pp. 1–26, doi:10.1080/0020739x.2023.2184282.'
short: H. Gilbert, M. Schürmann, M. Liebendörfer, D. Lawson, M. Hodds, International
Journal of Mathematical Education in Science and Technology (2023) 1–26.
date_created: 2024-03-25T10:02:09Z
date_updated: 2024-03-25T10:09:21Z
department:
- _id: '10'
- _id: '625'
- _id: '34'
- _id: '97'
- _id: '98'
doi: 10.1080/0020739x.2023.2184282
keyword:
- Applied Mathematics
- Education
- Mathematics (miscellaneous)
language:
- iso: eng
page: 1-26
publication: International Journal of Mathematical Education in Science and Technology
publication_identifier:
issn:
- 0020-739X
- 1464-5211
publication_status: published
publisher: Informa UK Limited
status: public
title: 'Post-pandemic online mathematics and statistics support: Practitioners’ opinions
in Germany and Great Britain & Ireland'
type: journal_article
user_id: '30933'
year: '2023'
...
---
_id: '35685'
author:
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: Robin
full_name: Göller, Robin
last_name: Göller
- first_name: Lara
full_name: Gildehaus, Lara
last_name: Gildehaus
- first_name: Jörg
full_name: Kortemeyer, Jörg
last_name: Kortemeyer
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Reinhard
full_name: Hochmuth, Reinhard
last_name: Hochmuth
- first_name: Laura
full_name: Ostsieker, Laura
last_name: Ostsieker
- first_name: Jana
full_name: Rode, Jana
last_name: Rode
- first_name: Niclas
full_name: Schaper, Niclas
last_name: Schaper
citation:
ama: Liebendörfer M, Göller R, Gildehaus L, et al. The role of learning strategies
for performance in mathematics courses for engineers. International Journal
of Mathematical Education in Science and Technology. 2022;53(5):1133-1152.
doi:10.1080/0020739x.2021.2023772
apa: Liebendörfer, M., Göller, R., Gildehaus, L., Kortemeyer, J., Biehler, R., Hochmuth,
R., Ostsieker, L., Rode, J., & Schaper, N. (2022). The role of learning strategies
for performance in mathematics courses for engineers. International Journal
of Mathematical Education in Science and Technology, 53(5), 1133–1152.
https://doi.org/10.1080/0020739x.2021.2023772
bibtex: '@article{Liebendörfer_Göller_Gildehaus_Kortemeyer_Biehler_Hochmuth_Ostsieker_Rode_Schaper_2022,
title={The role of learning strategies for performance in mathematics courses
for engineers}, volume={53}, DOI={10.1080/0020739x.2021.2023772},
number={5}, journal={International Journal of Mathematical Education in Science
and Technology}, publisher={Informa UK Limited}, author={Liebendörfer, Michael
and Göller, Robin and Gildehaus, Lara and Kortemeyer, Jörg and Biehler, Rolf and
Hochmuth, Reinhard and Ostsieker, Laura and Rode, Jana and Schaper, Niclas}, year={2022},
pages={1133–1152} }'
chicago: 'Liebendörfer, Michael, Robin Göller, Lara Gildehaus, Jörg Kortemeyer,
Rolf Biehler, Reinhard Hochmuth, Laura Ostsieker, Jana Rode, and Niclas Schaper.
“The Role of Learning Strategies for Performance in Mathematics Courses for Engineers.”
International Journal of Mathematical Education in Science and Technology
53, no. 5 (2022): 1133–52. https://doi.org/10.1080/0020739x.2021.2023772.'
ieee: 'M. Liebendörfer et al., “The role of learning strategies for performance
in mathematics courses for engineers,” International Journal of Mathematical
Education in Science and Technology, vol. 53, no. 5, pp. 1133–1152, 2022,
doi: 10.1080/0020739x.2021.2023772.'
mla: Liebendörfer, Michael, et al. “The Role of Learning Strategies for Performance
in Mathematics Courses for Engineers.” International Journal of Mathematical
Education in Science and Technology, vol. 53, no. 5, Informa UK Limited, 2022,
pp. 1133–52, doi:10.1080/0020739x.2021.2023772.
short: M. Liebendörfer, R. Göller, L. Gildehaus, J. Kortemeyer, R. Biehler, R. Hochmuth,
L. Ostsieker, J. Rode, N. Schaper, International Journal of Mathematical Education
in Science and Technology 53 (2022) 1133–1152.
date_created: 2023-01-10T08:56:30Z
date_updated: 2024-04-18T10:08:30Z
department:
- _id: '363'
- _id: '625'
doi: 10.1080/0020739x.2021.2023772
intvolume: ' 53'
issue: '5'
keyword:
- Applied Mathematics
- Education
- Mathematics (miscellaneous)
language:
- iso: eng
page: 1133-1152
publication: International Journal of Mathematical Education in Science and Technology
publication_identifier:
issn:
- 0020-739X
- 1464-5211
publication_status: published
publisher: Informa UK Limited
status: public
title: The role of learning strategies for performance in mathematics courses for
engineers
type: journal_article
user_id: '37888'
volume: 53
year: '2022'
...
---
_id: '37472'
abstract:
- lang: eng
text: AbstractAs earlier research results suggest
that many mathematics teaching students criticize a missing relevance in their
studies, we explore explanations and interrelationships of their relevance assessments.
We aim at finding out how one could support the students in attributing relevance
to their study programs. A two-fold model for relevance assessments in mathematics
teacher education is proposed, consisting of relevance content and relevance reasons.
We investigate students' relevance perceptions of mathematical topics and of topics’
complexities, as well as their rating of individual and societal/ vocational relevance
reasons, all in relation to their perception of the relevance of their overall
program of study. Contrary to earlier research findings, our results suggest that
mathematics teaching students already do attribute relevance to many content areas
and that a preparation for the teaching profession is not the only reason for
them to assign relevance. There also seem to be many students who would attribute
relevance if they could develop as individuals and pursue their interests. We
suggest that giving students opportunities to set individual priorities in their
studies could hence support their relevance assessments. As low relevance assessments
seem to be connected to students’ motivational problems, students might profit
from motivational support, as well.
author:
- first_name: Christiane
full_name: Büdenbender-Kuklinski, Christiane
last_name: Büdenbender-Kuklinski
- first_name: Reinhard
full_name: Hochmuth, Reinhard
last_name: Hochmuth
- first_name: Michael
full_name: Liebendörfer, Michael
last_name: Liebendörfer
citation:
ama: Büdenbender-Kuklinski C, Hochmuth R, Liebendörfer M. Exploring the Perceived
Relevance of University Mathematics Studies by First-Semester Teaching Students.
International Journal of Research in Undergraduate Mathematics Education.
Published online 2022. doi:10.1007/s40753-022-00188-7
apa: Büdenbender-Kuklinski, C., Hochmuth, R., & Liebendörfer, M. (2022). Exploring
the Perceived Relevance of University Mathematics Studies by First-Semester Teaching
Students. International Journal of Research in Undergraduate Mathematics Education.
https://doi.org/10.1007/s40753-022-00188-7
bibtex: '@article{Büdenbender-Kuklinski_Hochmuth_Liebendörfer_2022, title={Exploring
the Perceived Relevance of University Mathematics Studies by First-Semester Teaching
Students}, DOI={10.1007/s40753-022-00188-7},
journal={International Journal of Research in Undergraduate Mathematics Education},
publisher={Springer Science and Business Media LLC}, author={Büdenbender-Kuklinski,
Christiane and Hochmuth, Reinhard and Liebendörfer, Michael}, year={2022} }'
chicago: Büdenbender-Kuklinski, Christiane, Reinhard Hochmuth, and Michael Liebendörfer.
“Exploring the Perceived Relevance of University Mathematics Studies by First-Semester
Teaching Students.” International Journal of Research in Undergraduate Mathematics
Education, 2022. https://doi.org/10.1007/s40753-022-00188-7.
ieee: 'C. Büdenbender-Kuklinski, R. Hochmuth, and M. Liebendörfer, “Exploring the
Perceived Relevance of University Mathematics Studies by First-Semester Teaching
Students,” International Journal of Research in Undergraduate Mathematics Education,
2022, doi: 10.1007/s40753-022-00188-7.'
mla: Büdenbender-Kuklinski, Christiane, et al. “Exploring the Perceived Relevance
of University Mathematics Studies by First-Semester Teaching Students.” International
Journal of Research in Undergraduate Mathematics Education, Springer Science
and Business Media LLC, 2022, doi:10.1007/s40753-022-00188-7.
short: C. Büdenbender-Kuklinski, R. Hochmuth, M. Liebendörfer, International Journal
of Research in Undergraduate Mathematics Education (2022).
date_created: 2023-01-18T22:22:49Z
date_updated: 2023-01-18T22:43:43Z
department:
- _id: '10'
doi: 10.1007/s40753-022-00188-7
keyword:
- Education
- Mathematics (miscellaneous)
language:
- iso: eng
publication: International Journal of Research in Undergraduate Mathematics Education
publication_identifier:
issn:
- 2198-9745
- 2198-9753
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Exploring the Perceived Relevance of University Mathematics Studies by First-Semester
Teaching Students
type: journal_article
user_id: '30933'
year: '2022'
...
---
_id: '35778'
abstract:
- lang: eng
text: 'AbstractThe aim of the special issue is
to bring together important current international research on innovative teaching
and learning practices in mathematics in engineering education, and to develop
deeper understandings of the characteristics of current teaching and learning
practices that can inform the design and implementation of future innovative practice.
The focus of this review paper is to provide a state-of-the-art overview of this
emerging field at the cross-roads between mathematics and engineering education,
in addition to introducing the papers of this special issue. To guide this paper,
we posed three review questions: (1) How can current (teaching/learning/study)
practices of mathematics in engineering education be characterized with a view
towards innovation?; (2) What are the ‘resources’ (cognitive, material, digital,
social) used, and what are those that appear also well suited for innovative courses?;
(3) What are promising innovative practices in mathematics in engineering education,
and what are the implications for curriculum reform? Looking back across the studies
we summarized in the review, we conclude that they are lagging behind the more
fundamental changes that are happening in engineering education, whilst addressing
selected aspects of innovative changes within the current system of engineering
education. At the same time, the nine papers of this special issue contribute
new perspectives for innovative practices in mathematics in engineering education,
for a better understanding of current practices and for future research.'
author:
- first_name: Birgit
full_name: Pepin, Birgit
last_name: Pepin
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Ghislaine
full_name: Gueudet, Ghislaine
last_name: Gueudet
citation:
ama: 'Pepin B, Biehler R, Gueudet G. Mathematics in Engineering Education: a Review
of the Recent Literature with a View towards Innovative Practices. International
Journal of Research in Undergraduate Mathematics Education. 2021;7(2):163-188.
doi:10.1007/s40753-021-00139-8'
apa: 'Pepin, B., Biehler, R., & Gueudet, G. (2021). Mathematics in Engineering
Education: a Review of the Recent Literature with a View towards Innovative Practices.
International Journal of Research in Undergraduate Mathematics Education,
7(2), 163–188. https://doi.org/10.1007/s40753-021-00139-8'
bibtex: '@article{Pepin_Biehler_Gueudet_2021, title={Mathematics in Engineering
Education: a Review of the Recent Literature with a View towards Innovative Practices},
volume={7}, DOI={10.1007/s40753-021-00139-8},
number={2}, journal={International Journal of Research in Undergraduate Mathematics
Education}, publisher={Springer Science and Business Media LLC}, author={Pepin,
Birgit and Biehler, Rolf and Gueudet, Ghislaine}, year={2021}, pages={163–188}
}'
chicago: 'Pepin, Birgit, Rolf Biehler, and Ghislaine Gueudet. “Mathematics in Engineering
Education: A Review of the Recent Literature with a View towards Innovative Practices.”
International Journal of Research in Undergraduate Mathematics Education
7, no. 2 (2021): 163–88. https://doi.org/10.1007/s40753-021-00139-8.'
ieee: 'B. Pepin, R. Biehler, and G. Gueudet, “Mathematics in Engineering Education:
a Review of the Recent Literature with a View towards Innovative Practices,” International
Journal of Research in Undergraduate Mathematics Education, vol. 7, no. 2,
pp. 163–188, 2021, doi: 10.1007/s40753-021-00139-8.'
mla: 'Pepin, Birgit, et al. “Mathematics in Engineering Education: A Review of the
Recent Literature with a View towards Innovative Practices.” International
Journal of Research in Undergraduate Mathematics Education, vol. 7, no. 2,
Springer Science and Business Media LLC, 2021, pp. 163–88, doi:10.1007/s40753-021-00139-8.'
short: B. Pepin, R. Biehler, G. Gueudet, International Journal of Research in Undergraduate
Mathematics Education 7 (2021) 163–188.
date_created: 2023-01-10T10:43:08Z
date_updated: 2024-04-18T09:48:52Z
department:
- _id: '363'
doi: 10.1007/s40753-021-00139-8
intvolume: ' 7'
issue: '2'
keyword:
- Education
- Mathematics (miscellaneous)
language:
- iso: eng
page: 163-188
publication: International Journal of Research in Undergraduate Mathematics Education
publication_identifier:
issn:
- 2198-9745
- 2198-9753
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'Mathematics in Engineering Education: a Review of the Recent Literature with
a View towards Innovative Practices'
type: journal_article
user_id: '37888'
volume: 7
year: '2021'
...
---
_id: '35702'
abstract:
- lang: eng
text: AbstractMathematics Learning Support Centres
are becoming more and more common in higher education both internationally and
in Germany. Whereas it is clear that their quality largely depends on a functioning
interaction in consultations, little is known about how such consultations proceed
in detail. On the basis of models from the literature and recorded support sessions
(N = 36), we constructed a process model that divides consultations into four
ideal–typical phases. In the individual consultations, forward or backward leaps
occur, but overall the model seems to describe the data well. A high intercoder
reliability shows that it can be applied consistently on real data by different
researchers. An analysis of the consultations between students and tutors shows
that both mainly work on past attempts or thoughts of the students to solve the
exercise or problems and on concrete strategies to solve a problem within the
session. In contrast, very little time is dedicated to summarizing and reflecting
the solution. The data allows for a more in-depth discussion of what constitutes
quality in advising processes and how it might be further explored. Practically,
the model may structure support sessions and help in focussing on different goals
in different phases.
author:
- first_name: Mirko
full_name: Schürmann, Mirko
id: '59707'
last_name: Schürmann
orcid: 0000-0003-2646-085X
- first_name: Anja
full_name: Panse, Anja
last_name: Panse
- first_name: Zain
full_name: Shaikh, Zain
last_name: Shaikh
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Niclas
full_name: Schaper, Niclas
last_name: Schaper
- first_name: Michael
full_name: Liebendörfer, Michael
id: '30933'
last_name: Liebendörfer
orcid: 0000-0001-9887-2074
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: Schürmann M, Panse A, Shaikh Z, et al. Consultation Phases in Mathematics Learning
and Support Centres. International Journal of Research in Undergraduate Mathematics
Education. 2021;8(1):94-120. doi:10.1007/s40753-021-00154-9
apa: Schürmann, M., Panse, A., Shaikh, Z., Biehler, R., Schaper, N., Liebendörfer,
M., & Hilgert, J. (2021). Consultation Phases in Mathematics Learning and
Support Centres. International Journal of Research in Undergraduate Mathematics
Education, 8(1), 94–120. https://doi.org/10.1007/s40753-021-00154-9
bibtex: '@article{Schürmann_Panse_Shaikh_Biehler_Schaper_Liebendörfer_Hilgert_2021,
title={Consultation Phases in Mathematics Learning and Support Centres}, volume={8},
DOI={10.1007/s40753-021-00154-9},
number={1}, journal={International Journal of Research in Undergraduate Mathematics
Education}, publisher={Springer Science and Business Media LLC}, author={Schürmann,
Mirko and Panse, Anja and Shaikh, Zain and Biehler, Rolf and Schaper, Niclas and
Liebendörfer, Michael and Hilgert, Joachim}, year={2021}, pages={94–120} }'
chicago: 'Schürmann, Mirko, Anja Panse, Zain Shaikh, Rolf Biehler, Niclas Schaper,
Michael Liebendörfer, and Joachim Hilgert. “Consultation Phases in Mathematics
Learning and Support Centres.” International Journal of Research in Undergraduate
Mathematics Education 8, no. 1 (2021): 94–120. https://doi.org/10.1007/s40753-021-00154-9.'
ieee: 'M. Schürmann et al., “Consultation Phases in Mathematics Learning
and Support Centres,” International Journal of Research in Undergraduate Mathematics
Education, vol. 8, no. 1, pp. 94–120, 2021, doi: 10.1007/s40753-021-00154-9.'
mla: Schürmann, Mirko, et al. “Consultation Phases in Mathematics Learning and Support
Centres.” International Journal of Research in Undergraduate Mathematics Education,
vol. 8, no. 1, Springer Science and Business Media LLC, 2021, pp. 94–120, doi:10.1007/s40753-021-00154-9.
short: M. Schürmann, A. Panse, Z. Shaikh, R. Biehler, N. Schaper, M. Liebendörfer,
J. Hilgert, International Journal of Research in Undergraduate Mathematics Education
8 (2021) 94–120.
date_created: 2023-01-10T09:09:23Z
date_updated: 2024-04-18T10:09:08Z
department:
- _id: '363'
- _id: '423'
- _id: '91'
- _id: '625'
doi: 10.1007/s40753-021-00154-9
intvolume: ' 8'
issue: '1'
keyword:
- Education
- Mathematics (miscellaneous)
language:
- iso: eng
page: 94-120
publication: International Journal of Research in Undergraduate Mathematics Education
publication_identifier:
issn:
- 2198-9745
- 2198-9753
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Consultation Phases in Mathematics Learning and Support Centres
type: journal_article
user_id: '37888'
volume: 8
year: '2021'
...
---
_id: '37443'
abstract:
- lang: eng
text: 'AbstractThe range of teaching materials
now available is becoming increasingly diverse. Despite this, however, the use
and influence of textbooks in teaching still remains very high. When instructing
reading comprehension, teachers often use textbooks as the basis for teaching
in language lessons. Establishing a good match between textbooks and the skills
to be acquired is therefore essential. In this paper, I investigate whether textbooks
used in Austrian schools can adequately support the teaching of reading comprehension
skills. Since reading comprehension is the basis for acquiring knowledge in all
subjects, science textbooks are examined in addition to (German) language lesson
textbooks. Thus, the content pages of four language textbooks and four science
textbooks for fourth and sixth grade were analysed in terms of five different
categories, i.e. general structural setup, learning goals, text types, text structures,
and activities. The results reveal clear variations with respect to learning goals
in language textbooks. For example, the extent to which reading comprehension
is addressed ranges from 13.64 to 69.70%, depending on the book used. Although
not addressed as a learning goal in the science textbooks, reading comprehension
is often presupposed, especially in sixth grade. While the instruction of reading
comprehension ought to entail coverage of reading strategies, this is often neglected,
or only dealt with indirectly. Given the diversity of textbooks analysed, it seems
all the more important to stress that teachers should: 1) clarify the goals and
teaching strategies of a book before using it, 2) become aware of strategies that
support the development of students'' reading comprehension, and 3) use textbooks
as a complementary (and not sole) tool to support reading comprehension in all
subjects.'
author:
- first_name: Susanne
full_name: Seifert, Susanne
id: '97270'
last_name: Seifert
citation:
ama: Seifert S. Is Reading Comprehension Taken for Granted? An Analysis of Austrian
Textbooks in Fourth and Sixth Grade. Technology, Knowledge and Learning.
2021;26(2):383-405. doi:10.1007/s10758-021-09490-w
apa: Seifert, S. (2021). Is Reading Comprehension Taken for Granted? An Analysis
of Austrian Textbooks in Fourth and Sixth Grade. Technology, Knowledge and
Learning, 26(2), 383–405. https://doi.org/10.1007/s10758-021-09490-w
bibtex: '@article{Seifert_2021, title={Is Reading Comprehension Taken for Granted?
An Analysis of Austrian Textbooks in Fourth and Sixth Grade}, volume={26}, DOI={10.1007/s10758-021-09490-w},
number={2}, journal={Technology, Knowledge and Learning}, publisher={Springer
Science and Business Media LLC}, author={Seifert, Susanne}, year={2021}, pages={383–405}
}'
chicago: 'Seifert, Susanne. “Is Reading Comprehension Taken for Granted? An Analysis
of Austrian Textbooks in Fourth and Sixth Grade.” Technology, Knowledge and
Learning 26, no. 2 (2021): 383–405. https://doi.org/10.1007/s10758-021-09490-w.'
ieee: 'S. Seifert, “Is Reading Comprehension Taken for Granted? An Analysis of Austrian
Textbooks in Fourth and Sixth Grade,” Technology, Knowledge and Learning,
vol. 26, no. 2, pp. 383–405, 2021, doi: 10.1007/s10758-021-09490-w.'
mla: Seifert, Susanne. “Is Reading Comprehension Taken for Granted? An Analysis
of Austrian Textbooks in Fourth and Sixth Grade.” Technology, Knowledge and
Learning, vol. 26, no. 2, Springer Science and Business Media LLC, 2021, pp.
383–405, doi:10.1007/s10758-021-09490-w.
short: S. Seifert, Technology, Knowledge and Learning 26 (2021) 383–405.
date_created: 2023-01-18T16:10:52Z
date_updated: 2023-01-18T16:45:42Z
department:
- _id: '645'
doi: 10.1007/s10758-021-09490-w
intvolume: ' 26'
issue: '2'
keyword:
- Computer Science Applications
- Human-Computer Interaction
- Education
- Mathematics (miscellaneous)
language:
- iso: eng
page: 383-405
publication: Technology, Knowledge and Learning
publication_identifier:
issn:
- 2211-1662
- 2211-1670
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Is Reading Comprehension Taken for Granted? An Analysis of Austrian Textbooks
in Fourth and Sixth Grade
type: journal_article
user_id: '97270'
volume: 26
year: '2021'
...
---
_id: '53333'
author:
- first_name: Michael
full_name: Winkler, Michael
id: '31496'
last_name: Winkler
citation:
ama: Winkler M. $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary
superlinear degradation. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE.
Published online 2021:141-172. doi:10.2422/2036-2145.202005_016
apa: Winkler, M. (2021). $L^1$ solutions to parabolic Keller-Segel systems involving
arbitrary superlinear degradation. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
DI SCIENZE, 141–172. https://doi.org/10.2422/2036-2145.202005_016
bibtex: '@article{Winkler_2021, title={$L^1$ solutions to parabolic Keller-Segel
systems involving arbitrary superlinear degradation}, DOI={10.2422/2036-2145.202005_016},
journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, publisher={Scuola
Normale Superiore - Edizioni della Normale}, author={Winkler, Michael}, year={2021},
pages={141–172} }'
chicago: Winkler, Michael. “$L^1$ Solutions to Parabolic Keller-Segel Systems Involving
Arbitrary Superlinear Degradation.” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
DI SCIENZE, 2021, 141–72. https://doi.org/10.2422/2036-2145.202005_016.
ieee: 'M. Winkler, “$L^1$ solutions to parabolic Keller-Segel systems involving
arbitrary superlinear degradation,” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
DI SCIENZE, pp. 141–172, 2021, doi: 10.2422/2036-2145.202005_016.'
mla: Winkler, Michael. “$L^1$ Solutions to Parabolic Keller-Segel Systems Involving
Arbitrary Superlinear Degradation.” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE
DI SCIENZE, Scuola Normale Superiore - Edizioni della Normale, 2021, pp. 141–72,
doi:10.2422/2036-2145.202005_016.
short: M. Winkler, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (2021) 141–172.
date_created: 2024-04-07T12:45:49Z
date_updated: 2025-12-18T20:15:27Z
doi: 10.2422/2036-2145.202005_016
keyword:
- Mathematics (miscellaneous)
- Theoretical Computer Science
language:
- iso: eng
page: 141-172
publication: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
publication_identifier:
issn:
- 2036-2145
- 0391-173X
publication_status: published
publisher: Scuola Normale Superiore - Edizioni della Normale
status: public
title: $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear
degradation
type: journal_article
user_id: '31496'
year: '2021'
...
---
_id: '34665'
author:
- first_name: Tobias
full_name: Black, Tobias
id: '23686'
last_name: Black
orcid: 0000-0001-9963-0800
- first_name: Johannes
full_name: Lankeit, Johannes
last_name: Lankeit
- first_name: Masaaki
full_name: Mizukami, Masaaki
last_name: Mizukami
citation:
ama: Black T, Lankeit J, Mizukami M. Singular sensitivity in a Keller–Segel-fluid
system. Journal of Evolution Equations. 2017;18(2):561-581. doi:10.1007/s00028-017-0411-5
apa: Black, T., Lankeit, J., & Mizukami, M. (2017). Singular sensitivity in
a Keller–Segel-fluid system. Journal of Evolution Equations, 18(2),
561–581. https://doi.org/10.1007/s00028-017-0411-5
bibtex: '@article{Black_Lankeit_Mizukami_2017, title={Singular sensitivity in a
Keller–Segel-fluid system}, volume={18}, DOI={10.1007/s00028-017-0411-5},
number={2}, journal={Journal of Evolution Equations}, publisher={Springer Science
and Business Media LLC}, author={Black, Tobias and Lankeit, Johannes and Mizukami,
Masaaki}, year={2017}, pages={561–581} }'
chicago: 'Black, Tobias, Johannes Lankeit, and Masaaki Mizukami. “Singular Sensitivity
in a Keller–Segel-Fluid System.” Journal of Evolution Equations 18, no.
2 (2017): 561–81. https://doi.org/10.1007/s00028-017-0411-5.'
ieee: 'T. Black, J. Lankeit, and M. Mizukami, “Singular sensitivity in a Keller–Segel-fluid
system,” Journal of Evolution Equations, vol. 18, no. 2, pp. 561–581, 2017,
doi: 10.1007/s00028-017-0411-5.'
mla: Black, Tobias, et al. “Singular Sensitivity in a Keller–Segel-Fluid System.”
Journal of Evolution Equations, vol. 18, no. 2, Springer Science and Business
Media LLC, 2017, pp. 561–81, doi:10.1007/s00028-017-0411-5.
short: T. Black, J. Lankeit, M. Mizukami, Journal of Evolution Equations 18 (2017)
561–581.
date_created: 2022-12-21T09:47:13Z
date_updated: 2022-12-21T10:05:25Z
department:
- _id: '34'
- _id: '10'
- _id: '90'
doi: 10.1007/s00028-017-0411-5
intvolume: ' 18'
issue: '2'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
page: 561-581
publication: Journal of Evolution Equations
publication_identifier:
issn:
- 1424-3199
- 1424-3202
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Singular sensitivity in a Keller–Segel-fluid system
type: journal_article
user_id: '23686'
volume: 18
year: '2017'
...
---
_id: '34886'
abstract:
- lang: eng
text: We give asymptotic upper and lower bounds for the number of squarefree d (0
< d ≤ X) such that the equation x² − dy²= −1 is solvable. These estimates, as
usual, can equivalently be interpreted in terms of real quadratic fields with
a fundamental unit with norm −1 and give strong evidence in the direction of a
conjecture due to P. Stevenhagen.
author:
- first_name: Étienne
full_name: Fouvry, Étienne
last_name: Fouvry
- first_name: Jürgen
full_name: Klüners, Jürgen
id: '21202'
last_name: Klüners
citation:
ama: Fouvry É, Klüners J. On the negative Pell equation. Annals of Mathematics.
2010;172(3):2035-2104. doi:10.4007/annals.2010.172.2035
apa: Fouvry, É., & Klüners, J. (2010). On the negative Pell equation. Annals
of Mathematics, 172(3), 2035–2104. https://doi.org/10.4007/annals.2010.172.2035
bibtex: '@article{Fouvry_Klüners_2010, title={On the negative Pell equation}, volume={172},
DOI={10.4007/annals.2010.172.2035},
number={3}, journal={Annals of Mathematics}, publisher={Annals of Mathematics},
author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={2035–2104} }'
chicago: 'Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.”
Annals of Mathematics 172, no. 3 (2010): 2035–2104. https://doi.org/10.4007/annals.2010.172.2035.'
ieee: 'É. Fouvry and J. Klüners, “On the negative Pell equation,” Annals of Mathematics,
vol. 172, no. 3, pp. 2035–2104, 2010, doi: 10.4007/annals.2010.172.2035.'
mla: Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” Annals
of Mathematics, vol. 172, no. 3, Annals of Mathematics, 2010, pp. 2035–104,
doi:10.4007/annals.2010.172.2035.
short: É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.
date_created: 2022-12-23T09:09:02Z
date_updated: 2023-03-06T09:50:37Z
department:
- _id: '102'
doi: 10.4007/annals.2010.172.2035
intvolume: ' 172'
issue: '3'
keyword:
- Statistics
- Probability and Uncertainty
- Mathematics (miscellaneous)
language:
- iso: eng
page: 2035-2104
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Annals of Mathematics
status: public
title: On the negative Pell equation
type: journal_article
user_id: '93826'
volume: 172
year: '2010'
...