---
_id: '51208'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>Approximation of subdifferentials
    is one of the main tasks when computing descent directions for nonsmooth optimization
    problems. In this article, we propose a bisection method for weakly lower semismooth
    functions which is able to compute new subgradients that improve a given approximation
    in case a direction with insufficient descent was computed. Combined with a recently
    proposed deterministic gradient sampling approach, this yields a deterministic
    and provably convergent way to approximate subdifferentials for computing descent
    directions.</jats:p>
author:
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
citation:
  ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
    optimization. <i>Computational Optimization and Applications</i>. Published online
    2024. doi:<a href="https://doi.org/10.1007/s10589-024-00552-0">10.1007/s10589-024-00552-0</a>
  apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling
    in nonsmooth optimization. <i>Computational Optimization and Applications</i>.
    <a href="https://doi.org/10.1007/s10589-024-00552-0">https://doi.org/10.1007/s10589-024-00552-0</a>
  bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic
    gradient sampling in nonsmooth optimization}, DOI={<a href="https://doi.org/10.1007/s10589-024-00552-0">10.1007/s10589-024-00552-0</a>},
    journal={Computational Optimization and Applications}, publisher={Springer Science
    and Business Media LLC}, author={Gebken, Bennet}, year={2024} }'
  chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
    in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>,
    2024. <a href="https://doi.org/10.1007/s10589-024-00552-0">https://doi.org/10.1007/s10589-024-00552-0</a>.
  ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling
    in nonsmooth optimization,” <i>Computational Optimization and Applications</i>,
    2024, doi: <a href="https://doi.org/10.1007/s10589-024-00552-0">10.1007/s10589-024-00552-0</a>.'
  mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
    in Nonsmooth Optimization.” <i>Computational Optimization and Applications</i>,
    Springer Science and Business Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s10589-024-00552-0">10.1007/s10589-024-00552-0</a>.
  short: B. Gebken, Computational Optimization and Applications (2024).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
  issn:
  - 0926-6003
  - 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
year: '2024'
...
---
_id: '52218'
article_number: '112642'
author:
- first_name: Peter
  full_name: Lenz, Peter
  last_name: Lenz
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
citation:
  ama: Lenz P, Mahnken R. Multiscale simulation of polymer curing of composites combined
    mean-field homogenisation methods at large strains. <i>International Journal of
    Solids and Structures</i>. 2024;290. doi:<a href="https://doi.org/10.1016/j.ijsolstr.2023.112642">10.1016/j.ijsolstr.2023.112642</a>
  apa: Lenz, P., &#38; Mahnken, R. (2024). Multiscale simulation of polymer curing
    of composites combined mean-field homogenisation methods at large strains. <i>International
    Journal of Solids and Structures</i>, <i>290</i>, Article 112642. <a href="https://doi.org/10.1016/j.ijsolstr.2023.112642">https://doi.org/10.1016/j.ijsolstr.2023.112642</a>
  bibtex: '@article{Lenz_Mahnken_2024, title={Multiscale simulation of polymer curing
    of composites combined mean-field homogenisation methods at large strains}, volume={290},
    DOI={<a href="https://doi.org/10.1016/j.ijsolstr.2023.112642">10.1016/j.ijsolstr.2023.112642</a>},
    number={112642}, journal={International Journal of Solids and Structures}, publisher={Elsevier
    BV}, author={Lenz, Peter and Mahnken, Rolf}, year={2024} }'
  chicago: Lenz, Peter, and Rolf Mahnken. “Multiscale Simulation of Polymer Curing
    of Composites Combined Mean-Field Homogenisation Methods at Large Strains.” <i>International
    Journal of Solids and Structures</i> 290 (2024). <a href="https://doi.org/10.1016/j.ijsolstr.2023.112642">https://doi.org/10.1016/j.ijsolstr.2023.112642</a>.
  ieee: 'P. Lenz and R. Mahnken, “Multiscale simulation of polymer curing of composites
    combined mean-field homogenisation methods at large strains,” <i>International
    Journal of Solids and Structures</i>, vol. 290, Art. no. 112642, 2024, doi: <a
    href="https://doi.org/10.1016/j.ijsolstr.2023.112642">10.1016/j.ijsolstr.2023.112642</a>.'
  mla: Lenz, Peter, and Rolf Mahnken. “Multiscale Simulation of Polymer Curing of
    Composites Combined Mean-Field Homogenisation Methods at Large Strains.” <i>International
    Journal of Solids and Structures</i>, vol. 290, 112642, Elsevier BV, 2024, doi:<a
    href="https://doi.org/10.1016/j.ijsolstr.2023.112642">10.1016/j.ijsolstr.2023.112642</a>.
  short: P. Lenz, R. Mahnken, International Journal of Solids and Structures 290 (2024).
date_created: 2024-02-29T13:57:56Z
date_updated: 2024-02-29T13:58:14Z
department:
- _id: '9'
- _id: '154'
- _id: '321'
doi: 10.1016/j.ijsolstr.2023.112642
intvolume: '       290'
keyword:
- Applied Mathematics
- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics
- General Materials Science
- Modeling and Simulation
language:
- iso: eng
publication: International Journal of Solids and Structures
publication_identifier:
  issn:
  - 0020-7683
publication_status: published
publisher: Elsevier BV
quality_controlled: '1'
status: public
title: Multiscale simulation of polymer curing of composites combined mean-field homogenisation
  methods at large strains
type: journal_article
user_id: '335'
volume: 290
year: '2024'
...
---
_id: '52233'
abstract:
- lang: eng
  text: ELDIRK methods are defined to have an <jats:italic>Explicit Last</jats:italic>
    stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge-Kutta</jats:italic>
    methods, with the consequence, that no additional system of equations must be
    solved, compared to the embedded RK method. Two general formulations for second-
    and third-order ELDIRK methods have been obtained recently in Mahnken [21] with
    specific schemes,  e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule
    and the embedded Ellsiepen method. In the first part of this paper, we investigate
    some general stability characteristics of ELDIRK methods, and it will be shown
    that the above specific RK schemes are not A-stable. Therefore, in the second
    part, the above-mentioned general formulations are used for further stability
    investigations, with the aim to construct new second- and third-order ELDIRK methods
    which simultaneously are A-stable. Two numerical examples are concerned with the
    curing for a thermosetting material and phase-field RVE modeling for crystallinity
    and orientation. The numerical results confirm the theoretical results on convergence
    order and stability.
author:
- first_name: Rolf
  full_name: Mahnken, Rolf
  id: '335'
  last_name: Mahnken
- first_name: Hendrik
  full_name: Westermann, Hendrik
  id: '60816'
  last_name: Westermann
  orcid: 0000-0002-5034-9708
citation:
  ama: Mahnken R, Westermann H. Construction of A-stable explicit last-stage diagonal
    implicit Runge–Kutta (ELDIRK) methods. <i>Computational Mechanics</i>. Published
    online 2024. doi:<a href="https://doi.org/10.1007/s00466-024-02442-y">10.1007/s00466-024-02442-y</a>
  apa: Mahnken, R., &#38; Westermann, H. (2024). Construction of A-stable explicit
    last-stage diagonal implicit Runge–Kutta (ELDIRK) methods. <i>Computational Mechanics</i>.
    <a href="https://doi.org/10.1007/s00466-024-02442-y">https://doi.org/10.1007/s00466-024-02442-y</a>
  bibtex: '@article{Mahnken_Westermann_2024, title={Construction of A-stable explicit
    last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}, DOI={<a href="https://doi.org/10.1007/s00466-024-02442-y">10.1007/s00466-024-02442-y</a>},
    journal={Computational Mechanics}, publisher={Springer Science and Business Media
    LLC}, author={Mahnken, Rolf and Westermann, Hendrik}, year={2024} }'
  chicago: Mahnken, Rolf, and Hendrik Westermann. “Construction of A-Stable Explicit
    Last-Stage Diagonal Implicit Runge–Kutta (ELDIRK) Methods.” <i>Computational Mechanics</i>,
    2024. <a href="https://doi.org/10.1007/s00466-024-02442-y">https://doi.org/10.1007/s00466-024-02442-y</a>.
  ieee: 'R. Mahnken and H. Westermann, “Construction of A-stable explicit last-stage
    diagonal implicit Runge–Kutta (ELDIRK) methods,” <i>Computational Mechanics</i>,
    2024, doi: <a href="https://doi.org/10.1007/s00466-024-02442-y">10.1007/s00466-024-02442-y</a>.'
  mla: Mahnken, Rolf, and Hendrik Westermann. “Construction of A-Stable Explicit Last-Stage
    Diagonal Implicit Runge–Kutta (ELDIRK) Methods.” <i>Computational Mechanics</i>,
    Springer Science and Business Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s00466-024-02442-y">10.1007/s00466-024-02442-y</a>.
  short: R. Mahnken, H. Westermann, Computational Mechanics (2024).
date_created: 2024-03-03T13:23:28Z
date_updated: 2024-03-19T12:14:07Z
department:
- _id: '154'
- _id: '321'
doi: 10.1007/s00466-024-02442-y
keyword:
- Applied Mathematics
- Computational Mathematics
- Computational Theory and Mathematics
- Mechanical Engineering
- Ocean Engineering
- Computational Mechanics
language:
- iso: eng
publication: Computational Mechanics
publication_identifier:
  issn:
  - 0178-7675
  - 1432-0924
publication_status: published
publisher: Springer Science and Business Media LLC
quality_controlled: '1'
status: public
title: Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta
  (ELDIRK) methods
type: journal_article
user_id: '335'
year: '2024'
...
---
_id: '52726'
abstract:
- lang: eng
  text: Heteroclinic structures organize global features of dynamical systems. We
    analyse whether heteroclinic structures can arise in network dynamics with higher-order
    interactions which describe the nonlinear interactions between three or more units.
    We find that while commonly analysed model equations such as network dynamics
    on undirected hypergraphs may be useful to describe local dynamics such as cluster
    synchronization, they give rise to obstructions that allow to design of heteroclinic
    structures in phase space. By contrast, directed hypergraphs break the homogeneity
    and lead to vector fields that support heteroclinic structures.
article_type: original
author:
- first_name: Christian
  full_name: Bick, Christian
  last_name: Bick
- first_name: Sören
  full_name: von der Gracht, Sören
  id: '97359'
  last_name: von der Gracht
  orcid: 0000-0002-8054-2058
citation:
  ama: Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems
    with higher-order interactions. <i>Journal of Complex Networks</i>. 2024;12(2).
    doi:<a href="https://doi.org/10.1093/comnet/cnae009">10.1093/comnet/cnae009</a>
  apa: Bick, C., &#38; von der Gracht, S. (2024). Heteroclinic dynamics in network
    dynamical systems with higher-order interactions. <i>Journal of Complex Networks</i>,
    <i>12</i>(2). <a href="https://doi.org/10.1093/comnet/cnae009">https://doi.org/10.1093/comnet/cnae009</a>
  bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network
    dynamical systems with higher-order interactions}, volume={12}, DOI={<a href="https://doi.org/10.1093/comnet/cnae009">10.1093/comnet/cnae009</a>},
    number={2}, journal={Journal of Complex Networks}, publisher={Oxford University
    Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024}
    }'
  chicago: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
    Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i>
    12, no. 2 (2024). <a href="https://doi.org/10.1093/comnet/cnae009">https://doi.org/10.1093/comnet/cnae009</a>.
  ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical
    systems with higher-order interactions,” <i>Journal of Complex Networks</i>, vol.
    12, no. 2, 2024, doi: <a href="https://doi.org/10.1093/comnet/cnae009">10.1093/comnet/cnae009</a>.'
  mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
    Dynamical Systems with Higher-Order Interactions.” <i>Journal of Complex Networks</i>,
    vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:<a href="https://doi.org/10.1093/comnet/cnae009">10.1093/comnet/cnae009</a>.
  short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).
date_created: 2024-03-22T09:04:57Z
date_updated: 2024-03-22T09:11:53Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1093/comnet/cnae009
external_id:
  arxiv:
  - '2309.02006'
file:
- access_level: closed
  content_type: application/pdf
  creator: svdg
  date_created: 2024-03-22T09:06:07Z
  date_updated: 2024-03-22T09:06:07Z
  file_id: '52728'
  file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf
  file_size: 649155
  relation: main_file
  success: 1
file_date_updated: 2024-03-22T09:06:07Z
has_accepted_license: '1'
intvolume: '        12'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
- Management Science and Operations Research
- Computer Networks and Communications
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf
oa: '1'
publication: Journal of Complex Networks
publication_identifier:
  issn:
  - 2051-1329
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Heteroclinic dynamics in network dynamical systems with higher-order interactions
type: journal_article
user_id: '97359'
volume: 12
year: '2024'
...
---
_id: '49905'
abstract:
- lang: eng
  text: "For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected
    r-graph has s pairwise disjoint perfect matchings. There are only a few values
    of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for
    all t \x03 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤
    3l − 6 for every l ≥ 3 and r ≥ 2l."
author:
- first_name: Yulai
  full_name: Ma, Yulai
  id: '92748'
  last_name: Ma
- first_name: Davide
  full_name: Mattiolo, Davide
  last_name: Mattiolo
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint
    Perfect Matchings in Regular Graphs. <i>Combinatorica</i>. 2024;44:429-440. doi:<a
    href="https://doi.org/10.1007/s00493-023-00078-9">10.1007/s00493-023-00078-9</a>
  apa: Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2024). Edge-Connectivity
    and Pairwise Disjoint Perfect Matchings in Regular Graphs. <i>Combinatorica</i>,
    <i>44</i>, 429–440. <a href="https://doi.org/10.1007/s00493-023-00078-9">https://doi.org/10.1007/s00493-023-00078-9</a>
  bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise
    Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={<a href="https://doi.org/10.1007/s00493-023-00078-9">10.1007/s00493-023-00078-9</a>},
    journal={Combinatorica}, publisher={Springer Science and Business Media LLC},
    author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus},
    year={2024}, pages={429–440} }'
  chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
    “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.”
    <i>Combinatorica</i> 44 (2024): 429–40. <a href="https://doi.org/10.1007/s00493-023-00078-9">https://doi.org/10.1007/s00493-023-00078-9</a>.'
  ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise
    Disjoint Perfect Matchings in Regular Graphs,” <i>Combinatorica</i>, vol. 44,
    pp. 429–440, 2024, doi: <a href="https://doi.org/10.1007/s00493-023-00078-9">10.1007/s00493-023-00078-9</a>.'
  mla: Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings
    in Regular Graphs.” <i>Combinatorica</i>, vol. 44, Springer Science and Business
    Media LLC, 2024, pp. 429–40, doi:<a href="https://doi.org/10.1007/s00493-023-00078-9">10.1007/s00493-023-00078-9</a>.
  short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.
date_created: 2023-12-20T10:31:27Z
date_updated: 2024-03-22T12:11:35Z
department:
- _id: '542'
doi: 10.1007/s00493-023-00078-9
intvolume: '        44'
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 429-440
publication: Combinatorica
publication_identifier:
  issn:
  - 0209-9683
  - 1439-6912
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs
type: journal_article
user_id: '15540'
volume: 44
year: '2024'
...
---
_id: '53316'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>The quasilinear Keller–Segel system
    <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned} \\left\\{
    \\begin{array}{l} u_t=\\nabla \\cdot (D(u)\\nabla u) - \\nabla \\cdot (S(u)\\nabla
    v), \\\\ v_t=\\Delta v-v+u, \\end{array}\\right. \\end{aligned}$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n
    \                         <mml:mfenced>\r\n                            <mml:mrow>\r\n
    \                             <mml:mtable>\r\n                                <mml:mtr>\r\n
    \                                 <mml:mtd>\r\n                                    <mml:mrow>\r\n
    \                                     <mml:msub>\r\n                                        <mml:mi>u</mml:mi>\r\n
    \                                       <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n
    \                                     <mml:mo>=</mml:mo>\r\n                                      <mml:mi>∇</mml:mi>\r\n
    \                                     <mml:mo>·</mml:mo>\r\n                                      <mml:mrow>\r\n
    \                                       <mml:mo>(</mml:mo>\r\n                                        <mml:mi>D</mml:mi>\r\n
    \                                       <mml:mrow>\r\n                                          <mml:mo>(</mml:mo>\r\n
    \                                         <mml:mi>u</mml:mi>\r\n                                          <mml:mo>)</mml:mo>\r\n
    \                                       </mml:mrow>\r\n                                        <mml:mi>∇</mml:mi>\r\n
    \                                       <mml:mi>u</mml:mi>\r\n                                        <mml:mo>)</mml:mo>\r\n
    \                                     </mml:mrow>\r\n                                      <mml:mo>-</mml:mo>\r\n
    \                                     <mml:mi>∇</mml:mi>\r\n                                      <mml:mo>·</mml:mo>\r\n
    \                                     <mml:mrow>\r\n                                        <mml:mo>(</mml:mo>\r\n
    \                                       <mml:mi>S</mml:mi>\r\n                                        <mml:mrow>\r\n
    \                                         <mml:mo>(</mml:mo>\r\n                                          <mml:mi>u</mml:mi>\r\n
    \                                         <mml:mo>)</mml:mo>\r\n                                        </mml:mrow>\r\n
    \                                       <mml:mi>∇</mml:mi>\r\n                                        <mml:mi>v</mml:mi>\r\n
    \                                       <mml:mo>)</mml:mo>\r\n                                      </mml:mrow>\r\n
    \                                     <mml:mo>,</mml:mo>\r\n                                    </mml:mrow>\r\n
    \                                 </mml:mtd>\r\n                                </mml:mtr>\r\n
    \                               <mml:mtr>\r\n                                  <mml:mtd>\r\n
    \                                   <mml:mrow>\r\n                                      <mml:mrow
    />\r\n                                      <mml:msub>\r\n                                        <mml:mi>v</mml:mi>\r\n
    \                                       <mml:mi>t</mml:mi>\r\n                                      </mml:msub>\r\n
    \                                     <mml:mo>=</mml:mo>\r\n                                      <mml:mi>Δ</mml:mi>\r\n
    \                                     <mml:mi>v</mml:mi>\r\n                                      <mml:mo>-</mml:mo>\r\n
    \                                     <mml:mi>v</mml:mi>\r\n                                      <mml:mo>+</mml:mo>\r\n
    \                                     <mml:mi>u</mml:mi>\r\n                                      <mml:mo>,</mml:mo>\r\n
    \                                   </mml:mrow>\r\n                                  </mml:mtd>\r\n
    \                               </mml:mtr>\r\n                              </mml:mtable>\r\n
    \                           </mml:mrow>\r\n                          </mml:mfenced>\r\n
    \                       </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula>endowed
    with homogeneous Neumann boundary conditions is considered in a bounded domain
    <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Omega \\subset {\\mathbb
    {R}}^n$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>Ω</mml:mi>\r\n                    <mml:mo>⊂</mml:mo>\r\n
    \                   <mml:msup>\r\n                      <mml:mrow>\r\n                        <mml:mi>R</mml:mi>\r\n
    \                     </mml:mrow>\r\n                      <mml:mi>n</mml:mi>\r\n
    \                   </mml:msup>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \\ge 3$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>n</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n
    \                   <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    with smooth boundary for sufficiently regular functions <jats:italic>D</jats:italic>
    and <jats:italic>S</jats:italic> satisfying <jats:inline-formula><jats:alternatives><jats:tex-math>$$D&gt;0$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>D</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n
    \                   <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    on <jats:inline-formula><jats:alternatives><jats:tex-math>$$[0,\\infty )$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mo>[</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n
    \                   <mml:mo>,</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n
    \                   <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    <jats:inline-formula><jats:alternatives><jats:tex-math>$$S&gt;0$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>S</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n
    \                   <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    on <jats:inline-formula><jats:alternatives><jats:tex-math>$$(0,\\infty )$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mo>(</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n
    \                   <mml:mo>,</mml:mo>\r\n                    <mml:mi>∞</mml:mi>\r\n
    \                   <mml:mo>)</mml:mo>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    and <jats:inline-formula><jats:alternatives><jats:tex-math>$$S(0)=0$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>S</mml:mi>\r\n                    <mml:mo>(</mml:mo>\r\n
    \                   <mml:mn>0</mml:mn>\r\n                    <mml:mo>)</mml:mo>\r\n
    \                   <mml:mo>=</mml:mo>\r\n                    <mml:mn>0</mml:mn>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>.
    On the one hand, it is shown that if <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\frac{S}{D}$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mfrac>\r\n
    \                   <mml:mi>S</mml:mi>\r\n                    <mml:mi>D</mml:mi>\r\n
    \                 </mml:mfrac>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    satisfies the subcritical growth condition <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned}
    \\frac{S(s)}{D(s)} \\le C s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge
    1 \\qquad \\text{ with } \\text{ some } \\alpha &lt; \\frac{2}{n} \\end{aligned}$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n
    \                         <mml:mrow>\r\n                            <mml:mfrac>\r\n
    \                             <mml:mrow>\r\n                                <mml:mi>S</mml:mi>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mrow>\r\n                                <mml:mi>D</mml:mi>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                           </mml:mfrac>\r\n                            <mml:mo>≤</mml:mo>\r\n
    \                           <mml:mi>C</mml:mi>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>s</mml:mi>\r\n                              <mml:mi>α</mml:mi>\r\n
    \                           </mml:msup>\r\n                            <mml:mspace
    />\r\n                            <mml:mspace />\r\n                            <mml:mtext>for</mml:mtext>\r\n
    \                           <mml:mspace />\r\n                            <mml:mspace
    />\r\n                            <mml:mtext>all</mml:mtext>\r\n                            <mml:mspace
    />\r\n                            <mml:mi>s</mml:mi>\r\n                            <mml:mo>≥</mml:mo>\r\n
    \                           <mml:mn>1</mml:mn>\r\n                            <mml:mspace
    />\r\n                            <mml:mspace />\r\n                            <mml:mtext>with</mml:mtext>\r\n
    \                           <mml:mspace />\r\n                            <mml:mspace
    />\r\n                            <mml:mtext>some</mml:mtext>\r\n                            <mml:mspace
    />\r\n                            <mml:mi>α</mml:mi>\r\n                            <mml:mo>&lt;</mml:mo>\r\n
    \                           <mml:mfrac>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                             <mml:mi>n</mml:mi>\r\n                            </mml:mfrac>\r\n
    \                         </mml:mrow>\r\n                        </mml:mtd>\r\n
    \                     </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n
    \               </mml:math></jats:alternatives></jats:disp-formula>and <jats:inline-formula><jats:alternatives><jats:tex-math>$$C&gt;0$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>C</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n
    \                   <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    then for any sufficiently regular initial data there exists a global weak energy
    solution such that <jats:inline-formula><jats:alternatives><jats:tex-math>$${
    \\mathrm{{ess}}} \\sup _{t&gt;0} \\Vert u(t) \\Vert _{L^p(\\Omega )}&lt;\\infty
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>ess</mml:mi>\r\n                    <mml:msub>\r\n
    \                     <mml:mo>sup</mml:mo>\r\n                      <mml:mrow>\r\n
    \                       <mml:mi>t</mml:mi>\r\n                        <mml:mo>&gt;</mml:mo>\r\n
    \                       <mml:mn>0</mml:mn>\r\n                      </mml:mrow>\r\n
    \                   </mml:msub>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n
    \                       <mml:mo>‖</mml:mo>\r\n                        <mml:mi>u</mml:mi>\r\n
    \                       <mml:mrow>\r\n                          <mml:mo>(</mml:mo>\r\n
    \                         <mml:mi>t</mml:mi>\r\n                          <mml:mo>)</mml:mo>\r\n
    \                       </mml:mrow>\r\n                        <mml:mo>‖</mml:mo>\r\n
    \                     </mml:mrow>\r\n                      <mml:mrow>\r\n                        <mml:msup>\r\n
    \                         <mml:mi>L</mml:mi>\r\n                          <mml:mi>p</mml:mi>\r\n
    \                       </mml:msup>\r\n                        <mml:mrow>\r\n
    \                         <mml:mo>(</mml:mo>\r\n                          <mml:mi>Ω</mml:mi>\r\n
    \                         <mml:mo>)</mml:mo>\r\n                        </mml:mrow>\r\n
    \                     </mml:mrow>\r\n                    </mml:msub>\r\n                    <mml:mo>&lt;</mml:mo>\r\n
    \                   <mml:mi>∞</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    for some <jats:inline-formula><jats:alternatives><jats:tex-math>$$p &gt; \\frac{2n}{n+2}$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>p</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n
    \                   <mml:mfrac>\r\n                      <mml:mrow>\r\n                        <mml:mn>2</mml:mn>\r\n
    \                       <mml:mi>n</mml:mi>\r\n                      </mml:mrow>\r\n
    \                     <mml:mrow>\r\n                        <mml:mi>n</mml:mi>\r\n
    \                       <mml:mo>+</mml:mo>\r\n                        <mml:mn>2</mml:mn>\r\n
    \                     </mml:mrow>\r\n                    </mml:mfrac>\r\n                  </mml:mrow>\r\n
    \               </mml:math></jats:alternatives></jats:inline-formula>. On the
    other hand, if <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\frac{S}{D}$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mfrac>\r\n
    \                   <mml:mi>S</mml:mi>\r\n                    <mml:mi>D</mml:mi>\r\n
    \                 </mml:mfrac>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    satisfies the supercritical growth condition <jats:disp-formula><jats:alternatives><jats:tex-math>$$\\begin{aligned}
    \\frac{S(s)}{D(s)} \\ge c s^\\alpha \\qquad \\text{ for } \\text{ all } s\\ge
    1 \\qquad \\text{ with } \\text{ some } \\alpha &gt; \\frac{2}{n} \\end{aligned}$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n
    \                         <mml:mrow>\r\n                            <mml:mfrac>\r\n
    \                             <mml:mrow>\r\n                                <mml:mi>S</mml:mi>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                             <mml:mrow>\r\n                                <mml:mi>D</mml:mi>\r\n
    \                               <mml:mo>(</mml:mo>\r\n                                <mml:mi>s</mml:mi>\r\n
    \                               <mml:mo>)</mml:mo>\r\n                              </mml:mrow>\r\n
    \                           </mml:mfrac>\r\n                            <mml:mo>≥</mml:mo>\r\n
    \                           <mml:mi>c</mml:mi>\r\n                            <mml:msup>\r\n
    \                             <mml:mi>s</mml:mi>\r\n                              <mml:mi>α</mml:mi>\r\n
    \                           </mml:msup>\r\n                            <mml:mspace
    />\r\n                            <mml:mspace />\r\n                            <mml:mtext>for</mml:mtext>\r\n
    \                           <mml:mspace />\r\n                            <mml:mspace
    />\r\n                            <mml:mtext>all</mml:mtext>\r\n                            <mml:mspace
    />\r\n                            <mml:mi>s</mml:mi>\r\n                            <mml:mo>≥</mml:mo>\r\n
    \                           <mml:mn>1</mml:mn>\r\n                            <mml:mspace
    />\r\n                            <mml:mspace />\r\n                            <mml:mtext>with</mml:mtext>\r\n
    \                           <mml:mspace />\r\n                            <mml:mspace
    />\r\n                            <mml:mtext>some</mml:mtext>\r\n                            <mml:mspace
    />\r\n                            <mml:mi>α</mml:mi>\r\n                            <mml:mo>&gt;</mml:mo>\r\n
    \                           <mml:mfrac>\r\n                              <mml:mn>2</mml:mn>\r\n
    \                             <mml:mi>n</mml:mi>\r\n                            </mml:mfrac>\r\n
    \                         </mml:mrow>\r\n                        </mml:mtd>\r\n
    \                     </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n
    \               </mml:math></jats:alternatives></jats:disp-formula>and <jats:inline-formula><jats:alternatives><jats:tex-math>$$c&gt;0$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>c</mml:mi>\r\n                    <mml:mo>&gt;</mml:mo>\r\n
    \                   <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha
    = \\frac{2}{n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>α</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n
    \                   <mml:mfrac>\r\n                      <mml:mn>2</mml:mn>\r\n
    \                     <mml:mi>n</mml:mi>\r\n                    </mml:mfrac>\r\n
    \                 </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    for <jats:inline-formula><jats:alternatives><jats:tex-math>$$n \\ge 3$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>n</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n
    \                   <mml:mn>3</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    without any additional assumption on the behavior of <jats:italic>D</jats:italic>(<jats:italic>s</jats:italic>)
    as <jats:inline-formula><jats:alternatives><jats:tex-math>$$s \\rightarrow \\infty
    $$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>s</mml:mi>\r\n                    <mml:mo>→</mml:mo>\r\n
    \                   <mml:mi>∞</mml:mi>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    in particular without requiring any algebraic lower bound for <jats:italic>D</jats:italic>.
    When applied to the Keller–Segel system with volume-filling effect for probability
    distribution functions of the type <jats:inline-formula><jats:alternatives><jats:tex-math>$$Q(s)
    = \\exp (-s^\\beta )$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>Q</mml:mi>\r\n                    <mml:mrow>\r\n
    \                     <mml:mo>(</mml:mo>\r\n                      <mml:mi>s</mml:mi>\r\n
    \                     <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n
    \                   <mml:mo>=</mml:mo>\r\n                    <mml:mo>exp</mml:mo>\r\n
    \                   <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n
    \                     <mml:mo>-</mml:mo>\r\n                      <mml:msup>\r\n
    \                       <mml:mi>s</mml:mi>\r\n                        <mml:mi>β</mml:mi>\r\n
    \                     </mml:msup>\r\n                      <mml:mo>)</mml:mo>\r\n
    \                   </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    <jats:inline-formula><jats:alternatives><jats:tex-math>$$s \\ge 0$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n
    \                   <mml:mi>s</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n
    \                   <mml:mn>0</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>,
    for global solvability the exponent <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta
    = \\frac{n-2}{n}$$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>β</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n
    \                   <mml:mfrac>\r\n                      <mml:mrow>\r\n                        <mml:mi>n</mml:mi>\r\n
    \                       <mml:mo>-</mml:mo>\r\n                        <mml:mn>2</mml:mn>\r\n
    \                     </mml:mrow>\r\n                      <mml:mi>n</mml:mi>\r\n
    \                   </mml:mfrac>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    is seen to be critical.\r\n</jats:p>"
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.
    <i>Journal of Evolution Equations</i>. 2024;24(2). doi:<a href="https://doi.org/10.1007/s00028-024-00954-x">10.1007/s00028-024-00954-x</a>
  apa: Stinner, C., &#38; Winkler, M. (2024). A critical exponent in a quasilinear
    Keller–Segel system with arbitrarily fast decaying diffusivities accounting for
    volume-filling effects. <i>Journal of Evolution Equations</i>, <i>24</i>(2), Article
    26. <a href="https://doi.org/10.1007/s00028-024-00954-x">https://doi.org/10.1007/s00028-024-00954-x</a>
  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={<a href="https://doi.org/10.1007/s00028-024-00954-x">10.1007/s00028-024-00954-x</a>},
    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.” <i>Journal of Evolution Equations</i> 24, no. 2 (2024).
    <a href="https://doi.org/10.1007/s00028-024-00954-x">https://doi.org/10.1007/s00028-024-00954-x</a>.
  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,” <i>Journal of Evolution Equations</i>, vol. 24, no. 2, Art. no. 26,
    2024, doi: <a href="https://doi.org/10.1007/s00028-024-00954-x">10.1007/s00028-024-00954-x</a>.'
  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.” <i>Journal of Evolution Equations</i>, vol. 24, no. 2,
    26, Springer Science and Business Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s00028-024-00954-x">10.1007/s00028-024-00954-x</a>.
  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: '53315'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional
    domain  and for a given nondecreasing positive unbounded , for each  and  the
    inequality\r\n<jats:disp-formula />is shown to hold for any positive  fulfilling\r\n<jats:disp-formula
    />This is thereafter applied to nonglobal solutions of the Keller–Segel system
    coupled to the incompressible Navier–Stokes equations through transport and buoyancy,
    and it is seen that in any such blow‐up event the corresponding population density
    cannot remain uniformly integrable over  near its explosion time.</jats:p>"
author:
- first_name: Yulan
  full_name: Wang, Yulan
  last_name: Wang
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Wang Y, Winkler M. An interpolation inequality involving $L\log L$ spaces and
    application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes
    system. <i>Journal of the London Mathematical Society</i>. 2024;109(3). doi:<a
    href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>
  apa: Wang, Y., &#38; Winkler, M. (2024). An interpolation inequality involving $L\log
    L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional
    Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>,
    <i>109</i>(3). <a href="https://doi.org/10.1112/jlms.12885">https://doi.org/10.1112/jlms.12885</a>
  bibtex: '@article{Wang_Winkler_2024, title={An interpolation inequality involving
    $L\log L$ spaces and application to the characterization of blow‐up behavior in
    a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>},
    number={3}, journal={Journal of the London Mathematical Society}, publisher={Wiley},
    author={Wang, Yulan and Winkler, Michael}, year={2024} }'
  chicago: Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving
    $L\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in
    a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London
    Mathematical Society</i> 109, no. 3 (2024). <a href="https://doi.org/10.1112/jlms.12885">https://doi.org/10.1112/jlms.12885</a>.
  ieee: 'Y. Wang and M. Winkler, “An interpolation inequality involving $L\log L$
    spaces and application to the characterization of blow‐up behavior in a two‐dimensional
    Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>,
    vol. 109, no. 3, 2024, doi: <a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>.'
  mla: Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\log
    L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional
    Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>,
    vol. 109, no. 3, Wiley, 2024, doi:<a href="https://doi.org/10.1112/jlms.12885">10.1112/jlms.12885</a>.
  short: Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).
date_created: 2024-04-07T12:27:28Z
date_updated: 2024-04-07T12:36:25Z
doi: 10.1112/jlms.12885
intvolume: '       109'
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
publication: Journal of the London Mathematical Society
publication_identifier:
  issn:
  - 0024-6107
  - 1469-7750
publication_status: published
publisher: Wiley
status: public
title: An interpolation inequality involving $L\log L$ spaces and application to the
  characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes
  system
type: journal_article
user_id: '31496'
volume: 109
year: '2024'
...
---
_id: '53542'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>This work deals with the extension
    problem for the fractional Laplacian on Riemannian symmetric spaces <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic>
    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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n
    \                   <mml:mi>L</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n
    \                 </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    initial data. In the case of the Laplace–Beltrami operator, we show that if the
    initial data are bi-<jats:italic>K</jats:italic>-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-<jats:italic>K</jats:italic>-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
    <jats:italic>G</jats:italic>/<jats:italic>K</jats:italic>. In this case, we observe
    phenomena which are similar to the Euclidean setting for the Poisson semigroup,
    such as <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msup>\r\n
    \                   <mml:mi>L</mml:mi>\r\n                    <mml:mn>1</mml:mn>\r\n
    \                 </mml:msup>\r\n                </mml:math></jats:alternatives></jats:inline-formula>
    asymptotic convergence without the assumption of bi-<jats:italic>K</jats:italic>-invariance.</jats:p>"
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. <i>Journal of Evolution
    Equations</i>. 2024;24(2). doi:<a href="https://doi.org/10.1007/s00028-024-00959-6">10.1007/s00028-024-00959-6</a>
  apa: Papageorgiou, E. (2024). Asymptotic behavior of solutions to the extension
    problem for the fractional Laplacian on noncompact symmetric spaces. <i>Journal
    of Evolution Equations</i>, <i>24</i>(2), Article 34. <a href="https://doi.org/10.1007/s00028-024-00959-6">https://doi.org/10.1007/s00028-024-00959-6</a>
  bibtex: '@article{Papageorgiou_2024, title={Asymptotic behavior of solutions to
    the extension problem for the fractional Laplacian on noncompact symmetric spaces},
    volume={24}, DOI={<a href="https://doi.org/10.1007/s00028-024-00959-6">10.1007/s00028-024-00959-6</a>},
    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.” <i>Journal
    of Evolution Equations</i> 24, no. 2 (2024). <a href="https://doi.org/10.1007/s00028-024-00959-6">https://doi.org/10.1007/s00028-024-00959-6</a>.
  ieee: 'E. Papageorgiou, “Asymptotic behavior of solutions to the extension problem
    for the fractional Laplacian on noncompact symmetric spaces,” <i>Journal of Evolution
    Equations</i>, vol. 24, no. 2, Art. no. 34, 2024, doi: <a href="https://doi.org/10.1007/s00028-024-00959-6">10.1007/s00028-024-00959-6</a>.'
  mla: Papageorgiou, Efthymia. “Asymptotic Behavior of Solutions to the Extension
    Problem for the Fractional Laplacian on Noncompact Symmetric Spaces.” <i>Journal
    of Evolution Equations</i>, vol. 24, no. 2, 34, Springer Science and Business
    Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s00028-024-00959-6">10.1007/s00028-024-00959-6</a>.
  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: '55191'
author:
- first_name: Sebastian
  full_name: Rezat, Sebastian
  id: '31132'
  last_name: Rezat
- first_name: Jana
  full_name: Visnovska, Jana
  last_name: Visnovska
- first_name: Guorui
  full_name: Yan, Guorui
  last_name: Yan
- first_name: Moneoang
  full_name: Leshota, Moneoang
  last_name: Leshota
- first_name: Hussein
  full_name: Sabra, Hussein
  last_name: Sabra
citation:
  ama: 'Rezat S, Visnovska J, Yan G, Leshota M, Sabra H. Topic Study Group 41: Research
    and development on textbooks and resources for learning and teaching mathematics.
    In: <i>Proceedings of the 14th International Congress on Mathematical Education</i>.
    Vol 1. World Scientific; 2024:537–545. doi:<a href="https://doi.org/10.1142/9789811287152_0065">10.1142/9789811287152_0065</a>'
  apa: 'Rezat, S., Visnovska, J., Yan, G., Leshota, M., &#38; Sabra, H. (2024). Topic
    Study Group 41: Research and development on textbooks and resources for learning
    and teaching mathematics. <i>Proceedings of the 14th International Congress on
    Mathematical Education</i>, <i>1</i>, 537–545. <a href="https://doi.org/10.1142/9789811287152_0065">https://doi.org/10.1142/9789811287152_0065</a>'
  bibtex: '@inproceedings{Rezat_Visnovska_Yan_Leshota_Sabra_2024, place={Shanghai,
    China}, title={Topic Study Group 41: Research and development on textbooks and
    resources for learning and teaching mathematics}, volume={1}, DOI={<a href="https://doi.org/10.1142/9789811287152_0065">10.1142/9789811287152_0065</a>},
    booktitle={Proceedings of the 14th International Congress on Mathematical Education},
    publisher={World Scientific}, author={Rezat, Sebastian and Visnovska, Jana and
    Yan, Guorui and Leshota, Moneoang and Sabra, Hussein}, year={2024}, pages={537–545}
    }'
  chicago: 'Rezat, Sebastian, Jana Visnovska, Guorui Yan, Moneoang Leshota, and Hussein
    Sabra. “Topic Study Group 41: Research and Development on Textbooks and Resources
    for Learning and Teaching Mathematics.” In <i>Proceedings of the 14th International
    Congress on Mathematical Education</i>, 1:537–545. Shanghai, China: World Scientific,
    2024. <a href="https://doi.org/10.1142/9789811287152_0065">https://doi.org/10.1142/9789811287152_0065</a>.'
  ieee: 'S. Rezat, J. Visnovska, G. Yan, M. Leshota, and H. Sabra, “Topic Study Group
    41: Research and development on textbooks and resources for learning and teaching
    mathematics,” in <i>Proceedings of the 14th International Congress on Mathematical
    Education</i>, 2024, vol. 1, pp. 537–545, doi: <a href="https://doi.org/10.1142/9789811287152_0065">10.1142/9789811287152_0065</a>.'
  mla: 'Rezat, Sebastian, et al. “Topic Study Group 41: Research and Development on
    Textbooks and Resources for Learning and Teaching Mathematics.” <i>Proceedings
    of the 14th International Congress on Mathematical Education</i>, vol. 1, World
    Scientific, 2024, pp. 537–545, doi:<a href="https://doi.org/10.1142/9789811287152_0065">10.1142/9789811287152_0065</a>.'
  short: 'S. Rezat, J. Visnovska, G. Yan, M. Leshota, H. Sabra, in: Proceedings of
    the 14th International Congress on Mathematical Education, World Scientific, Shanghai,
    China, 2024, pp. 537–545.'
date_created: 2024-07-12T06:58:06Z
date_updated: 2024-07-12T07:02:20Z
department:
- _id: '360'
doi: 10.1142/9789811287152_0065
intvolume: '         1'
keyword:
- Mathematics
- Mathematik
- Textbook
- Curriculum Resources
- Schulbuch
language:
- iso: eng
page: 537–545
place: Shanghai, China
publication: Proceedings of the 14th International Congress on Mathematical Education
publication_status: published
publisher: World Scientific
status: public
title: 'Topic Study Group 41: Research and development on textbooks and resources
  for learning and teaching mathematics'
type: conference
user_id: '31132'
volume: 1
year: '2024'
...
---
_id: '53300'
article_number: '128125'
author:
- first_name: Dominik
  full_name: Brennecken, Dominik
  id: '55911'
  last_name: Brennecken
citation:
  ama: Brennecken D. Hankel transform, K-Bessel functions and zeta distributions in
    the Dunkl setting. <i>Journal of Mathematical Analysis and Applications</i>. 2024;535(2).
    doi:<a href="https://doi.org/10.1016/j.jmaa.2024.128125">10.1016/j.jmaa.2024.128125</a>
  apa: Brennecken, D. (2024). Hankel transform, K-Bessel functions and zeta distributions
    in the Dunkl setting. <i>Journal of Mathematical Analysis and Applications</i>,
    <i>535</i>(2), Article 128125. <a href="https://doi.org/10.1016/j.jmaa.2024.128125">https://doi.org/10.1016/j.jmaa.2024.128125</a>
  bibtex: '@article{Brennecken_2024, title={Hankel transform, K-Bessel functions and
    zeta distributions in the Dunkl setting}, volume={535}, DOI={<a href="https://doi.org/10.1016/j.jmaa.2024.128125">10.1016/j.jmaa.2024.128125</a>},
    number={2128125}, journal={Journal of Mathematical Analysis and Applications},
    publisher={Elsevier BV}, author={Brennecken, Dominik}, year={2024} }'
  chicago: Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions
    in the Dunkl Setting.” <i>Journal of Mathematical Analysis and Applications</i>
    535, no. 2 (2024). <a href="https://doi.org/10.1016/j.jmaa.2024.128125">https://doi.org/10.1016/j.jmaa.2024.128125</a>.
  ieee: 'D. Brennecken, “Hankel transform, K-Bessel functions and zeta distributions
    in the Dunkl setting,” <i>Journal of Mathematical Analysis and Applications</i>,
    vol. 535, no. 2, Art. no. 128125, 2024, doi: <a href="https://doi.org/10.1016/j.jmaa.2024.128125">10.1016/j.jmaa.2024.128125</a>.'
  mla: Brennecken, Dominik. “Hankel Transform, K-Bessel Functions and Zeta Distributions
    in the Dunkl Setting.” <i>Journal of Mathematical Analysis and Applications</i>,
    vol. 535, no. 2, 128125, Elsevier BV, 2024, doi:<a href="https://doi.org/10.1016/j.jmaa.2024.128125">10.1016/j.jmaa.2024.128125</a>.
  short: D. Brennecken, Journal of Mathematical Analysis and Applications 535 (2024).
date_created: 2024-04-05T13:55:33Z
date_updated: 2024-09-03T14:40:46Z
department:
- _id: '555'
doi: 10.1016/j.jmaa.2024.128125
intvolume: '       535'
issue: '2'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
publication: Journal of Mathematical Analysis and Applications
publication_identifier:
  issn:
  - 0022-247X
publication_status: published
publisher: Elsevier BV
status: public
title: Hankel transform, K-Bessel functions and zeta distributions in the Dunkl setting
type: journal_article
user_id: '55911'
volume: 535
year: '2024'
...
---
_id: '52089'
abstract:
- lang: eng
  text: |-
    <jats:title>Abstract</jats:title><jats:p>Image restoration via alternating direction method of multipliers (ADMM) has gained large interest within the last decade. Solving standard problems of Gaussian and Poisson noise, the set of “Total Variation” (TV)-based regularizers proved to be efficient and versatile. In the last few years, the “Total Generalized Variation” (TGV) approach combined TV regularizers of different orders adaptively to better suit local regions in the image. This improved the technique significantly. The approach solved the staircase problem inherent of the first-order TV while keeping the beneficial edge preservation. The iterative minimization for the augmented Lagrangian of TGV problems requires four important parameters: two penalty parameters <jats:inline-formula><jats:alternatives><jats:tex-math>$${\rho }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mi>ρ</mml:mi>
                  </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$${\eta }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mi>η</mml:mi>
                  </mml:math></jats:alternatives></jats:inline-formula> and two regularization parameters <jats:inline-formula><jats:alternatives><jats:tex-math>$${\lambda _{0}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:msub>
                      <mml:mi>λ</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                  </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$${\lambda _{1}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:msub>
                      <mml:mi>λ</mml:mi>
                      <mml:mn>1</mml:mn>
                    </mml:msub>
                  </mml:math></jats:alternatives></jats:inline-formula>. The choice of penalty parameters decides on the convergence speed, and the regularization parameters decide on the impact of the respective regularizer and are determined by the noise level in the image. For scientific applications of such algorithms, an automated and thus objective method to determine these parameters is essential to receive unbiased results independent of the user. Obviously, both sets of parameters are to be well chosen to achieve optimal results, too. In this paper, a method is proposed to adaptively choose optimal <jats:inline-formula><jats:alternatives><jats:tex-math>$${\rho }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mi>ρ</mml:mi>
                  </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$${\eta }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:mi>η</mml:mi>
                  </mml:math></jats:alternatives></jats:inline-formula> values for the iteration to converge faster, based on the primal and dual residuals arising from the optimality conditions of the augmented Lagrangian. Further, we show how to choose <jats:inline-formula><jats:alternatives><jats:tex-math>$${\lambda _{0}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:msub>
                      <mml:mi>λ</mml:mi>
                      <mml:mn>0</mml:mn>
                    </mml:msub>
                  </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$${\lambda _{1}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                    <mml:msub>
                      <mml:mi>λ</mml:mi>
                      <mml:mn>1</mml:mn>
                    </mml:msub>
                  </mml:math></jats:alternatives></jats:inline-formula> based on the inherent noise in the image.</jats:p>
author:
- first_name: Christian
  full_name: Zietlow, Christian
  last_name: Zietlow
- first_name: Jörg K. N.
  full_name: Lindner, Jörg K. N.
  last_name: Lindner
citation:
  ama: Zietlow C, Lindner JKN. ADMM-TGV image restoration for scientific applications
    with unbiased parameter choice. <i>Numerical Algorithms</i>. Published online
    2024. doi:<a href="https://doi.org/10.1007/s11075-024-01759-2">10.1007/s11075-024-01759-2</a>
  apa: Zietlow, C., &#38; Lindner, J. K. N. (2024). ADMM-TGV image restoration for
    scientific applications with unbiased parameter choice. <i>Numerical Algorithms</i>.
    <a href="https://doi.org/10.1007/s11075-024-01759-2">https://doi.org/10.1007/s11075-024-01759-2</a>
  bibtex: '@article{Zietlow_Lindner_2024, title={ADMM-TGV image restoration for scientific
    applications with unbiased parameter choice}, DOI={<a href="https://doi.org/10.1007/s11075-024-01759-2">10.1007/s11075-024-01759-2</a>},
    journal={Numerical Algorithms}, publisher={Springer Science and Business Media
    LLC}, author={Zietlow, Christian and Lindner, Jörg K. N.}, year={2024} }'
  chicago: Zietlow, Christian, and Jörg K. N. Lindner. “ADMM-TGV Image Restoration
    for Scientific Applications with Unbiased Parameter Choice.” <i>Numerical Algorithms</i>,
    2024. <a href="https://doi.org/10.1007/s11075-024-01759-2">https://doi.org/10.1007/s11075-024-01759-2</a>.
  ieee: 'C. Zietlow and J. K. N. Lindner, “ADMM-TGV image restoration for scientific
    applications with unbiased parameter choice,” <i>Numerical Algorithms</i>, 2024,
    doi: <a href="https://doi.org/10.1007/s11075-024-01759-2">10.1007/s11075-024-01759-2</a>.'
  mla: Zietlow, Christian, and Jörg K. N. Lindner. “ADMM-TGV Image Restoration for
    Scientific Applications with Unbiased Parameter Choice.” <i>Numerical Algorithms</i>,
    Springer Science and Business Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s11075-024-01759-2">10.1007/s11075-024-01759-2</a>.
  short: C. Zietlow, J.K.N. Lindner, Numerical Algorithms (2024).
date_created: 2024-02-27T07:35:36Z
date_updated: 2025-01-22T09:06:50Z
department:
- _id: '286'
- _id: '15'
doi: 10.1007/s11075-024-01759-2
keyword:
- Applied Mathematics
language:
- iso: eng
publication: Numerical Algorithms
publication_identifier:
  issn:
  - 1017-1398
  - 1572-9265
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: ADMM-TGV image restoration for scientific applications with unbiased parameter
  choice
type: journal_article
user_id: '77496'
year: '2024'
...
---
_id: '52958'
author:
- first_name: Christoph
  full_name: Boeddeker, Christoph
  id: '40767'
  last_name: Boeddeker
- first_name: Aswin Shanmugam
  full_name: Subramanian, Aswin Shanmugam
  last_name: Subramanian
- first_name: Gordon
  full_name: Wichern, Gordon
  last_name: Wichern
- first_name: Reinhold
  full_name: Haeb-Umbach, Reinhold
  id: '242'
  last_name: Haeb-Umbach
- first_name: Jonathan
  full_name: Le Roux, Jonathan
  last_name: Le Roux
citation:
  ama: 'Boeddeker C, Subramanian AS, Wichern G, Haeb-Umbach R, Le Roux J. TS-SEP:
    Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings.
    <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i>. 2024;32:1185-1197.
    doi:<a href="https://doi.org/10.1109/taslp.2024.3350887">10.1109/taslp.2024.3350887</a>'
  apa: 'Boeddeker, C., Subramanian, A. S., Wichern, G., Haeb-Umbach, R., &#38; Le
    Roux, J. (2024). TS-SEP: Joint Diarization and Separation Conditioned on Estimated
    Speaker Embeddings. <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i>,
    <i>32</i>, 1185–1197. <a href="https://doi.org/10.1109/taslp.2024.3350887">https://doi.org/10.1109/taslp.2024.3350887</a>'
  bibtex: '@article{Boeddeker_Subramanian_Wichern_Haeb-Umbach_Le Roux_2024, title={TS-SEP:
    Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings},
    volume={32}, DOI={<a href="https://doi.org/10.1109/taslp.2024.3350887">10.1109/taslp.2024.3350887</a>},
    journal={IEEE/ACM Transactions on Audio, Speech, and Language Processing}, publisher={Institute
    of Electrical and Electronics Engineers (IEEE)}, author={Boeddeker, Christoph
    and Subramanian, Aswin Shanmugam and Wichern, Gordon and Haeb-Umbach, Reinhold
    and Le Roux, Jonathan}, year={2024}, pages={1185–1197} }'
  chicago: 'Boeddeker, Christoph, Aswin Shanmugam Subramanian, Gordon Wichern, Reinhold
    Haeb-Umbach, and Jonathan Le Roux. “TS-SEP: Joint Diarization and Separation Conditioned
    on Estimated Speaker Embeddings.” <i>IEEE/ACM Transactions on Audio, Speech, and
    Language Processing</i> 32 (2024): 1185–97. <a href="https://doi.org/10.1109/taslp.2024.3350887">https://doi.org/10.1109/taslp.2024.3350887</a>.'
  ieee: 'C. Boeddeker, A. S. Subramanian, G. Wichern, R. Haeb-Umbach, and J. Le Roux,
    “TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker Embeddings,”
    <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i>, vol. 32,
    pp. 1185–1197, 2024, doi: <a href="https://doi.org/10.1109/taslp.2024.3350887">10.1109/taslp.2024.3350887</a>.'
  mla: 'Boeddeker, Christoph, et al. “TS-SEP: Joint Diarization and Separation Conditioned
    on Estimated Speaker Embeddings.” <i>IEEE/ACM Transactions on Audio, Speech, and
    Language Processing</i>, vol. 32, Institute of Electrical and Electronics Engineers
    (IEEE), 2024, pp. 1185–97, doi:<a href="https://doi.org/10.1109/taslp.2024.3350887">10.1109/taslp.2024.3350887</a>.'
  short: C. Boeddeker, A.S. Subramanian, G. Wichern, R. Haeb-Umbach, J. Le Roux, IEEE/ACM
    Transactions on Audio, Speech, and Language Processing 32 (2024) 1185–1197.
date_created: 2024-03-26T16:11:54Z
date_updated: 2025-04-16T10:21:45Z
ddc:
- '000'
department:
- _id: '54'
doi: 10.1109/taslp.2024.3350887
file:
- access_level: open_access
  content_type: application/pdf
  creator: cbj
  date_created: 2025-04-16T10:14:47Z
  date_updated: 2025-04-16T10:21:45Z
  file_id: '59602'
  file_name: main.pdf
  file_size: 3432879
  relation: main_file
- access_level: open_access
  content_type: application/pdf
  creator: cbj
  date_created: 2025-04-16T10:15:08Z
  date_updated: 2025-04-16T10:21:45Z
  file_id: '59603'
  file_name: slides.pdf
  file_size: 2838635
  relation: main_file
- access_level: open_access
  content_type: application/pdf
  creator: cbj
  date_created: 2025-04-16T10:15:22Z
  date_updated: 2025-04-16T10:21:45Z
  file_id: '59604'
  file_name: poster.pdf
  file_size: 2038741
  relation: main_file
file_date_updated: 2025-04-16T10:21:45Z
has_accepted_license: '1'
intvolume: '        32'
keyword:
- Electrical and Electronic Engineering
- Acoustics and Ultrasonics
- Computer Science (miscellaneous)
- Computational Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2303.03849
oa: '1'
page: 1185-1197
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
- _id: '508'
  grant_number: '448568305'
  name: Automatische Transkription von Gesprächssituationen
publication: IEEE/ACM Transactions on Audio, Speech, and Language Processing
publication_identifier:
  issn:
  - 2329-9290
  - 2329-9304
publication_status: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
status: public
title: 'TS-SEP: Joint Diarization and Separation Conditioned on Estimated Speaker
  Embeddings'
type: journal_article
user_id: '40767'
volume: 32
year: '2024'
...
---
_id: '57895'
abstract:
- lang: eng
  text: "In our paper, we present a study in which we investigate which strategies
    pre-service teachers (PSTs) use to find and, if necessary, reject possible candidates
    for congruence theorems for quadrilaterals. This study was conducted before the
    PTSs attended a university geometry course. In this way, statements about learning
    prerequisites can be made. For the study, we analyzed group discussions of PSTs
    to identify typical approaches and evaluate them from a mathematical perspective.
    The results can be considered for the further development of courses for PSTs
    and generate hypotheses\r\nfor further research."
author:
- first_name: Max
  full_name: Hoffmann, Max
  id: '32202'
  last_name: Hoffmann
  orcid: 0000-0002-6964-7123
- first_name: Sarah
  full_name: Schlüter, Sarah
  last_name: Schlüter
citation:
  ama: 'Hoffmann M, Schlüter S. How Do Advanced Pre-Service Teachers Develop Congruence
    Theorems for Quadrilaterals? In: González-Martín AS, Gueudet G, Florensa I, Lombard
    N, eds. <i>Proceedings of the Fifth Conference of the International Network for
    Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024)</i>.
    Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and
    INDRUM; 2024.'
  apa: Hoffmann, M., &#38; Schlüter, S. (2024). How Do Advanced Pre-Service Teachers
    Develop Congruence Theorems for Quadrilaterals? In A. S. González-Martín, G. Gueudet,
    I. Florensa, &#38; N. Lombard (Eds.), <i>Proceedings of the Fifth Conference of
    the International Network for Didactic Research in University Mathematics (INDRUM
    2024, 10-14 June 2024)</i>. Escola Univerist`aria Salesiana de Sarri`a – Univ.
    Aut`onoma de Barcelona and INDRUM.
  bibtex: '@inproceedings{Hoffmann_Schlüter_2024, place={Barcelona}, title={How Do
    Advanced Pre-Service Teachers Develop Congruence Theorems for Quadrilaterals?},
    booktitle={Proceedings of the Fifth Conference of the International Network for
    Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024)}, publisher={Escola
    Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM},
    author={Hoffmann, Max and Schlüter, Sarah}, editor={González-Martín, Alejandro
    S. and Gueudet, Ghislaine and Florensa, Ignasi and Lombard, Nathan}, year={2024}
    }'
  chicago: 'Hoffmann, Max, and Sarah Schlüter. “How Do Advanced Pre-Service Teachers
    Develop Congruence Theorems for Quadrilaterals?” In <i>Proceedings of the Fifth
    Conference of the International Network for Didactic Research in University Mathematics
    (INDRUM 2024, 10-14 June 2024)</i>, edited by Alejandro S. González-Martín, Ghislaine
    Gueudet, Ignasi Florensa, and Nathan Lombard. Barcelona: Escola Univerist`aria
    Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM, 2024.'
  ieee: M. Hoffmann and S. Schlüter, “How Do Advanced Pre-Service Teachers Develop
    Congruence Theorems for Quadrilaterals?,” in <i>Proceedings of the Fifth Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2024, 10-14 June 2024)</i>, 2024.
  mla: Hoffmann, Max, and Sarah Schlüter. “How Do Advanced Pre-Service Teachers Develop
    Congruence Theorems for Quadrilaterals?” <i>Proceedings of the Fifth Conference
    of the International Network for Didactic Research in University Mathematics (INDRUM
    2024, 10-14 June 2024)</i>, edited by Alejandro S. González-Martín et al., Escola
    Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM,
    2024.
  short: 'M. Hoffmann, S. Schlüter, in: A.S. González-Martín, G. Gueudet, I. Florensa,
    N. Lombard (Eds.), Proceedings of the Fifth Conference of the International Network
    for Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024),
    Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and
    INDRUM, Barcelona, 2024.'
date_created: 2025-01-02T10:45:53Z
date_updated: 2025-01-02T10:45:59Z
ddc:
- '370'
- '510'
department:
- _id: '97'
- _id: '643'
editor:
- first_name: Alejandro S.
  full_name: González-Martín, Alejandro S.
  last_name: González-Martín
- first_name: Ghislaine
  full_name: Gueudet, Ghislaine
  last_name: Gueudet
- first_name: Ignasi
  full_name: Florensa, Ignasi
  last_name: Florensa
- first_name: Nathan
  full_name: Lombard, Nathan
  last_name: Lombard
file:
- access_level: closed
  content_type: application/pdf
  creator: maxh
  date_created: 2025-01-02T10:42:21Z
  date_updated: 2025-01-02T10:42:21Z
  file_id: '57896'
  file_name: 2024_Hoffmann_Schlueter_CongruenceQuadrilaterals.pdf
  file_size: 315111
  relation: main_file
  success: 1
file_date_updated: 2025-01-02T10:42:21Z
has_accepted_license: '1'
keyword:
- Teachers’ and students’ practices at university level
- Transition to
- across and from university mathematics
- Teaching and learning of specific topics in university mathematics
- Congruence
- Quadrilaterals
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://indrum2024.sciencesconf.org/data/pages/Proceedings_INDRUM2024.pdf
oa: '1'
place: Barcelona
publication: Proceedings of the Fifth Conference of the International Network for
  Didactic Research in University Mathematics (INDRUM 2024, 10-14 June 2024)
publication_status: published
publisher: Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona
  and INDRUM
quality_controlled: '1'
status: public
title: How Do Advanced Pre-Service Teachers Develop Congruence Theorems for Quadrilaterals?
type: conference
user_id: '32202'
year: '2024'
...
---
_id: '49326'
abstract:
- lang: eng
  text: Many networked systems are governed by non-pairwise interactions between nodes.
    The resulting higher-order interaction structure can then be encoded by means
    of a hypernetwork. In this paper we consider dynamical systems on hypernetworks
    by defining a class of admissible maps for every such hypernetwork. We explain
    how to classify robust cluster synchronization patterns on hypernetworks by finding
    balanced partitions, and we generalize the concept of a graph fibration to the
    hypernetwork context. We also show that robust synchronization patterns are only
    fully determined by polynomial admissible maps of high order. This means that,
    unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order,
    i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork,
    for the degree of the polynomial admissible maps that determine robust synchronization
    patterns. We also demonstrate that this degree is optimal by investigating a class
    of examples. We conclude by demonstrating how this effect may cause remarkable
    synchrony breaking bifurcations that occur at high polynomial degree.
author:
- first_name: Sören
  full_name: von der Gracht, Sören
  id: '97359'
  last_name: von der Gracht
  orcid: 0000-0002-8054-2058
- first_name: Eddie
  full_name: Nijholt, Eddie
  last_name: Nijholt
- first_name: Bob
  full_name: Rink, Bob
  last_name: Rink
citation:
  ama: 'von der Gracht S, Nijholt E, Rink B. Hypernetworks: Cluster Synchronization
    Is a Higher-Order Effect. <i>SIAM Journal on Applied Mathematics</i>. 2023;83(6):2329-2353.
    doi:<a href="https://doi.org/10.1137/23m1561075">10.1137/23m1561075</a>'
  apa: 'von der Gracht, S., Nijholt, E., &#38; Rink, B. (2023). Hypernetworks: Cluster
    Synchronization Is a Higher-Order Effect. <i>SIAM Journal on Applied Mathematics</i>,
    <i>83</i>(6), 2329–2353. <a href="https://doi.org/10.1137/23m1561075">https://doi.org/10.1137/23m1561075</a>'
  bibtex: '@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster
    Synchronization Is a Higher-Order Effect}, volume={83}, DOI={<a href="https://doi.org/10.1137/23m1561075">10.1137/23m1561075</a>},
    number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society
    for Industrial &#38; Applied Mathematics (SIAM)}, author={von der Gracht, Sören
    and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }'
  chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster
    Synchronization Is a Higher-Order Effect.” <i>SIAM Journal on Applied Mathematics</i>
    83, no. 6 (2023): 2329–53. <a href="https://doi.org/10.1137/23m1561075">https://doi.org/10.1137/23m1561075</a>.'
  ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization
    Is a Higher-Order Effect,” <i>SIAM Journal on Applied Mathematics</i>, vol. 83,
    no. 6, pp. 2329–2353, 2023, doi: <a href="https://doi.org/10.1137/23m1561075">10.1137/23m1561075</a>.'
  mla: 'von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a
    Higher-Order Effect.” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no.
    6, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 2329–53,
    doi:<a href="https://doi.org/10.1137/23m1561075">10.1137/23m1561075</a>.'
  short: S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics
    83 (2023) 2329–2353.
date_created: 2023-11-29T10:50:05Z
date_updated: 2023-11-29T10:52:23Z
department:
- _id: '101'
doi: 10.1137/23m1561075
external_id:
  arxiv:
  - '2302.08974'
intvolume: '        83'
issue: '6'
keyword:
- Applied Mathematics
language:
- iso: eng
page: 2329-2353
publication: SIAM Journal on Applied Mathematics
publication_identifier:
  issn:
  - 0036-1399
  - 1095-712X
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: 'Hypernetworks: Cluster Synchronization Is a Higher-Order Effect'
type: journal_article
user_id: '97359'
volume: 83
year: '2023'
...
---
_id: '50271'
author:
- first_name: Sevag
  full_name: Gharibian, Sevag
  id: '71541'
  last_name: Gharibian
  orcid: 0000-0002-9992-3379
- first_name: François
  full_name: Le Gall, François
  last_name: Le Gall
citation:
  ama: 'Gharibian S, Le Gall F. Dequantizing the Quantum Singular Value Transformation:
    Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture.
    <i>SIAM Journal on Computing</i>. 2023;52(4):1009-1038. doi:<a href="https://doi.org/10.1137/22m1513721">10.1137/22m1513721</a>'
  apa: 'Gharibian, S., &#38; Le Gall, F. (2023). Dequantizing the Quantum Singular
    Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum
    PCP Conjecture. <i>SIAM Journal on Computing</i>, <i>52</i>(4), 1009–1038. <a
    href="https://doi.org/10.1137/22m1513721">https://doi.org/10.1137/22m1513721</a>'
  bibtex: '@article{Gharibian_Le Gall_2023, title={Dequantizing the Quantum Singular
    Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum
    PCP Conjecture}, volume={52}, DOI={<a href="https://doi.org/10.1137/22m1513721">10.1137/22m1513721</a>},
    number={4}, journal={SIAM Journal on Computing}, publisher={Society for Industrial
    &#38; Applied Mathematics (SIAM)}, author={Gharibian, Sevag and Le Gall, François},
    year={2023}, pages={1009–1038} }'
  chicago: 'Gharibian, Sevag, and François Le Gall. “Dequantizing the Quantum Singular
    Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum
    PCP Conjecture.” <i>SIAM Journal on Computing</i> 52, no. 4 (2023): 1009–38. <a
    href="https://doi.org/10.1137/22m1513721">https://doi.org/10.1137/22m1513721</a>.'
  ieee: 'S. Gharibian and F. Le Gall, “Dequantizing the Quantum Singular Value Transformation:
    Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture,”
    <i>SIAM Journal on Computing</i>, vol. 52, no. 4, pp. 1009–1038, 2023, doi: <a
    href="https://doi.org/10.1137/22m1513721">10.1137/22m1513721</a>.'
  mla: 'Gharibian, Sevag, and François Le Gall. “Dequantizing the Quantum Singular
    Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum
    PCP Conjecture.” <i>SIAM Journal on Computing</i>, vol. 52, no. 4, Society for
    Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 1009–38, doi:<a href="https://doi.org/10.1137/22m1513721">10.1137/22m1513721</a>.'
  short: S. Gharibian, F. Le Gall, SIAM Journal on Computing 52 (2023) 1009–1038.
date_created: 2024-01-07T18:19:42Z
date_updated: 2024-01-07T18:20:37Z
doi: 10.1137/22m1513721
intvolume: '        52'
issue: '4'
keyword:
- General Mathematics
- General Computer Science
language:
- iso: eng
page: 1009-1038
publication: SIAM Journal on Computing
publication_identifier:
  issn:
  - 0097-5397
  - 1095-7111
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: 'Dequantizing the Quantum Singular Value Transformation: Hardness and Applications
  to Quantum Chemistry and the Quantum PCP Conjecture'
type: journal_article
user_id: '71541'
volume: 52
year: '2023'
...
---
_id: '50458'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>Consider a set of jobs connected
    to a directed acyclic task graph with a fixed source and sink. The edges of this
    graph model precedence constraints and the jobs have to be scheduled with respect
    to those. We introduce the server cloud scheduling problem, in which the jobs
    have to be processed either on a single local machine or on one of infinitely
    many cloud machines. For each job, processing times both on the server and in
    the cloud are given. Furthermore, for each edge in the task graph, a communication
    delay is included in the input and has to be taken into account if one of the
    two jobs is scheduled on the server and the other in the cloud. The server processes
    jobs sequentially, whereas the cloud can serve as many as needed in parallel,
    but induces costs. We consider both makespan and cost minimization. The main results
    are an FPTAS for the makespan objective for graphs with a constant source and
    sink dividing cut and strong hardness for the case with unit processing times
    and delays.</jats:p>
author:
- first_name: Marten
  full_name: Maack, Marten
  id: '88252'
  last_name: Maack
- first_name: Friedhelm
  full_name: Meyer auf der Heide, Friedhelm
  id: '15523'
  last_name: Meyer auf der Heide
- first_name: Simon
  full_name: Pukrop, Simon
  id: '44428'
  last_name: Pukrop
citation:
  ama: Maack M, Meyer auf der Heide F, Pukrop S. Server Cloud Scheduling. <i>Algorithmica</i>.
    Published online 2023. doi:<a href="https://doi.org/10.1007/s00453-023-01189-x">10.1007/s00453-023-01189-x</a>
  apa: Maack, M., Meyer auf der Heide, F., &#38; Pukrop, S. (2023). Server Cloud Scheduling.
    <i>Algorithmica</i>. <a href="https://doi.org/10.1007/s00453-023-01189-x">https://doi.org/10.1007/s00453-023-01189-x</a>
  bibtex: '@article{Maack_Meyer auf der Heide_Pukrop_2023, title={Server Cloud Scheduling},
    DOI={<a href="https://doi.org/10.1007/s00453-023-01189-x">10.1007/s00453-023-01189-x</a>},
    journal={Algorithmica}, publisher={Springer Science and Business Media LLC}, author={Maack,
    Marten and Meyer auf der Heide, Friedhelm and Pukrop, Simon}, year={2023} }'
  chicago: Maack, Marten, Friedhelm Meyer auf der Heide, and Simon Pukrop. “Server
    Cloud Scheduling.” <i>Algorithmica</i>, 2023. <a href="https://doi.org/10.1007/s00453-023-01189-x">https://doi.org/10.1007/s00453-023-01189-x</a>.
  ieee: 'M. Maack, F. Meyer auf der Heide, and S. Pukrop, “Server Cloud Scheduling,”
    <i>Algorithmica</i>, 2023, doi: <a href="https://doi.org/10.1007/s00453-023-01189-x">10.1007/s00453-023-01189-x</a>.'
  mla: Maack, Marten, et al. “Server Cloud Scheduling.” <i>Algorithmica</i>, Springer
    Science and Business Media LLC, 2023, doi:<a href="https://doi.org/10.1007/s00453-023-01189-x">10.1007/s00453-023-01189-x</a>.
  short: M. Maack, F. Meyer auf der Heide, S. Pukrop, Algorithmica (2023).
date_created: 2024-01-11T11:10:53Z
date_updated: 2024-01-11T11:19:33Z
department:
- _id: '63'
doi: 10.1007/s00453-023-01189-x
extern: '1'
keyword:
- Applied Mathematics
- Computer Science Applications
- General Computer Science
language:
- iso: eng
project:
- _id: '1'
  grant_number: '160364472'
  name: 'SFB 901: SFB 901: On-The-Fly Computing - Individualisierte IT-Dienstleistungen
    in dynamischen Märkten '
- _id: '4'
  name: 'SFB 901 - C: SFB 901 - Project Area C'
- _id: '16'
  grant_number: '160364472'
  name: 'SFB 901 - C4: SFB 901 - On-The-Fly Compute Centers II: Ausführung komponierter
    Dienste in konfigurierbaren Rechenzentren (Subproject C4)'
publication: Algorithmica
publication_identifier:
  issn:
  - 0178-4617
  - 1432-0541
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Server Cloud Scheduling
type: journal_article
user_id: '44428'
year: '2023'
...
---
_id: '51351'
author:
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Steffen E, Wolf IH. Bounds for the chromatic index of signed multigraphs. <i>Discrete
    Applied Mathematics</i>. 2023;337:185-189. doi:<a href="https://doi.org/10.1016/j.dam.2023.05.008">10.1016/j.dam.2023.05.008</a>
  apa: Steffen, E., &#38; Wolf, I. H. (2023). Bounds for the chromatic index of signed
    multigraphs. <i>Discrete Applied Mathematics</i>, <i>337</i>, 185–189. <a href="https://doi.org/10.1016/j.dam.2023.05.008">https://doi.org/10.1016/j.dam.2023.05.008</a>
  bibtex: '@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed
    multigraphs}, volume={337}, DOI={<a href="https://doi.org/10.1016/j.dam.2023.05.008">10.1016/j.dam.2023.05.008</a>},
    journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Steffen,
    Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={185–189} }'
  chicago: 'Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic
    Index of Signed Multigraphs.” <i>Discrete Applied Mathematics</i> 337 (2023):
    185–89. <a href="https://doi.org/10.1016/j.dam.2023.05.008">https://doi.org/10.1016/j.dam.2023.05.008</a>.'
  ieee: 'E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,”
    <i>Discrete Applied Mathematics</i>, vol. 337, pp. 185–189, 2023, doi: <a href="https://doi.org/10.1016/j.dam.2023.05.008">10.1016/j.dam.2023.05.008</a>.'
  mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index
    of Signed Multigraphs.” <i>Discrete Applied Mathematics</i>, vol. 337, Elsevier
    BV, 2023, pp. 185–89, doi:<a href="https://doi.org/10.1016/j.dam.2023.05.008">10.1016/j.dam.2023.05.008</a>.
  short: E. Steffen, I.H. Wolf, Discrete Applied Mathematics 337 (2023) 185–189.
date_created: 2024-02-14T17:33:29Z
date_updated: 2024-02-14T17:33:59Z
department:
- _id: '542'
doi: 10.1016/j.dam.2023.05.008
intvolume: '       337'
keyword:
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 185-189
publication: Discrete Applied Mathematics
publication_identifier:
  issn:
  - 0166-218X
publication_status: published
publisher: Elsevier BV
status: public
title: Bounds for the chromatic index of signed multigraphs
type: journal_article
user_id: '15540'
volume: 337
year: '2023'
...
---
_id: '51357'
article_number: '113457'
author:
- first_name: Eckhard
  full_name: Steffen, Eckhard
  id: '15548'
  last_name: Steffen
  orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
  full_name: Wolf, Isaak Hieronymus
  id: '88145'
  last_name: Wolf
citation:
  ama: Steffen E, Wolf IH. Rotation r-graphs. <i>Discrete Mathematics</i>. Published
    online 2023. doi:<a href="https://doi.org/10.1016/j.disc.2023.113457">10.1016/j.disc.2023.113457</a>
  apa: Steffen, E., &#38; Wolf, I. H. (2023). Rotation r-graphs. <i>Discrete Mathematics</i>,
    Article 113457. <a href="https://doi.org/10.1016/j.disc.2023.113457">https://doi.org/10.1016/j.disc.2023.113457</a>
  bibtex: '@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={<a href="https://doi.org/10.1016/j.disc.2023.113457">10.1016/j.disc.2023.113457</a>},
    number={113457}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Steffen,
    Eckhard and Wolf, Isaak Hieronymus}, year={2023} }'
  chicago: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete
    Mathematics</i>, 2023. <a href="https://doi.org/10.1016/j.disc.2023.113457">https://doi.org/10.1016/j.disc.2023.113457</a>.
  ieee: 'E. Steffen and I. H. Wolf, “Rotation r-graphs,” <i>Discrete Mathematics</i>,
    Art. no. 113457, 2023, doi: <a href="https://doi.org/10.1016/j.disc.2023.113457">10.1016/j.disc.2023.113457</a>.'
  mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete
    Mathematics</i>, 113457, Elsevier BV, 2023, doi:<a href="https://doi.org/10.1016/j.disc.2023.113457">10.1016/j.disc.2023.113457</a>.
  short: E. Steffen, I.H. Wolf, Discrete Mathematics (2023).
date_created: 2024-02-16T08:44:50Z
date_updated: 2024-02-16T08:45:10Z
department:
- _id: '542'
doi: 10.1016/j.disc.2023.113457
keyword:
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
language:
- iso: eng
publication: Discrete Mathematics
publication_identifier:
  issn:
  - 0012-365X
publication_status: published
publisher: Elsevier BV
status: public
title: Rotation r-graphs
type: journal_article
user_id: '15540'
year: '2023'
...
---
_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 &#38;amp; Ireland. <i>International Journal of Mathematical Education
    in Science and Technology</i>. Published online 2023:1-26. doi:<a href="https://doi.org/10.1080/0020739x.2023.2184282">10.1080/0020739x.2023.2184282</a>'
  apa: 'Gilbert, H., Schürmann, M., Liebendörfer, M., Lawson, D., &#38; Hodds, M.
    (2023). Post-pandemic online mathematics and statistics support: Practitioners’
    opinions in Germany and Great Britain &#38;amp; Ireland. <i>International Journal
    of Mathematical Education in Science and Technology</i>, 1–26. <a href="https://doi.org/10.1080/0020739x.2023.2184282">https://doi.org/10.1080/0020739x.2023.2184282</a>'
  bibtex: '@article{Gilbert_Schürmann_Liebendörfer_Lawson_Hodds_2023, title={Post-pandemic
    online mathematics and statistics support: Practitioners’ opinions in Germany
    and Great Britain &#38;amp; Ireland}, DOI={<a href="https://doi.org/10.1080/0020739x.2023.2184282">10.1080/0020739x.2023.2184282</a>},
    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 &#38;amp; Ireland.” <i>International Journal of Mathematical
    Education in Science and Technology</i>, 2023, 1–26. <a href="https://doi.org/10.1080/0020739x.2023.2184282">https://doi.org/10.1080/0020739x.2023.2184282</a>.'
  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 &#38;amp; Ireland,” <i>International Journal of Mathematical
    Education in Science and Technology</i>, pp. 1–26, 2023, doi: <a href="https://doi.org/10.1080/0020739x.2023.2184282">10.1080/0020739x.2023.2184282</a>.'
  mla: 'Gilbert, H., et al. “Post-Pandemic Online Mathematics and Statistics Support:
    Practitioners’ Opinions in Germany and Great Britain &#38;amp; Ireland.” <i>International
    Journal of Mathematical Education in Science and Technology</i>, Informa UK Limited,
    2023, pp. 1–26, doi:<a href="https://doi.org/10.1080/0020739x.2023.2184282">10.1080/0020739x.2023.2184282</a>.'
  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 &amp; Ireland'
type: journal_article
user_id: '30933'
year: '2023'
...
---
_id: '45971'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>An error estimate
    for a canonical discretization of the harmonic map heat flow into spheres is derived.
    The numerical scheme uses standard finite elements with a nodal treatment of linearized
    unit-length constraints. The analysis is based on elementary approximation results
    and only uses the discrete weak formulation.</jats:p>"
author:
- first_name: Sören
  full_name: Bartels, Sören
  last_name: Bartels
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Zhangxian
  full_name: Wang, Zhangxian
  last_name: Wang
citation:
  ama: Bartels S, Kovács B, Wang Z. Error analysis for the numerical approximation
    of the harmonic map heat flow with nodal constraints. <i>IMA Journal of Numerical
    Analysis</i>. Published online 2023. doi:<a href="https://doi.org/10.1093/imanum/drad037">10.1093/imanum/drad037</a>
  apa: Bartels, S., Kovács, B., &#38; Wang, Z. (2023). Error analysis for the numerical
    approximation of the harmonic map heat flow with nodal constraints. <i>IMA Journal
    of Numerical Analysis</i>. <a href="https://doi.org/10.1093/imanum/drad037">https://doi.org/10.1093/imanum/drad037</a>
  bibtex: '@article{Bartels_Kovács_Wang_2023, title={Error analysis for the numerical
    approximation of the harmonic map heat flow with nodal constraints}, DOI={<a href="https://doi.org/10.1093/imanum/drad037">10.1093/imanum/drad037</a>},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}, year={2023}
    }'
  chicago: Bartels, Sören, Balázs Kovács, and Zhangxian Wang. “Error Analysis for
    the Numerical Approximation of the Harmonic Map Heat Flow with Nodal Constraints.”
    <i>IMA Journal of Numerical Analysis</i>, 2023. <a href="https://doi.org/10.1093/imanum/drad037">https://doi.org/10.1093/imanum/drad037</a>.
  ieee: 'S. Bartels, B. Kovács, and Z. Wang, “Error analysis for the numerical approximation
    of the harmonic map heat flow with nodal constraints,” <i>IMA Journal of Numerical
    Analysis</i>, 2023, doi: <a href="https://doi.org/10.1093/imanum/drad037">10.1093/imanum/drad037</a>.'
  mla: Bartels, Sören, et al. “Error Analysis for the Numerical Approximation of the
    Harmonic Map Heat Flow with Nodal Constraints.” <i>IMA Journal of Numerical Analysis</i>,
    Oxford University Press (OUP), 2023, doi:<a href="https://doi.org/10.1093/imanum/drad037">10.1093/imanum/drad037</a>.
  short: S. Bartels, B. Kovács, Z. Wang, IMA Journal of Numerical Analysis (2023).
date_created: 2023-07-10T12:32:10Z
date_updated: 2024-04-03T09:15:27Z
department:
- _id: '841'
doi: 10.1093/imanum/drad037
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 analysis for the numerical approximation of the harmonic map heat flow
  with nodal constraints
type: journal_article
user_id: '100441'
year: '2023'
...