---
_id: '62291'
abstract:
- lang: eng
  text: |-
    In [Jalowy, Kabluchko, Marynych, arXiv:2504.11593v1, 2025], the authors discuss a user-friendly approach to determine the limiting empirical zero distribution of a sequence of real-rooted polynomials, as the degree goes to $\infty$. In this note, we aim to apply it to a vast range of examples of polynomials providing a unifying source for limiting empirical zero distributions.
     We cover Touchard, Fubini, Eulerian, Narayana and little $q$-Laguerre polynomials as well as hypergeometric polynomials including the classical Hermite, Laguerre and Jacobi polynomials. We construct polynomials whose empirical zero distributions converge to the free multiplicative normal and Poisson distributions. Furthermore, we study polynomials generated by some differential operators. As one inverse result, we derive coefficient asymptotics of the characteristic polynomial of random covariance matrices.
citation:
  ama: 'Zeros and exponential profiles of polynomials II: Examples. Published online
    2025. doi:<a href="https://doi.org/10.48550/ARXIV.2509.11248">10.48550/ARXIV.2509.11248</a>'
  apa: '<i>Zeros and exponential profiles of polynomials II: Examples</i>. (2025).
    <a href="https://doi.org/10.48550/ARXIV.2509.11248">https://doi.org/10.48550/ARXIV.2509.11248</a>'
  bibtex: '@article{Zeros and exponential profiles of polynomials II: Examples_2025,
    DOI={<a href="https://doi.org/10.48550/ARXIV.2509.11248">10.48550/ARXIV.2509.11248</a>},
    year={2025} }'
  chicago: '“Zeros and Exponential Profiles of Polynomials II: Examples,” 2025. <a
    href="https://doi.org/10.48550/ARXIV.2509.11248">https://doi.org/10.48550/ARXIV.2509.11248</a>.'
  ieee: '“Zeros and exponential profiles of polynomials II: Examples,” 2025, doi:
    <a href="https://doi.org/10.48550/ARXIV.2509.11248">10.48550/ARXIV.2509.11248</a>.'
  mla: '<i>Zeros and Exponential Profiles of Polynomials II: Examples</i>. 2025, doi:<a
    href="https://doi.org/10.48550/ARXIV.2509.11248">10.48550/ARXIV.2509.11248</a>.'
  short: (2025).
date_created: 2025-11-24T13:55:55Z
date_updated: 2026-03-19T14:45:35Z
department:
- _id: '94'
doi: 10.48550/ARXIV.2509.11248
status: public
title: 'Zeros and exponential profiles of polynomials II: Examples'
type: journal_article
user_id: '113768'
year: '2025'
...
---
_id: '56131'
abstract:
- lang: eng
  text: 'This article provides a comprehensive mathematical-didactic analysis of how
    the highly relevant topic symmetry can be prepared for the university education
    of PSTs. Methodologically, the analysis is embedded in a design research cycle
    and serves as preparation for the actual design of learning activities. The procedure
    of "specifying and structuring" learning objects is used and adapted in such a
    way that, in addition to mathematical aspects, profession-oriented references
    to school mathematics are also considered. An essential result of the analysis
    is the formulation of so-called interface aspects to symmetry, which prove to
    be helpful in establishing such references. '
article_type: original
author:
- first_name: Max
  full_name: Hoffmann, Max
  id: '32202'
  last_name: Hoffmann
  orcid: 0000-0002-6964-7123
citation:
  ama: Hoffmann M. Symmetry as a Topic for the University Education of Pre-Service
    Teachers. <i>Recherches en Didactique des Mathématiques</i>. 2025;45(2):85-120.
    doi:<a href="https://doi.org/10.46298/rdm.14256">10.46298/rdm.14256</a>
  apa: Hoffmann, M. (2025). Symmetry as a Topic for the University Education of Pre-Service
    Teachers. <i>Recherches En Didactique Des Mathématiques</i>, <i>45</i>(2), 85–120.
    <a href="https://doi.org/10.46298/rdm.14256">https://doi.org/10.46298/rdm.14256</a>
  bibtex: '@article{Hoffmann_2025, title={Symmetry as a Topic for the University Education
    of Pre-Service Teachers}, volume={45}, DOI={<a href="https://doi.org/10.46298/rdm.14256">10.46298/rdm.14256</a>},
    number={2}, journal={Recherches en Didactique des Mathématiques}, author={Hoffmann,
    Max}, year={2025}, pages={85–120} }'
  chicago: 'Hoffmann, Max. “Symmetry as a Topic for the University Education of Pre-Service
    Teachers.” <i>Recherches En Didactique Des Mathématiques</i> 45, no. 2 (2025):
    85–120. <a href="https://doi.org/10.46298/rdm.14256">https://doi.org/10.46298/rdm.14256</a>.'
  ieee: 'M. Hoffmann, “Symmetry as a Topic for the University Education of Pre-Service
    Teachers,” <i>Recherches en Didactique des Mathématiques</i>, vol. 45, no. 2,
    pp. 85–120, 2025, doi: <a href="https://doi.org/10.46298/rdm.14256">10.46298/rdm.14256</a>.'
  mla: Hoffmann, Max. “Symmetry as a Topic for the University Education of Pre-Service
    Teachers.” <i>Recherches En Didactique Des Mathématiques</i>, vol. 45, no. 2,
    2025, pp. 85–120, doi:<a href="https://doi.org/10.46298/rdm.14256">10.46298/rdm.14256</a>.
  short: M. Hoffmann, Recherches En Didactique Des Mathématiques 45 (2025) 85–120.
date_created: 2024-09-14T08:08:22Z
date_updated: 2026-03-30T13:52:29Z
department:
- _id: '97'
- _id: '643'
doi: 10.46298/rdm.14256
intvolume: '        45'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://rdm.episciences.org/17761/pdf
oa: '1'
page: 85-120
publication: Recherches en Didactique des Mathématiques
publication_status: published
quality_controlled: '1'
status: public
title: Symmetry as a Topic for the University Education of Pre-Service Teachers
type: journal_article
user_id: '32202'
volume: 45
year: '2025'
...
---
_id: '65246'
author:
- first_name: Max
  full_name: Hoffmann, Max
  last_name: Hoffmann
citation:
  ama: 'Hoffmann M. Using scriptwriting as a response format for interface tasks:
    Exemplary analyses in the context of symmetry. In: Bosch M, Bolondi G, Carreira
    S, Gaidoschik M, Spagnolo C, eds. <i>Proceedings of the Fourteenth Congress of
    the European Society for Research in Mathematics Education (CERME14)</i>. Free
    University of Bozen-Bolzano and ERME; 2025:2245-2252.'
  apa: 'Hoffmann, M. (2025). Using scriptwriting as a response format for interface
    tasks: Exemplary analyses in the context of symmetry. In M. Bosch, G. Bolondi,
    S. Carreira, M. Gaidoschik, &#38; C. Spagnolo (Eds.), <i>Proceedings of the Fourteenth
    Congress of the European Society for Research in Mathematics Education (CERME14)</i>
    (pp. 2245–2252). Free University of Bozen-Bolzano and ERME.'
  bibtex: '@inproceedings{Hoffmann_2025, title={Using scriptwriting as a response
    format for interface tasks: Exemplary analyses in the context of symmetry}, booktitle={Proceedings
    of the Fourteenth Congress of the European Society for Research in Mathematics
    Education (CERME14)}, publisher={Free University of Bozen-Bolzano and ERME}, author={Hoffmann,
    Max}, editor={Bosch, Marianna and Bolondi, Giorgio and Carreira, Susana and Gaidoschik,
    Michael and Spagnolo, Camilla}, year={2025}, pages={2245–2252} }'
  chicago: 'Hoffmann, Max. “Using Scriptwriting as a Response Format for Interface
    Tasks: Exemplary Analyses in the Context of Symmetry.” In <i>Proceedings of the
    Fourteenth Congress of the European Society for Research in Mathematics Education
    (CERME14)</i>, edited by Marianna Bosch, Giorgio Bolondi, Susana Carreira, Michael
    Gaidoschik, and Camilla Spagnolo, 2245–52. Free University of Bozen-Bolzano and
    ERME, 2025.'
  ieee: 'M. Hoffmann, “Using scriptwriting as a response format for interface tasks:
    Exemplary analyses in the context of symmetry,” in <i>Proceedings of the Fourteenth
    Congress of the European Society for Research in Mathematics Education (CERME14)</i>,
    2025, pp. 2245–2252.'
  mla: 'Hoffmann, Max. “Using Scriptwriting as a Response Format for Interface Tasks:
    Exemplary Analyses in the Context of Symmetry.” <i>Proceedings of the Fourteenth
    Congress of the European Society for Research in Mathematics Education (CERME14)</i>,
    edited by Marianna Bosch et al., Free University of Bozen-Bolzano and ERME, 2025,
    pp. 2245–52.'
  short: 'M. Hoffmann, in: M. Bosch, G. Bolondi, S. Carreira, M. Gaidoschik, C. Spagnolo
    (Eds.), Proceedings of the Fourteenth Congress of the European Society for Research
    in Mathematics Education (CERME14), Free University of Bozen-Bolzano and ERME,
    2025, pp. 2245–2252.'
date_created: 2026-03-30T14:57:31Z
date_updated: 2026-03-30T15:03:09Z
department:
- _id: '97'
- _id: '643'
editor:
- first_name: Marianna
  full_name: Bosch, Marianna
  last_name: Bosch
- first_name: Giorgio
  full_name: Bolondi, Giorgio
  last_name: Bolondi
- first_name: Susana
  full_name: Carreira, Susana
  last_name: Carreira
- first_name: Michael
  full_name: Gaidoschik, Michael
  last_name: Gaidoschik
- first_name: Camilla
  full_name: Spagnolo, Camilla
  last_name: Spagnolo
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://hal.science/CERME14/hal-05237875v1
oa: '1'
page: 2245-2252
publication: Proceedings of the Fourteenth Congress of the European Society for Research
  in Mathematics Education (CERME14)
publication_status: published
publisher: Free University of Bozen-Bolzano and ERME
quality_controlled: '1'
status: public
title: 'Using scriptwriting as a response format for interface tasks: Exemplary analyses
  in the context of symmetry'
type: conference
user_id: '32202'
year: '2025'
...
---
_id: '53413'
abstract:
- lang: eng
  text: "For negatively curved symmetric spaces it is known that the poles of the\r\nscattering
    matrices defined via the standard intertwining operators for the\r\nspherical
    principal representations of the isometry group are either given as\r\npoles of
    the intertwining operators or as quantum resonances, i.e. poles of the\r\nmeromorphically
    continued resolvents of the Laplace-Beltrami operator. We\r\nextend this result
    to classical locally symmetric spaces of negative curvature\r\nwith convex-cocompact
    fundamental group using results of Bunke and Olbrich. The\r\nmethod of proof forces
    us to exclude the spectral parameters corresponding to\r\nsingular Poisson transforms."
article_type: original
author:
- first_name: Benjamin
  full_name: Delarue, Benjamin
  id: '70575'
  last_name: Delarue
- first_name: Joachim
  full_name: Hilgert, Joachim
  id: '220'
  last_name: Hilgert
citation:
  ama: Delarue B, Hilgert J. Quantum resonances and scattering poles of classical
    rank one locally  symmetric spaces. <i>Journal of Lie Theory</i>. 35((4)):787--804.
  apa: Delarue, B., &#38; Hilgert, J. (n.d.). Quantum resonances and scattering poles
    of classical rank one locally  symmetric spaces. <i>Journal of Lie Theory</i>,
    <i>35</i>((4)), 787--804.
  bibtex: '@article{Delarue_Hilgert, title={Quantum resonances and scattering poles
    of classical rank one locally  symmetric spaces}, volume={35}, number={(4)}, journal={Journal
    of Lie Theory}, author={Delarue, Benjamin and Hilgert, Joachim}, pages={787--804}
    }'
  chicago: 'Delarue, Benjamin, and Joachim Hilgert. “Quantum Resonances and Scattering
    Poles of Classical Rank One Locally  Symmetric Spaces.” <i>Journal of Lie Theory</i>
    35, no. (4) (n.d.): 787--804.'
  ieee: B. Delarue and J. Hilgert, “Quantum resonances and scattering poles of classical
    rank one locally  symmetric spaces,” <i>Journal of Lie Theory</i>, vol. 35, no.
    (4), pp. 787--804.
  mla: Delarue, Benjamin, and Joachim Hilgert. “Quantum Resonances and Scattering
    Poles of Classical Rank One Locally  Symmetric Spaces.” <i>Journal of Lie Theory</i>,
    vol. 35, no. (4), pp. 787--804.
  short: B. Delarue, J. Hilgert, Journal of Lie Theory 35 (n.d.) 787--804.
date_created: 2024-04-11T12:31:18Z
date_updated: 2026-03-31T09:07:17Z
department:
- _id: '548'
intvolume: '        35'
issue: (4)
language:
- iso: eng
page: 787--804
publication: Journal of Lie Theory
publication_identifier:
  issn:
  - 0949-5932
publication_status: inpress
status: public
title: Quantum resonances and scattering poles of classical rank one locally  symmetric
  spaces
type: journal_article
user_id: '220'
volume: 35
year: '2025'
...
---
_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: '46019'
abstract:
- lang: eng
  text: We derive efficient algorithms to compute weakly Pareto optimal solutions
    for smooth, convex and unconstrained multiobjective optimization problems in general
    Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical
    system in the multiobjective setting, which trajectories converge weakly to Pareto
    optimal solutions. Discretization of this system yields an inertial multiobjective
    algorithm which generates sequences that converge weakly to Pareto optimal solutions.
    We employ Nesterov acceleration to define an algorithm with an improved convergence
    rate compared to the plain multiobjective steepest descent method (Algorithm 1).
    A further improvement in terms of efficiency is achieved by avoiding the solution
    of a quadratic subproblem to compute a common step direction for all objective
    functions, which is usually required in first-order methods. Using a different
    discretization of our inertial gradient-like dynamical system, we obtain an accelerated
    multiobjective gradient method that does not require the solution of a subproblem
    in each step (Algorithm 2). While this algorithm does not converge in general,
    it yields good results on test problems while being faster than standard steepest
    descent.
author:
- first_name: Konstantin
  full_name: Sonntag, Konstantin
  id: '56399'
  last_name: Sonntag
  orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration
    via Inertial Gradient-Like Systems. <i>Journal of Optimization Theory and Applications</i>.
    Published online 2024. doi:<a href="https://doi.org/10.1007/s10957-024-02389-3">10.1007/s10957-024-02389-3</a>
  apa: Sonntag, K., &#38; Peitz, S. (2024). Fast Multiobjective Gradient Methods with
    Nesterov Acceleration via Inertial Gradient-Like Systems. <i>Journal of Optimization
    Theory and Applications</i>. <a href="https://doi.org/10.1007/s10957-024-02389-3">https://doi.org/10.1007/s10957-024-02389-3</a>
  bibtex: '@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods
    with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={<a href="https://doi.org/10.1007/s10957-024-02389-3">10.1007/s10957-024-02389-3</a>},
    journal={Journal of Optimization Theory and Applications}, publisher={Springer},
    author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }'
  chicago: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient
    Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” <i>Journal
    of Optimization Theory and Applications</i>, 2024. <a href="https://doi.org/10.1007/s10957-024-02389-3">https://doi.org/10.1007/s10957-024-02389-3</a>.
  ieee: 'K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov
    Acceleration via Inertial Gradient-Like Systems,” <i>Journal of Optimization Theory
    and Applications</i>, 2024, doi: <a href="https://doi.org/10.1007/s10957-024-02389-3">10.1007/s10957-024-02389-3</a>.'
  mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods
    with Nesterov Acceleration via Inertial Gradient-Like Systems.” <i>Journal of
    Optimization Theory and Applications</i>, Springer, 2024, doi:<a href="https://doi.org/10.1007/s10957-024-02389-3">10.1007/s10957-024-02389-3</a>.
  short: K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).
date_created: 2023-07-12T06:35:58Z
date_updated: 2024-02-21T10:13:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10957-024-02389-3
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf
oa: '1'
publication: Journal of Optimization Theory and Applications
publication_status: published
publisher: Springer
status: public
title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial
  Gradient-Like Systems
type: journal_article
user_id: '56399'
year: '2024'
...
---
_id: '51334'
abstract:
- lang: eng
  text: The efficient optimization method for locally Lipschitz continuous multiobjective
    optimization problems from [1] is extended from finite-dimensional problems to
    general Hilbert spaces. The method iteratively computes Pareto critical points,
    where in each iteration, an approximation of the subdifferential is computed in
    an efficient manner and then used to compute a common descent direction for all
    objective functions. To prove convergence, we present some new optimality results
    for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these,
    we can show that every accumulation point of the sequence generated by our algorithm
    is Pareto critical under common assumptions. Computational efficiency for finding
    Pareto critical points is numerically demonstrated for multiobjective optimal
    control of an obstacle problem.
author:
- first_name: Konstantin
  full_name: Sonntag, Konstantin
  id: '56399'
  last_name: Sonntag
  orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Bennet
  full_name: Gebken, Bennet
  id: '32643'
  last_name: Gebken
- first_name: Georg
  full_name: Müller, Georg
  last_name: Müller
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
- first_name: Stefan
  full_name: Volkwein, Stefan
  last_name: Volkwein
citation:
  ama: Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth
    Multiobjective Optimization in Hilbert Spaces. <i>arXiv:240206376</i>. Published
    online 2024.
  apa: Sonntag, K., Gebken, B., Müller, G., Peitz, S., &#38; Volkwein, S. (2024).
    A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.
    In <i>arXiv:2402.06376</i>.
  bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method
    for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376},
    author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian
    and Volkwein, Stefan}, year={2024} }'
  chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and
    Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in
    Hilbert Spaces.” <i>ArXiv:2402.06376</i>, 2024.
  ieee: K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method
    for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” <i>arXiv:2402.06376</i>.
    2024.
  mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective
    Optimization in Hilbert Spaces.” <i>ArXiv:2402.06376</i>, 2024.
  short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376
    (2024).
date_created: 2024-02-13T09:35:26Z
date_updated: 2024-02-21T10:21:03Z
department:
- _id: '101'
- _id: '655'
external_id:
  arxiv:
  - "\t2402.06376"
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2402.06376
oa: '1'
publication: arXiv:2402.06376
status: public
title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
type: preprint
user_id: '56399'
year: '2024'
...
---
_id: '52691'
abstract:
- lang: eng
  text: "We prove Feynman-Kac formulas for the semigroups generated by selfadjoint\r\noperators
    in a class containing Fr\\\"ohlich Hamiltonians known from solid state\r\nphysics.
    The latter model multi-polarons, i.e., a fixed number of quantum\r\nmechanical
    electrons moving in a polarizable crystal and interacting with the\r\nquantized
    phonon field generated by the crystal's vibrational modes. Both the\r\nelectrons
    and phonons can be confined to suitable open subsets of Euclidean\r\nspace. We
    also include possibly very singular magnetic vector potentials and\r\nelectrostatic
    potentials. Our Feynman-Kac formulas comprise Fock space\r\noperator-valued multiplicative
    functionals and can be applied to every vector\r\nin the underlying Hilbert space.
    In comparison to the renormalized Nelson\r\nmodel, for which analogous Feynman-Kac
    formulas are known, the analysis of the\r\ncreation and annihilation terms in
    the multiplicative functionals requires\r\nnovel ideas to overcome difficulties
    caused by the phonon dispersion relation\r\nbeing constant. Getting these terms
    under control and generalizing other\r\nconstruction steps so as to cover confined
    systems are the main achievements of\r\nthis article."
author:
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Oliver
  full_name: Matte, Oliver
  last_name: Matte
citation:
  ama: Hinrichs B, Matte O. Feynman-Kac formulas for semigroups generated by multi-polaron 
    Hamiltonians in magnetic fields and on general domains. <i>arXiv:240312147</i>.
    Published online 2024.
  apa: Hinrichs, B., &#38; Matte, O. (2024). Feynman-Kac formulas for semigroups generated
    by multi-polaron  Hamiltonians in magnetic fields and on general domains. In <i>arXiv:2403.12147</i>.
  bibtex: '@article{Hinrichs_Matte_2024, title={Feynman-Kac formulas for semigroups
    generated by multi-polaron  Hamiltonians in magnetic fields and on general domains},
    journal={arXiv:2403.12147}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2024}
    }'
  chicago: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups
    Generated by Multi-Polaron  Hamiltonians in Magnetic Fields and on General Domains.”
    <i>ArXiv:2403.12147</i>, 2024.
  ieee: B. Hinrichs and O. Matte, “Feynman-Kac formulas for semigroups generated by
    multi-polaron  Hamiltonians in magnetic fields and on general domains,” <i>arXiv:2403.12147</i>.
    2024.
  mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups
    Generated by Multi-Polaron  Hamiltonians in Magnetic Fields and on General Domains.”
    <i>ArXiv:2403.12147</i>, 2024.
  short: B. Hinrichs, O. Matte, ArXiv:2403.12147 (2024).
date_created: 2024-03-20T14:56:05Z
date_updated: 2024-03-20T14:56:50Z
department:
- _id: '799'
external_id:
  arxiv:
  - '2403.12147'
language:
- iso: eng
publication: arXiv:2403.12147
status: public
title: Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians
  in magnetic fields and on general domains
type: preprint
user_id: '99427'
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: '53101'
abstract:
- lang: eng
  text: In this work, we consider optimal control problems for mechanical systems
    with fixed initial and free final state and a quadratic Lagrange term. Specifically,
    the dynamics is described by a second order ODE containing an affine control term.
    Classically, Pontryagin's maximum principle gives necessary optimality conditions
    for the optimal control problem. For smooth problems, alternatively, a variational
    approach based on an augmented objective can be followed. Here, we propose a new
    Lagrangian approach leading to equivalent necessary optimality conditions in the
    form of Euler-Lagrange equations. Thus, the differential geometric structure (similar
    to classical Lagrangian dynamics) can be exploited in the framework of optimal
    control problems. In particular, the formulation enables the symplectic discretisation
    of the optimal control problem via variational integrators in a straightforward
    way.
article_type: original
author:
- first_name: Sigrid
  full_name: Leyendecker, Sigrid
  last_name: Leyendecker
- first_name: Sofya
  full_name: Maslovskaya, Sofya
  id: '87909'
  last_name: Maslovskaya
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
- first_name: Rodrigo T. Sato Martín de
  full_name: Almagro, Rodrigo T. Sato Martín de
  last_name: Almagro
- first_name: Flóra Orsolya
  full_name: Szemenyei, Flóra Orsolya
  last_name: Szemenyei
citation:
  ama: Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO.
    A new Lagrangian approach to control affine systems with a quadratic Lagrange
    term. <i>Journal of Computational Dynamics</i>. 2024;0(0):0-0. doi:<a href="https://doi.org/10.3934/jcd.2024017">10.3934/jcd.2024017</a>
  apa: Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de,
    &#38; Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems
    with a quadratic Lagrange term. <i>Journal of Computational Dynamics</i>, <i>0</i>(0),
    0–0. <a href="https://doi.org/10.3934/jcd.2024017">https://doi.org/10.3934/jcd.2024017</a>
  bibtex: '@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A
    new Lagrangian approach to control affine systems with a quadratic Lagrange term},
    volume={0}, DOI={<a href="https://doi.org/10.3934/jcd.2024017">10.3934/jcd.2024017</a>},
    number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute
    of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya,
    Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei,
    Flóra Orsolya}, year={2024}, pages={0–0} }'
  chicago: 'Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T.
    Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach
    to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Computational
    Dynamics</i> 0, no. 0 (2024): 0–0. <a href="https://doi.org/10.3934/jcd.2024017">https://doi.org/10.3934/jcd.2024017</a>.'
  ieee: 'S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro,
    and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with
    a quadratic Lagrange term,” <i>Journal of Computational Dynamics</i>, vol. 0,
    no. 0, pp. 0–0, 2024, doi: <a href="https://doi.org/10.3934/jcd.2024017">10.3934/jcd.2024017</a>.'
  mla: Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems
    with a Quadratic Lagrange Term.” <i>Journal of Computational Dynamics</i>, vol.
    0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:<a
    href="https://doi.org/10.3934/jcd.2024017">10.3934/jcd.2024017</a>.
  short: S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O.
    Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0.
date_created: 2024-03-28T15:58:02Z
date_updated: 2024-03-28T16:07:34Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jcd.2024017
has_accepted_license: '1'
issue: '0'
keyword:
- Optimal control problem
- Lagrangian system
- Hamiltonian system
- Variations
- Pontryagin's maximum principle.
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://www.aimsciences.org/article/doi/10.3934/jcd.2024017
oa: '1'
page: 0-0
publication: Journal of Computational Dynamics
publication_identifier:
  issn:
  - 2158-2491
  - 2158-2505
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: A new Lagrangian approach to control affine systems with a quadratic Lagrange
  term
type: journal_article
user_id: '87909'
volume: '0'
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: '52584'
author:
- first_name: Sebastian
  full_name: Rezat, Sebastian
  id: '31132'
  last_name: Rezat
citation:
  ama: 'Rezat S. Research on curriculum resources in mathematics education: a survey
    of the field. <i>ZDM – Mathematics Education</i>. Published online 2024. doi:<a
    href="https://doi.org/10.1007/s11858-024-01559-x">10.1007/s11858-024-01559-x</a>'
  apa: 'Rezat, S. (2024). Research on curriculum resources in mathematics education:
    a survey of the field. <i>ZDM – Mathematics Education</i>. <a href="https://doi.org/10.1007/s11858-024-01559-x">https://doi.org/10.1007/s11858-024-01559-x</a>'
  bibtex: '@article{Rezat_2024, title={Research on curriculum resources in mathematics
    education: a survey of the field}, DOI={<a href="https://doi.org/10.1007/s11858-024-01559-x">10.1007/s11858-024-01559-x</a>},
    journal={ZDM – Mathematics Education}, publisher={Springer}, author={Rezat, Sebastian},
    year={2024} }'
  chicago: 'Rezat, Sebastian. “Research on Curriculum Resources in Mathematics Education:
    A Survey of the Field.” <i>ZDM – Mathematics Education</i>, 2024. <a href="https://doi.org/10.1007/s11858-024-01559-x">https://doi.org/10.1007/s11858-024-01559-x</a>.'
  ieee: 'S. Rezat, “Research on curriculum resources in mathematics education: a survey
    of the field,” <i>ZDM – Mathematics Education</i>, 2024, doi: <a href="https://doi.org/10.1007/s11858-024-01559-x">10.1007/s11858-024-01559-x</a>.'
  mla: 'Rezat, Sebastian. “Research on Curriculum Resources in Mathematics Education:
    A Survey of the Field.” <i>ZDM – Mathematics Education</i>, Springer, 2024, doi:<a
    href="https://doi.org/10.1007/s11858-024-01559-x">10.1007/s11858-024-01559-x</a>.'
  short: S. Rezat, ZDM – Mathematics Education (2024).
date_created: 2024-03-15T08:46:00Z
date_updated: 2024-04-18T08:20:42Z
department:
- _id: '360'
doi: 10.1007/s11858-024-01559-x
has_accepted_license: '1'
language:
- iso: eng
publication: ZDM – Mathematics Education
publication_status: epub_ahead
publisher: Springer
status: public
title: 'Research on curriculum resources in mathematics education: a survey of the
  field'
type: journal_article
user_id: '31132'
year: '2024'
...
---
_id: '51841'
abstract:
- lang: ger
  text: 'athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch
    zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf
    eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für
    das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete
    Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten
    Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive
    Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung.
    Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich.
    Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen?
    Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen,
    ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.'
article_type: original
author:
- first_name: Bärbel
  full_name: Barzel, Bärbel
  last_name: Barzel
- first_name: Gilbert
  full_name: Greefrath, Gilbert
  last_name: Greefrath
- first_name: Mareike
  full_name: Nagel, Mareike
  last_name: Nagel
- first_name: Max
  full_name: Hoffmann, Max
  id: '32202'
  last_name: Hoffmann
  orcid: 0000-0002-6964-7123
citation:
  ama: Barzel B, Greefrath G, Nagel M, Hoffmann M. Digitalisierung als Chance für
    alle Prinzipien guten Unterrichts. <i>mathematik lehren</i>. 2024;242:42-47.
  apa: Barzel, B., Greefrath, G., Nagel, M., &#38; Hoffmann, M. (2024). Digitalisierung
    als Chance für alle Prinzipien guten Unterrichts. <i>mathematik lehren</i>, <i>242</i>,
    42–47.
  bibtex: '@article{Barzel_Greefrath_Nagel_Hoffmann_2024, title={Digitalisierung als
    Chance für alle Prinzipien guten Unterrichts}, volume={242}, journal={mathematik
    lehren}, author={Barzel, Bärbel and Greefrath, Gilbert and Nagel, Mareike and
    Hoffmann, Max}, year={2024}, pages={42–47} }'
  chicago: 'Barzel, Bärbel, Gilbert Greefrath, Mareike Nagel, and Max Hoffmann. “Digitalisierung
    als Chance für alle Prinzipien guten Unterrichts.” <i>mathematik lehren</i> 242
    (2024): 42–47.'
  ieee: B. Barzel, G. Greefrath, M. Nagel, and M. Hoffmann, “Digitalisierung als Chance
    für alle Prinzipien guten Unterrichts,” <i>mathematik lehren</i>, vol. 242, pp.
    42–47, 2024.
  mla: Barzel, Bärbel, et al. “Digitalisierung als Chance für alle Prinzipien guten
    Unterrichts.” <i>mathematik lehren</i>, vol. 242, 2024, pp. 42–47.
  short: B. Barzel, G. Greefrath, M. Nagel, M. Hoffmann, mathematik lehren 242 (2024)
    42–47.
date_created: 2024-02-25T20:58:51Z
date_updated: 2024-04-18T08:57:42Z
ddc:
- '510'
- '370'
department:
- _id: '643'
file:
- access_level: closed
  content_type: application/pdf
  creator: maxh
  date_created: 2024-02-25T20:55:29Z
  date_updated: 2024-02-25T20:55:29Z
  file_id: '51842'
  file_name: Barzel_etal_2024_DigitalisierungalsChancefrallePrinzipiengut.pdf
  file_size: 1410541
  relation: main_file
  success: 1
file_date_updated: 2024-02-25T20:55:29Z
has_accepted_license: '1'
intvolume: '       242'
language:
- iso: ger
main_file_link:
- open_access: '1'
  url: https://www.friedrich-verlag.de/shop/mwdownloads/download/link/id/114555/
oa: '1'
page: 42 - 47
publication: mathematik lehren
publication_status: published
status: public
title: Digitalisierung als Chance für alle Prinzipien guten Unterrichts
type: journal_article
user_id: '37888'
volume: 242
year: '2024'
...
---
_id: '50554'
author:
- first_name: Susanne
  full_name: Prediger, Susanne
  last_name: Prediger
- first_name: Lena
  full_name: Wessel, Lena
  id: '85190'
  last_name: Wessel
citation:
  ama: 'Prediger S, Wessel L. 31 Sprachbildung im berufsbezogenen Mathematikunterricht.
    In: Efing C, Kalkavan-Aydin Z, eds. <i>Berufs-und Fachsprache Deutsch in Wissenschaft
    und Praxis</i>. Vol Band 3. DaZ-Handbücher. DE GRUYTER; 2024:363-372.'
  apa: 'Prediger, S., &#38; Wessel, L. (2024). 31 Sprachbildung im berufsbezogenen
    Mathematikunterricht. In C. Efing &#38; Z. Kalkavan-Aydin (Eds.), <i>Berufs-und
    Fachsprache Deutsch in Wissenschaft und Praxis: Vol. Band 3</i> (pp. 363–372).
    DE GRUYTER.'
  bibtex: '@inbook{Prediger_Wessel_2024, place={Berlin}, series={DaZ-Handbücher},
    title={31 Sprachbildung im berufsbezogenen Mathematikunterricht.}, volume={Band
    3}, booktitle={Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis}, publisher={DE
    GRUYTER}, author={Prediger, Susanne and Wessel, Lena}, editor={Efing, Christian
    and Kalkavan-Aydin, Zeynep}, year={2024}, pages={363–372}, collection={DaZ-Handbücher}
    }'
  chicago: 'Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen
    Mathematikunterricht.” In <i>Berufs-und Fachsprache Deutsch in Wissenschaft und
    Praxis</i>, edited by Christian Efing and Zeynep Kalkavan-Aydin, Band 3:363–72.
    DaZ-Handbücher. Berlin: DE GRUYTER, 2024.'
  ieee: 'S. Prediger and L. Wessel, “31 Sprachbildung im berufsbezogenen Mathematikunterricht.,”
    in <i>Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis</i>, vol. Band
    3, C. Efing and Z. Kalkavan-Aydin, Eds. Berlin: DE GRUYTER, 2024, pp. 363–372.'
  mla: Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.”
    <i>Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis</i>, edited by Christian
    Efing and Zeynep Kalkavan-Aydin, vol. Band 3, DE GRUYTER, 2024, pp. 363–72.
  short: 'S. Prediger, L. Wessel, in: C. Efing, Z. Kalkavan-Aydin (Eds.), Berufs-und
    Fachsprache Deutsch in Wissenschaft und Praxis, DE GRUYTER, Berlin, 2024, pp.
    363–372.'
date_created: 2024-01-17T10:58:04Z
date_updated: 2024-04-18T08:58:14Z
department:
- _id: '643'
editor:
- first_name: Christian
  full_name: Efing, Christian
  last_name: Efing
- first_name: Zeynep
  full_name: Kalkavan-Aydin, Zeynep
  last_name: Kalkavan-Aydin
language:
- iso: ger
main_file_link:
- open_access: '1'
  url: https://www.degruyter.com/document/doi/10.1515/9783110745504/pdf?licenseType=restricted#page=381
oa: '1'
page: 363-372
place: Berlin
publication: Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis
publication_identifier:
  isbn:
  - 978-3-11-074544-3
publication_status: published
publisher: DE GRUYTER
series_title: DaZ-Handbücher
status: public
title: 31 Sprachbildung im berufsbezogenen Mathematikunterricht.
type: book_chapter
user_id: '37888'
volume: Band 3
year: '2024'
...
---
_id: '51207'
abstract:
- lang: eng
  text: "Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact
    type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We
    show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic
    growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain
    that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$."
article_number: '76'
author:
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Lasse Lennart
  full_name: Wolf, Lasse Lennart
  id: '45027'
  last_name: Wolf
  orcid: 0000-0001-8893-2045
citation:
  ama: 'Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case.
    <i>Geom Dedicata</i>. 2024;218. doi:<a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>'
  apa: 'Weich, T., &#38; Wolf, L. L. (2024). Temperedness of locally symmetric spaces:
    The product case. <i>Geom Dedicata</i>, <i>218</i>, Article 76. <a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>'
  bibtex: '@article{Weich_Wolf_2024, title={Temperedness of locally symmetric spaces:
    The product case}, volume={218}, DOI={<a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>},
    number={76}, journal={Geom Dedicata}, author={Weich, Tobias and Wolf, Lasse Lennart},
    year={2024} }'
  chicago: 'Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric
    Spaces: The Product Case.” <i>Geom Dedicata</i> 218 (2024). <a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>.'
  ieee: 'T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product
    case,” <i>Geom Dedicata</i>, vol. 218, Art. no. 76, 2024, doi: <a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>.'
  mla: 'Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric
    Spaces: The Product Case.” <i>Geom Dedicata</i>, vol. 218, 76, 2024, doi:<a href="https://doi.org/10.1007/s10711-024-00904-4">https://doi.org/10.1007/s10711-024-00904-4</a>.'
  short: T. Weich, L.L. Wolf, Geom Dedicata 218 (2024).
date_created: 2024-02-06T21:00:55Z
date_updated: 2024-05-07T11:44:34Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: https://doi.org/10.1007/s10711-024-00904-4
external_id:
  arxiv:
  - '2304.09573'
intvolume: '       218'
language:
- iso: eng
publication: Geom Dedicata
status: public
title: 'Temperedness of locally symmetric spaces: The product case'
type: journal_article
user_id: '45027'
volume: 218
year: '2024'
...
---
_id: '54078'
author:
- first_name: Uta
  full_name: Häsel-Weide, Uta
  id: '60267'
  last_name: Häsel-Weide
- first_name: Lara Marie
  full_name: Graf, Lara Marie
  id: '89837'
  last_name: Graf
- first_name: K.
  full_name: Höveler, K.
  last_name: Höveler
- first_name: M.
  full_name: Nührenbörger, M.
  last_name: Nührenbörger
citation:
  ama: 'Häsel-Weide U, Graf LM, Höveler K, Nührenbörger M. Fachbezogene Professionalisierung
    von fachfremd Mathematik unterrichtenden Lehrkräften: Retrospektive Selbsteinschätzungen
    zur Expertise im Umgang mit Schwierigkeiten beim Mathematiklernen im Anfangsunterricht
    der Grundschule. <i>HLZ – Herausforderung Lehrer*innenbildung</i>. 2024;7(1).
    doi:<a href="https://doi.org/10.11576/hlz-6727">10.11576/hlz-6727</a>'
  apa: 'Häsel-Weide, U., Graf, L. M., Höveler, K., &#38; Nührenbörger, M. (2024).
    Fachbezogene Professionalisierung von fachfremd Mathematik unterrichtenden Lehrkräften:
    Retrospektive Selbsteinschätzungen zur Expertise im Umgang mit Schwierigkeiten
    beim Mathematiklernen im Anfangsunterricht der Grundschule. <i>HLZ – Herausforderung
    Lehrer*innenbildung</i>, <i>7</i>(1). <a href="https://doi.org/10.11576/hlz-6727">https://doi.org/10.11576/hlz-6727</a>'
  bibtex: '@article{Häsel-Weide_Graf_Höveler_Nührenbörger_2024, title={Fachbezogene
    Professionalisierung von fachfremd Mathematik unterrichtenden Lehrkräften: Retrospektive
    Selbsteinschätzungen zur Expertise im Umgang mit Schwierigkeiten beim Mathematiklernen
    im Anfangsunterricht der Grundschule}, volume={7}, DOI={<a href="https://doi.org/10.11576/hlz-6727">10.11576/hlz-6727</a>},
    number={1}, journal={HLZ – Herausforderung Lehrer*innenbildung}, author={Häsel-Weide,
    Uta and Graf, Lara Marie and Höveler, K. and Nührenbörger, M.}, year={2024} }'
  chicago: 'Häsel-Weide, Uta, Lara Marie Graf, K. Höveler, and M. Nührenbörger. “Fachbezogene
    Professionalisierung von Fachfremd Mathematik Unterrichtenden Lehrkräften: Retrospektive
    Selbsteinschätzungen Zur Expertise Im Umgang Mit Schwierigkeiten Beim Mathematiklernen
    Im Anfangsunterricht Der Grundschule.” <i>HLZ – Herausforderung Lehrer*innenbildung</i>
    7, no. 1 (2024). <a href="https://doi.org/10.11576/hlz-6727">https://doi.org/10.11576/hlz-6727</a>.'
  ieee: 'U. Häsel-Weide, L. M. Graf, K. Höveler, and M. Nührenbörger, “Fachbezogene
    Professionalisierung von fachfremd Mathematik unterrichtenden Lehrkräften: Retrospektive
    Selbsteinschätzungen zur Expertise im Umgang mit Schwierigkeiten beim Mathematiklernen
    im Anfangsunterricht der Grundschule,” <i>HLZ – Herausforderung Lehrer*innenbildung</i>,
    vol. 7, no. 1, 2024, doi: <a href="https://doi.org/10.11576/hlz-6727">10.11576/hlz-6727</a>.'
  mla: 'Häsel-Weide, Uta, et al. “Fachbezogene Professionalisierung von Fachfremd
    Mathematik Unterrichtenden Lehrkräften: Retrospektive Selbsteinschätzungen Zur
    Expertise Im Umgang Mit Schwierigkeiten Beim Mathematiklernen Im Anfangsunterricht
    Der Grundschule.” <i>HLZ – Herausforderung Lehrer*innenbildung</i>, vol. 7, no.
    1, 2024, doi:<a href="https://doi.org/10.11576/hlz-6727">10.11576/hlz-6727</a>.'
  short: U. Häsel-Weide, L.M. Graf, K. Höveler, M. Nührenbörger, HLZ – Herausforderung
    Lehrer*innenbildung 7 (2024).
date_created: 2024-05-08T08:40:45Z
date_updated: 2024-05-08T08:42:20Z
department:
- _id: '543'
doi: 10.11576/hlz-6727
intvolume: '         7'
issue: '1'
language:
- iso: eng
publication: HLZ – Herausforderung Lehrer*innenbildung
status: public
title: 'Fachbezogene Professionalisierung von fachfremd Mathematik unterrichtenden
  Lehrkräften: Retrospektive Selbsteinschätzungen zur Expertise im Umgang mit Schwierigkeiten
  beim Mathematiklernen im Anfangsunterricht der Grundschule'
type: journal_article
user_id: '44184'
volume: 7
year: '2024'
...
---
_id: '54144'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title><jats:p>In this paper, we propose a novel
    conceptual framework tailored for modeling the meaning of mathematical concepts
    in university-level mathematics, addressing their rigorous nature and their relationships
    with related concepts as well as interpretations in various contexts. Within this
    framework, we present a model of meaning for the concepts of total differentiability
    and total derivative that provides a variety of possible interpretations and aspects.
    We then use the proposed model of meaning as a tool for analyzing three different
    textbooks for mathematics majors on the topic of multidimensional differentiability.
    \uFEFFOur paper is an example of a subject matter analysis of a topic in university
    mathematics carried out in a structured way. The model of meaning for total differentiability
    presented in this paper could inspire course design and analysis including the
    design of assignments and assessments for students. Moreover, it could serve as
    a valuable research tool for further analyses. For example, it could be used as
    a framework for analyzing courses taught or as a basis for developing a test instrument
    to assess students’ understanding. With our textbook analysis, we begin to examine
    the landscape of textbooks regarding differentiability concepts in the multidimensional
    case, shedding light on the diversity of meaning facets that are covered in the
    textbooks. These results could be useful for guiding instructors and learners
    in selecting and using textbooks for teaching and learning based on their respective
    needs.</jats:p>"
author:
- first_name: Elisa
  full_name: Lankeit, Elisa
  last_name: Lankeit
- first_name: Rolf
  full_name: Biehler, Rolf
  id: '16274'
  last_name: Biehler
citation:
  ama: 'Lankeit E, Biehler R. The meaning landscape of the concept of the total derivative
    in multivariable real analysis textbooks: an analysis based on a new model of
    meaning. <i>ZDM – Mathematics Education</i>. Published online 2024. doi:<a href="https://doi.org/10.1007/s11858-024-01584-w">10.1007/s11858-024-01584-w</a>'
  apa: 'Lankeit, E., &#38; Biehler, R. (2024). The meaning landscape of the concept
    of the total derivative in multivariable real analysis textbooks: an analysis
    based on a new model of meaning. <i>ZDM – Mathematics Education</i>. <a href="https://doi.org/10.1007/s11858-024-01584-w">https://doi.org/10.1007/s11858-024-01584-w</a>'
  bibtex: '@article{Lankeit_Biehler_2024, title={The meaning landscape of the concept
    of the total derivative in multivariable real analysis textbooks: an analysis
    based on a new model of meaning}, DOI={<a href="https://doi.org/10.1007/s11858-024-01584-w">10.1007/s11858-024-01584-w</a>},
    journal={ZDM – Mathematics Education}, publisher={Springer Science and Business
    Media LLC}, author={Lankeit, Elisa and Biehler, Rolf}, year={2024} }'
  chicago: 'Lankeit, Elisa, and Rolf Biehler. “The Meaning Landscape of the Concept
    of the Total Derivative in Multivariable Real Analysis Textbooks: An Analysis
    Based on a New Model of Meaning.” <i>ZDM – Mathematics Education</i>, 2024. <a
    href="https://doi.org/10.1007/s11858-024-01584-w">https://doi.org/10.1007/s11858-024-01584-w</a>.'
  ieee: 'E. Lankeit and R. Biehler, “The meaning landscape of the concept of the total
    derivative in multivariable real analysis textbooks: an analysis based on a new
    model of meaning,” <i>ZDM – Mathematics Education</i>, 2024, doi: <a href="https://doi.org/10.1007/s11858-024-01584-w">10.1007/s11858-024-01584-w</a>.'
  mla: 'Lankeit, Elisa, and Rolf Biehler. “The Meaning Landscape of the Concept of
    the Total Derivative in Multivariable Real Analysis Textbooks: An Analysis Based
    on a New Model of Meaning.” <i>ZDM – Mathematics Education</i>, Springer Science
    and Business Media LLC, 2024, doi:<a href="https://doi.org/10.1007/s11858-024-01584-w">10.1007/s11858-024-01584-w</a>.'
  short: E. Lankeit, R. Biehler, ZDM – Mathematics Education (2024).
date_created: 2024-05-10T07:48:10Z
date_updated: 2024-05-10T07:49:19Z
department:
- _id: '363'
doi: 10.1007/s11858-024-01584-w
language:
- iso: eng
publication: ZDM – Mathematics Education
publication_identifier:
  issn:
  - 1863-9690
  - 1863-9704
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'The meaning landscape of the concept of the total derivative in multivariable
  real analysis textbooks: an analysis based on a new model of meaning'
type: journal_article
user_id: '37888'
year: '2024'
...
---
_id: '53534'
abstract:
- lang: eng
  text: "It is known that the notion of a transitive subgroup of a permutation group\r\n$G$
    extends naturally to subsets of $G$. We consider subsets of the general\r\nlinear
    group $\\operatorname{GL}(n,q)$ acting transitively on flag-like\r\nstructures,
    which are common generalisations of $t$-dimensional subspaces of\r\n$\\mathbb{F}_q^n$
    and bases of $t$-dimensional subspaces of $\\mathbb{F}_q^n$. We\r\ngive structural
    characterisations of transitive subsets of\r\n$\\operatorname{GL}(n,q)$ using
    the character theory of $\\operatorname{GL}(n,q)$\r\nand interpret such subsets
    as designs in the conjugacy class association\r\nscheme of $\\operatorname{GL}(n,q)$.
    In particular we generalise a theorem of\r\nPerin on subgroups of $\\operatorname{GL}(n,q)$
    acting transitively on\r\n$t$-dimensional subspaces. We survey transitive subgroups
    of\r\n$\\operatorname{GL}(n,q)$, showing that there is no subgroup of\r\n$\\operatorname{GL}(n,q)$
    with $1<t<n$ acting transitively on $t$-dimensional\r\nsubspaces unless it contains
    $\\operatorname{SL}(n,q)$ or is one of two\r\nexceptional groups. On the other
    hand, for all fixed $t$, we show that there\r\nexist nontrivial subsets of $\\operatorname{GL}(n,q)$
    that are transitive on\r\nlinearly independent $t$-tuples of $\\mathbb{F}_q^n$,
    which also shows the\r\nexistence of nontrivial subsets of $\\operatorname{GL}(n,q)$
    that are transitive\r\non more general flag-like structures. We establish connections
    with orthogonal\r\npolynomials, namely the Al-Salam-Carlitz polynomials, and generalise
    a result\r\nby Rudvalis and Shinoda on the distribution of the number of fixed
    points of\r\nthe elements in $\\operatorname{GL}(n,q)$. Many of our results can
    be\r\ninterpreted as $q$-analogs of corresponding results for the symmetric group."
author:
- first_name: Alena
  full_name: Ernst, Alena
  id: '46953'
  last_name: Ernst
- first_name: Kai-Uwe
  full_name: Schmidt, Kai-Uwe
  last_name: Schmidt
citation:
  ama: Ernst A, Schmidt K-U. Transitivity in finite general linear groups. <i>Mathematische
    Zeitschrift</i>. 2024;307(45). doi:<a href="https://doi.org/10.1007/s00209-024-03511-x">10.1007/s00209-024-03511-x</a>
  apa: Ernst, A., &#38; Schmidt, K.-U. (2024). Transitivity in finite general linear
    groups. <i>Mathematische Zeitschrift</i>, <i>307</i>(45). <a href="https://doi.org/10.1007/s00209-024-03511-x">https://doi.org/10.1007/s00209-024-03511-x</a>
  bibtex: '@article{Ernst_Schmidt_2024, title={Transitivity in finite general linear
    groups}, volume={307}, DOI={<a href="https://doi.org/10.1007/s00209-024-03511-x">10.1007/s00209-024-03511-x</a>},
    number={45}, journal={Mathematische Zeitschrift}, author={Ernst, Alena and Schmidt,
    Kai-Uwe}, year={2024} }'
  chicago: Ernst, Alena, and Kai-Uwe Schmidt. “Transitivity in Finite General Linear
    Groups.” <i>Mathematische Zeitschrift</i> 307, no. 45 (2024). <a href="https://doi.org/10.1007/s00209-024-03511-x">https://doi.org/10.1007/s00209-024-03511-x</a>.
  ieee: 'A. Ernst and K.-U. Schmidt, “Transitivity in finite general linear groups,”
    <i>Mathematische Zeitschrift</i>, vol. 307, no. 45, 2024, doi: <a href="https://doi.org/10.1007/s00209-024-03511-x">10.1007/s00209-024-03511-x</a>.'
  mla: Ernst, Alena, and Kai-Uwe Schmidt. “Transitivity in Finite General Linear Groups.”
    <i>Mathematische Zeitschrift</i>, vol. 307, no. 45, 2024, doi:<a href="https://doi.org/10.1007/s00209-024-03511-x">10.1007/s00209-024-03511-x</a>.
  short: A. Ernst, K.-U. Schmidt, Mathematische Zeitschrift 307 (2024).
date_created: 2024-04-17T12:26:51Z
date_updated: 2024-06-17T10:04:29Z
department:
- _id: '100'
doi: 10.1007/s00209-024-03511-x
intvolume: '       307'
issue: '45'
language:
- iso: eng
publication: Mathematische Zeitschrift
status: public
title: Transitivity in finite general linear groups
type: journal_article
user_id: '46953'
volume: 307
year: '2024'
...
---
_id: '32447'
abstract:
- lang: eng
  text: 'We present a new gradient-like dynamical system related to unconstrained
    convex smooth multiobjective optimization which involves inertial effects and
    asymptotic vanishing damping. To the best of our knowledge, this system is the
    first inertial gradient-like system for multiobjective optimization problems including
    asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch
    and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to
    Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions
    to this system in finite dimensions and further prove that its bounded solutions
    converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence
    rate of order \(\mathcal{O}(t^{-2})\) for the function values measured with a
    merit function. This approach presents a good basis for the development of fast
    gradient methods for multiobjective optimization.'
article_type: original
author:
- first_name: Konstantin
  full_name: Sonntag, Konstantin
  id: '56399'
  last_name: Sonntag
  orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-Like
    Systems with Asymptotic Vanishing Damping. <i>SIAM Journal on Optimization</i>.
    2024;34(3):2259-2286. doi:<a href="https://doi.org/10.1137/23M1588512">10.1137/23M1588512</a>
  apa: Sonntag, K., &#38; Peitz, S. (2024). Fast Convergence of Inertial Multiobjective
    Gradient-Like Systems with Asymptotic Vanishing Damping. <i>SIAM Journal on Optimization</i>,
    <i>34</i>(3), 2259–2286. <a href="https://doi.org/10.1137/23M1588512">https://doi.org/10.1137/23M1588512</a>
  bibtex: '@article{Sonntag_Peitz_2024, title={Fast Convergence of Inertial Multiobjective
    Gradient-Like Systems with Asymptotic Vanishing Damping}, volume={34}, DOI={<a
    href="https://doi.org/10.1137/23M1588512">10.1137/23M1588512</a>}, number={3},
    journal={SIAM Journal on Optimization}, publisher={Society for Industrial and
    Applied Mathematics}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024},
    pages={2259–2286} }'
  chicago: 'Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial
    Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping.” <i>SIAM
    Journal on Optimization</i> 34, no. 3 (2024): 2259–86. <a href="https://doi.org/10.1137/23M1588512">https://doi.org/10.1137/23M1588512</a>.'
  ieee: 'K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-Like
    Systems with Asymptotic Vanishing Damping,” <i>SIAM Journal on Optimization</i>,
    vol. 34, no. 3, pp. 2259–2286, 2024, doi: <a href="https://doi.org/10.1137/23M1588512">10.1137/23M1588512</a>.'
  mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective
    Gradient-Like Systems with Asymptotic Vanishing Damping.” <i>SIAM Journal on Optimization</i>,
    vol. 34, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 2259–86,
    doi:<a href="https://doi.org/10.1137/23M1588512">10.1137/23M1588512</a>.
  short: K. Sonntag, S. Peitz, SIAM Journal on Optimization 34 (2024) 2259–2286.
date_created: 2022-07-28T11:53:02Z
date_updated: 2024-07-02T09:27:39Z
department:
- _id: '101'
- _id: '655'
doi: 10.1137/23M1588512
intvolume: '        34'
issue: '3'
keyword:
- multiobjective optimization
- Pareto optimization
- Lyapunov analysis
- gradient-likedynamical systems
- inertial dynamics
- asymptotic vanishing damping
- fast convergence
language:
- iso: eng
page: 2259 - 2286
publication: SIAM Journal on Optimization
publication_identifier:
  issn:
  - 1095-7189
publication_status: published
publisher: Society for Industrial and Applied Mathematics
status: public
title: Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic
  Vanishing Damping
type: journal_article
user_id: '56399'
volume: 34
year: '2024'
...