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Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. doi:<a href=\"https://doi.org/10.1093/imanum/draf009\">10.1093/imanum/draf009</a>","mla":"Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, doi:<a href=\"https://doi.org/10.1093/imanum/draf009\">10.1093/imanum/draf009</a>."},"publication":"IMA Journal of Numerical Analysis","date_created":"2024-07-31T09:03:45Z","department":[{"_id":"841"}],"type":"journal_article","author":[{"last_name":"Bullerjahn","orcid":"https://orcid.org/0009-0003-8460-1574","first_name":"Nils","full_name":"Bullerjahn, Nils","id":"103797"},{"last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs","id":"100441"}],"title":"Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions","status":"public","year":"2025","article_type":"original","publication_status":"accepted","date_updated":"2026-02-18T14:46:18Z","_id":"55459","language":[{"iso":"eng"}],"user_id":"100441","doi":"10.1093/imanum/draf009"},{"citation":{"apa":"Edelmann, D., Kovács, B., &#38; Lubich, C. (2025). Numerical analysis of an evolving bulk--surface model of tumour growth. <i>IMA Journal of Numerical Analysis</i>, <i>45</i>(5), 2581--2627. <a href=\"https://doi.org/10.1093/imanum/drae077\">https://doi.org/10.1093/imanum/drae077</a>","ieee":"D. Edelmann, B. Kovács, and C. Lubich, “Numerical analysis of an evolving bulk--surface model of tumour growth,” <i>IMA Journal of Numerical Analysis</i>, vol. 45, no. 5, pp. 2581--2627, 2025, doi: <a href=\"https://doi.org/10.1093/imanum/drae077\">10.1093/imanum/drae077</a>.","short":"D. Edelmann, B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 45 (2025) 2581--2627.","chicago":"Edelmann, Dominik, Balázs Kovács, and Christian Lubich. “Numerical Analysis of an Evolving Bulk--Surface Model of Tumour Growth.” <i>IMA Journal of Numerical Analysis</i> 45, no. 5 (2025): 2581--2627. <a href=\"https://doi.org/10.1093/imanum/drae077\">https://doi.org/10.1093/imanum/drae077</a>.","mla":"Edelmann, Dominik, et al. “Numerical Analysis of an Evolving Bulk--Surface Model of Tumour Growth.” <i>IMA Journal of Numerical Analysis</i>, vol. 45, no. 5, 2025, pp. 2581--2627, doi:<a href=\"https://doi.org/10.1093/imanum/drae077\">10.1093/imanum/drae077</a>.","ama":"Edelmann D, Kovács B, Lubich C. Numerical analysis of an evolving bulk--surface model of tumour growth. <i>IMA Journal of Numerical Analysis</i>. 2025;45(5):2581--2627. doi:<a href=\"https://doi.org/10.1093/imanum/drae077\">10.1093/imanum/drae077</a>","bibtex":"@article{Edelmann_Kovács_Lubich_2025, title={Numerical analysis of an evolving bulk--surface model of tumour growth}, volume={45}, DOI={<a href=\"https://doi.org/10.1093/imanum/drae077\">10.1093/imanum/drae077</a>}, number={5}, journal={IMA Journal of Numerical Analysis}, author={Edelmann, Dominik and Kovács, Balázs and Lubich, Christian}, year={2025}, pages={2581--2627} }"},"issue":"5","publication":"IMA Journal of Numerical Analysis","date_created":"2024-04-03T09:11:36Z","department":[{"_id":"841"}],"type":"journal_article","author":[{"full_name":"Edelmann, Dominik","first_name":"Dominik","last_name":"Edelmann"},{"full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","first_name":"Balázs","last_name":"Kovács","id":"100441"},{"full_name":"Lubich, Christian","first_name":"Christian","last_name":"Lubich"}],"year":"2025","title":"Numerical analysis of an evolving bulk--surface model of tumour growth","status":"public","intvolume":"        45","date_updated":"2026-02-18T14:44:54Z","_id":"53141","language":[{"iso":"eng"}],"page":"2581--2627","volume":45,"doi":"10.1093/imanum/drae077","user_id":"100441"},{"publication":"IMA Journal of Numerical Analysis","citation":{"chicago":"Bai, Genming, Balázs Kovács, and Buyang Li. “Maximal Regularity of Evolving FEMs for Parabolic Equations on an  Evolving Surface.” <i>IMA Journal of Numerical Analysis</i>, 2025. <a href=\"https://doi.org/10.1093/imanum/draf082.\">https://doi.org/10.1093/imanum/draf082.</a>","short":"G. Bai, B. Kovács, B. Li, IMA Journal of Numerical Analysis (2025).","ieee":"G. Bai, B. Kovács, and B. Li, “Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface,” <i>IMA Journal of Numerical Analysis</i>, 2025, doi: <a href=\"https://doi.org/10.1093/imanum/draf082.\">10.1093/imanum/draf082.</a>","apa":"Bai, G., Kovács, B., &#38; Li, B. (2025). Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface. <i>IMA Journal of Numerical Analysis</i>. <a href=\"https://doi.org/10.1093/imanum/draf082.\">https://doi.org/10.1093/imanum/draf082.</a>","bibtex":"@article{Bai_Kovács_Li_2025, title={Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface}, DOI={<a href=\"https://doi.org/10.1093/imanum/draf082.\">10.1093/imanum/draf082.</a>}, journal={IMA Journal of Numerical Analysis}, author={Bai, Genming and Kovács, Balázs and Li, Buyang}, year={2025} }","ama":"Bai G, Kovács B, Li B. Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface. <i>IMA Journal of Numerical Analysis</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1093/imanum/draf082.\">10.1093/imanum/draf082.</a>","mla":"Bai, Genming, et al. “Maximal Regularity of Evolving FEMs for Parabolic Equations on an  Evolving Surface.” <i>IMA Journal of Numerical Analysis</i>, 2025, doi:<a href=\"https://doi.org/10.1093/imanum/draf082.\">10.1093/imanum/draf082.</a>"},"abstract":[{"text":"In this paper, we prove that spatially semi-discrete evolving finite element\r\nmethod for parabolic equations on a given evolving hypersurface of arbitrary\r\ndimensions preserves the maximal $L^p$-regularity at the discrete level. We\r\nfirst establish the results on a stationary surface and then extend them, via a\r\nperturbation argument, to the case where the underlying surface is evolving\r\nunder a prescribed velocity field. The proof combines techniques in evolving\r\nfinite element method, properties of Green's functions on (discretised) closed\r\nsurfaces, and local energy estimates for finite element methods","lang":"eng"}],"external_id":{"arxiv":["2408.14096"]},"date_created":"2024-08-27T07:37:39Z","type":"journal_article","department":[{"_id":"841"}],"title":"Maximal regularity of evolving FEMs for parabolic equations on an  evolving surface","year":"2025","status":"public","author":[{"full_name":"Bai, Genming","last_name":"Bai","first_name":"Genming"},{"full_name":"Kovács, Balázs","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","id":"100441"},{"first_name":"Buyang","last_name":"Li","full_name":"Li, Buyang"}],"date_updated":"2026-02-18T14:47:34Z","_id":"55781","language":[{"iso":"eng"}],"doi":"10.1093/imanum/draf082.","user_id":"100441"},{"date_created":"2024-10-22T09:31:19Z","file":[{"creator":"llangen","date_created":"2026-02-19T14:14:39Z","date_updated":"2026-02-19T14:14:39Z","relation":"main_file","access_level":"closed","file_size":443262,"file_name":"MSA_hermitsch_published.pdf","success":1,"content_type":"application/pdf","file_id":"64288"}],"department":[{"_id":"555"}],"type":"journal_article","publication":"Indagationes Mathematicae","issue":"6","related_material":{"link":[{"relation":"research_paper","url":"https://arxiv.org/abs/2410.10364"}]},"abstract":[{"lang":"eng","text":"We establish a multiresolution analysis on the space $\\text{Herm}(n)$ of\r\n$n\\times n$ complex Hermitian matrices which is adapted to invariance under\r\nconjugation by the unitary group $U(n).$ The orbits under this action are\r\nparametrized by the possible ordered spectra of Hermitian matrices, which\r\nconstitute a closed Weyl chamber of type $A_{n-1}$ in $\\mathbb R^n.$ The space\r\n$L^2(\\text{Herm}(n))^{U(n)}$ of radial, i.e. $U(n)$-invariant $L^2$-functions\r\non $\\text{Herm}(n)$ is naturally identified with a certain weighted $L^2$-space\r\non this chamber.\r\n  The scale spaces of our multiresolution analysis are obtained by usual dyadic\r\ndilations as well as generalized translations of a scaling function, where the\r\ngeneralized translation is a hypergroup translation which respects the radial\r\ngeometry. We provide a concise criterion to characterize orthonormal wavelet\r\nbases and show that such bases always exist. They provide natural orthonormal\r\nbases of the space $L^2(\\text{Herm}(n))^{U(n)}.$\r\n  Furthermore, we show how to obtain radial scaling functions from classical\r\nscaling functions on $\\mathbb R^{n}$. Finally, generalizations related to the\r\nCartan decompositions for general compact Lie groups are indicated."}],"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.1016/j.indag.2025.03.009"}],"author":[{"last_name":"Langen","first_name":"Lukas","full_name":"Langen, Lukas","id":"73664"},{"first_name":"Margit","last_name":"Rösler","full_name":"Rösler, Margit","id":"37390"}],"year":"2025","title":"Multiresolution analysis on spectra of hermitian matrices","article_type":"original","intvolume":"        36","publication_status":"published","date_updated":"2026-02-19T14:16:43Z","external_id":{"arxiv":["2410.10364"]},"citation":{"mla":"Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra of Hermitian Matrices.” <i>Indagationes Mathematicae</i>, vol. 36, no. 6, Elsevier, 2025, pp. 1671–94.","ama":"Langen L, Rösler M. Multiresolution analysis on spectra of hermitian matrices. <i>Indagationes Mathematicae</i>. 2025;36(6):1671-1694.","bibtex":"@article{Langen_Rösler_2025, title={Multiresolution analysis on spectra of hermitian matrices}, volume={36}, number={6}, journal={Indagationes Mathematicae}, publisher={Elsevier}, author={Langen, Lukas and Rösler, Margit}, year={2025}, pages={1671–1694} }","apa":"Langen, L., &#38; Rösler, M. (2025). Multiresolution analysis on spectra of hermitian matrices. <i>Indagationes Mathematicae</i>, <i>36</i>(6), 1671–1694.","ieee":"L. Langen and M. Rösler, “Multiresolution analysis on spectra of hermitian matrices,” <i>Indagationes Mathematicae</i>, vol. 36, no. 6, pp. 1671–1694, 2025.","chicago":"Langen, Lukas, and Margit Rösler. “Multiresolution Analysis on Spectra of Hermitian Matrices.” <i>Indagationes Mathematicae</i> 36, no. 6 (2025): 1671–94.","short":"L. Langen, M. Rösler, Indagationes Mathematicae 36 (2025) 1671–1694."},"file_date_updated":"2026-02-19T14:14:39Z","project":[{"_id":"357","name":"TRR 358 - Ganzzahlige Strukturen in Geometrie und Darstellungstheorie"}],"_id":"56717","publisher":"Elsevier","page":"1671-1694","volume":36,"user_id":"73664","ddc":["510"],"status":"public","has_accepted_license":"1"},{"citation":{"apa":"Janssens, B., &#38; Niestijl, M. (2025). Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms. <i>Communications in Mathematical Physics</i>, <i>406</i>(2), Article 45. <a href=\"https://doi.org/10.1007/s00220-024-05226-w\">https://doi.org/10.1007/s00220-024-05226-w</a>","ieee":"B. Janssens and M. Niestijl, “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 2, Art. no. 45, 2025, doi: <a href=\"https://doi.org/10.1007/s00220-024-05226-w\">10.1007/s00220-024-05226-w</a>.","chicago":"Janssens, Bas, and Milan Niestijl. “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms.” <i>Communications in Mathematical Physics</i> 406, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00220-024-05226-w\">https://doi.org/10.1007/s00220-024-05226-w</a>.","short":"B. Janssens, M. Niestijl, Communications in Mathematical Physics 406 (2025).","mla":"Janssens, Bas, and Milan Niestijl. “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 2, 45, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-024-05226-w\">10.1007/s00220-024-05226-w</a>.","ama":"Janssens B, Niestijl M. Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms. <i>Communications in Mathematical Physics</i>. 2025;406(2). doi:<a href=\"https://doi.org/10.1007/s00220-024-05226-w\">10.1007/s00220-024-05226-w</a>","bibtex":"@article{Janssens_Niestijl_2025, title={Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms}, volume={406}, DOI={<a href=\"https://doi.org/10.1007/s00220-024-05226-w\">10.1007/s00220-024-05226-w</a>}, number={245}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Janssens, Bas and Niestijl, Milan}, year={2025} }"},"user_id":"104095","volume":406,"publisher":"Springer Science and Business Media LLC","_id":"64289","status":"public","type":"journal_article","department":[{"_id":"93"}],"date_created":"2026-02-20T09:33:11Z","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\overline{\\rho }$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mover>\r\n                    <mml:mi>ρ</mml:mi>\r\n                    <mml:mo>¯</mml:mo>\r\n                  </mml:mover>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> of the Lie group <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$${{\\,\\textrm{Diff}\\,}}_c(M)$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mspace/>\r\n                        <mml:mtext>Diff</mml:mtext>\r\n                        <mml:mspace/>\r\n                      </mml:mrow>\r\n                      <mml:mi>c</mml:mi>\r\n                    </mml:msub>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:mi>M</mml:mi>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> of compactly supported diffeomorphisms of a smooth manifold <jats:italic>M</jats:italic> that satisfy a so-called generalized positive energy condition. In particular, this captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\overline{\\rho }$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mover>\r\n                    <mml:mi>ρ</mml:mi>\r\n                    <mml:mo>¯</mml:mo>\r\n                  </mml:mover>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>. We show that if <jats:italic>M</jats:italic> is connected and <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$\\dim (M) &gt; 1$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>dim</mml:mo>\r\n                    <mml:mo>(</mml:mo>\r\n                    <mml:mi>M</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n                    <mml:mo>&gt;</mml:mo>\r\n                    <mml:mn>1</mml:mn>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>, then any such representation is necessarily trivial on the identity component <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$${{\\,\\textrm{Diff}\\,}}_c(M)_0$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mspace/>\r\n                        <mml:mtext>Diff</mml:mtext>\r\n                        <mml:mspace/>\r\n                      </mml:mrow>\r\n                      <mml:mi>c</mml:mi>\r\n                    </mml:msub>\r\n                    <mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mo>(</mml:mo>\r\n                        <mml:mi>M</mml:mi>\r\n                        <mml:mo>)</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mn>0</mml:mn>\r\n                    </mml:msub>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula>. As an intermediate step towards this result, we determine the continuous second Lie algebra cohomology <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$H^2_\\textrm{ct}(\\mathcal {X}_c(M), \\mathbb {R})$$</jats:tex-math>\r\n                <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:msubsup>\r\n                      <mml:mi>H</mml:mi>\r\n                      <mml:mtext>ct</mml:mtext>\r\n                      <mml:mn>2</mml:mn>\r\n                    </mml:msubsup>\r\n                    <mml:mrow>\r\n                      <mml:mo>(</mml:mo>\r\n                      <mml:msub>\r\n                        <mml:mi>X</mml:mi>\r\n                        <mml:mi>c</mml:mi>\r\n                      </mml:msub>\r\n                      <mml:mrow>\r\n                        <mml:mo>(</mml:mo>\r\n                        <mml:mi>M</mml:mi>\r\n                        <mml:mo>)</mml:mo>\r\n                      </mml:mrow>\r\n                      <mml:mo>,</mml:mo>\r\n                      <mml:mi>R</mml:mi>\r\n                      <mml:mo>)</mml:mo>\r\n                    </mml:mrow>\r\n                  </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n            </jats:inline-formula> of the Lie algebra of compactly supported vector fields. This is subtly different from Gelfand–Fuks cohomology in view of the compact support condition.</jats:p>"}],"issue":"2","publication":"Communications in Mathematical Physics","doi":"10.1007/s00220-024-05226-w","article_number":"45","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2026-02-20T09:41:41Z","intvolume":"       406","title":"Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms","year":"2025","author":[{"last_name":"Janssens","first_name":"Bas","full_name":"Janssens, Bas"},{"last_name":"Niestijl","first_name":"Milan","full_name":"Niestijl, Milan"}],"publication_identifier":{"issn":["0010-3616","1432-0916"]}},{"doi":"10.1007/s10623-024-01471-1","user_id":"70420","volume":93,"page":"971 - 981","_id":"50299","language":[{"iso":"eng"}],"date_updated":"2026-02-25T13:51:50Z","publication_status":"published","intvolume":"        93","title":"Nontrivial $t$-designs in polar spaces exist for all $t$","status":"public","year":"2025","author":[{"id":"70420","first_name":"Charlene","last_name":"Weiß","full_name":"Weiß, Charlene"}],"type":"journal_article","department":[{"_id":"100"}],"date_created":"2024-01-08T14:39:54Z","abstract":[{"lang":"eng","text":"A finite classical polar space of rank $n$ consists of the totally isotropic\r\nsubspaces of a finite vector space over $\\mathbb{F}_q$ equipped with a\r\nnondegenerate form such that $n$ is the maximal dimension of such a subspace. A\r\n$t$-$(n,k,\\lambda)$ design in a finite classical polar space of rank $n$ is a\r\ncollection $Y$ of totally isotropic $k$-spaces such that each totally isotropic\r\n$t$-space is contained in exactly $\\lambda$ members of $Y$. Nontrivial examples\r\nare currently only known for $t\\leq 2$. We show that $t$-$(n,k,\\lambda)$\r\ndesigns in polar spaces exist for all $t$ and $q$ provided that\r\n$k>\\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a\r\nprobabilistic method by Kuperberg, Lovett, and Peled, and it is thus\r\nnonconstructive."}],"publication":"Des. Codes Cryptogr.","citation":{"bibtex":"@article{Weiß_2025, title={Nontrivial $t$-designs in polar spaces exist for all $t$}, volume={93}, DOI={<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>}, journal={Des. Codes Cryptogr.}, author={Weiß, Charlene}, year={2025}, pages={971–981} }","ama":"Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. <i>Des Codes Cryptogr</i>. 2025;93:971-981. doi:<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>","mla":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>Des. Codes Cryptogr.</i>, vol. 93, 2025, pp. 971–81, doi:<a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>.","chicago":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>Des. Codes Cryptogr.</i> 93 (2025): 971–81. <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">https://doi.org/10.1007/s10623-024-01471-1</a>.","short":"C. Weiß, Des. Codes Cryptogr. 93 (2025) 971–981.","ieee":"C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” <i>Des. Codes Cryptogr.</i>, vol. 93, pp. 971–981, 2025, doi: <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">10.1007/s10623-024-01471-1</a>.","apa":"Weiß, C. (2025). Nontrivial $t$-designs in polar spaces exist for all $t$. <i>Des. Codes Cryptogr.</i>, <i>93</i>, 971–981. <a href=\"https://doi.org/10.1007/s10623-024-01471-1\">https://doi.org/10.1007/s10623-024-01471-1</a>"}},{"citation":{"ama":"Winkler M. Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters. <i>Applied Mathematics &#38; Optimization</i>. 2025;91(2). doi:<a href=\"https://doi.org/10.1007/s00245-025-10243-9\">10.1007/s00245-025-10243-9</a>","bibtex":"@article{Winkler_2025, title={Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}, volume={91}, DOI={<a href=\"https://doi.org/10.1007/s00245-025-10243-9\">10.1007/s00245-025-10243-9</a>}, number={244}, journal={Applied Mathematics &#38; Optimization}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2025} }","mla":"Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters.” <i>Applied Mathematics &#38; Optimization</i>, vol. 91, no. 2, 44, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00245-025-10243-9\">10.1007/s00245-025-10243-9</a>.","short":"M. Winkler, Applied Mathematics &#38; Optimization 91 (2025).","chicago":"Winkler, Michael. “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters.” <i>Applied Mathematics &#38; Optimization</i> 91, no. 2 (2025). <a href=\"https://doi.org/10.1007/s00245-025-10243-9\">https://doi.org/10.1007/s00245-025-10243-9</a>.","apa":"Winkler, M. (2025). Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters. <i>Applied Mathematics &#38; Optimization</i>, <i>91</i>(2), Article 44. <a href=\"https://doi.org/10.1007/s00245-025-10243-9\">https://doi.org/10.1007/s00245-025-10243-9</a>","ieee":"M. Winkler, “Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters,” <i>Applied Mathematics &#38; Optimization</i>, vol. 91, no. 2, Art. no. 44, 2025, doi: <a href=\"https://doi.org/10.1007/s00245-025-10243-9\">10.1007/s00245-025-10243-9</a>."},"project":[{"name":"FOR 5208: Modellbasierte Bestimmung nichtlinearer Eigenschaften von Piezokeramiken für Leistungsschallanwendungen (NEPTUN)","_id":"245"}],"status":"public","_id":"59258","publisher":"Springer Science and Business Media LLC","user_id":"11829","volume":91,"publication":"Applied Mathematics & Optimization","issue":"2","date_created":"2025-04-02T11:23:25Z","type":"journal_article","department":[{"_id":"90"}],"title":"Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters","year":"2025","author":[{"last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael","id":"31496"}],"publication_identifier":{"issn":["0095-4616","1432-0606"]},"date_updated":"2026-02-26T15:59:30Z","publication_status":"published","intvolume":"        91","article_number":"44","language":[{"iso":"eng"}],"doi":"10.1007/s00245-025-10243-9"},{"volume":35,"editor":[{"full_name":"Frahm, Jan","first_name":"Jan","last_name":"Frahm"},{"full_name":"Glöckner, Helge","first_name":"Helge","last_name":"Glöckner","id":"178"},{"id":"220","full_name":"Hilgert, Joachim","first_name":"Joachim","last_name":"Hilgert"},{"last_name":"Olafsson","first_name":"Gestur","full_name":"Olafsson, Gestur"}],"user_id":"178","_id":"64736","language":[{"iso":"eng"}],"intvolume":"        35","date_updated":"2026-02-26T17:51:43Z","title":"Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday","year":"2025","status":"public","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"type":"journal_editor","date_created":"2026-02-26T17:42:01Z","quality_controlled":"1","citation":{"apa":"Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday. (2025). In J. Frahm, H. Glöckner, J. Hilgert, &#38; G. Olafsson (Eds.), <i>J. Lie Theory</i> (Vol. 35, Issue 4).","ieee":"J. Frahm, H. Glöckner, J. Hilgert, and G. Olafsson, Eds., <i>Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday</i>, vol. 35, no. 4. 2025.","short":"J. Frahm, H. Glöckner, J. Hilgert, G. Olafsson, eds., Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday, 2025.","chicago":"Frahm, Jan, Helge Glöckner, Joachim Hilgert, and Gestur Olafsson, eds. <i>Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday</i>. <i>J. Lie Theory</i>. Vol. 35, 2025.","mla":"Frahm, Jan, et al., editors. “Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday.” <i>J. Lie Theory</i>, vol. 35, no. 4, 2025.","ama":"Frahm J, Glöckner H, Hilgert J, Olafsson G, eds. <i>Special Issue of Journal of Lie Theory Dedicated to Karl-Hermann Neeb on the Occasion of His 60th Birthday</i>. Vol 35.; 2025.","bibtex":"@book{Frahm_Glöckner_Hilgert_Olafsson_2025, title={Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday}, volume={35}, number={4}, journal={J. Lie Theory}, year={2025} }"},"publication":"J. Lie Theory","issue":"4"},{"status":"public","year":"2025","title":"Manifold of mappings and regularity properties of half-Lie groups","author":[{"full_name":"Pinaud, Matthieu","first_name":"Matthieu","last_name":"Pinaud"}],"date_updated":"2026-02-26T21:58:36Z","main_file_link":[{"open_access":"1","url":"https://nbn-resolving.org/urn:nbn:de:hbz:466:2-54221"}],"language":[{"iso":"eng"}],"_id":"64770","doi":"10.17619/UNIPB/1-2211","user_id":"178","supervisor":[{"first_name":"Helge","last_name":"Glöckner","full_name":"Glöckner, Helge","id":"178"}],"citation":{"ieee":"M. Pinaud, <i>Manifold of mappings and regularity properties of half-Lie groups</i>. 2025.","mla":"Pinaud, Matthieu. <i>Manifold of Mappings and Regularity Properties of Half-Lie Groups</i>. 2025, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2211\">10.17619/UNIPB/1-2211</a>.","apa":"Pinaud, M. (2025). <i>Manifold of mappings and regularity properties of half-Lie groups</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-2211\">https://doi.org/10.17619/UNIPB/1-2211</a>","bibtex":"@book{Pinaud_2025, title={Manifold of mappings and regularity properties of half-Lie groups}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-2211\">10.17619/UNIPB/1-2211</a>}, author={Pinaud, Matthieu}, year={2025} }","chicago":"Pinaud, Matthieu. <i>Manifold of Mappings and Regularity Properties of Half-Lie Groups</i>, 2025. <a href=\"https://doi.org/10.17619/UNIPB/1-2211\">https://doi.org/10.17619/UNIPB/1-2211</a>.","short":"M. Pinaud, Manifold of Mappings and Regularity Properties of Half-Lie Groups, 2025.","ama":"Pinaud M. <i>Manifold of Mappings and Regularity Properties of Half-Lie Groups</i>.; 2025. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2211\">10.17619/UNIPB/1-2211</a>"},"date_created":"2026-02-26T21:58:22Z","type":"dissertation","oa":"1","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}]},{"file_date_updated":"2025-05-05T09:28:02Z","citation":{"ama":"Maslovskaya S, Ober-Blöbaum S, Offen C, Singh P, Wembe Moafo BE. Adaptive higher order reversible integrators for memory efficient deep learning. Published online 2025.","bibtex":"@article{Maslovskaya_Ober-Blöbaum_Offen_Singh_Wembe Moafo_2025, title={Adaptive higher order reversible integrators for memory efficient deep learning}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina and Offen, Christian and Singh, Pranav and Wembe Moafo, Boris Edgar}, year={2025} }","mla":"Maslovskaya, Sofya, et al. <i>Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning</i>. 2025.","chicago":"Maslovskaya, Sofya, Sina Ober-Blöbaum, Christian Offen, Pranav Singh, and Boris Edgar Wembe Moafo. “Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning,” 2025.","short":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).","apa":"Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., &#38; Wembe Moafo, B. E. (2025). <i>Adaptive higher order reversible integrators for memory efficient deep learning</i>.","ieee":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, and B. E. Wembe Moafo, “Adaptive higher order reversible integrators for memory efficient deep learning.” 2025."},"abstract":[{"lang":"eng","text":"The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep networks are often unable to handle time-series data appearing at irregular intervals. These issues can be resolved by considering continuous-depth networks based on the neural ODE framework in combination with reversible integration methods that allow for variable time-steps. Reversibility of the method ensures that the memory requirement for training is independent of network depth, while variable time-steps are required for assimilating time-series data on irregular intervals. However, at present, there are no known higher-order reversible methods with this property. High-order methods are especially important when a high level of accuracy in learning is required or when small time-steps are necessary due to large errors in time integration of neural ODEs, for instance in context of complex dynamical systems such as Kepler systems and molecular dynamics. The requirement of small time-steps when using a low-order method can significantly increase the computational cost of training as well as inference. In this work, we present an approach for constructing high-order reversible methods that allow adaptive time-stepping. Our numerical tests show the advantages in computational speed when applied to the task of learning dynamical systems."}],"external_id":{"arxiv":["2410.09537"]},"file":[{"date_created":"2025-05-05T09:28:02Z","creator":"sofyam","content_type":"application/pdf","success":1,"file_id":"59795","date_updated":"2025-05-05T09:28:02Z","relation":"main_file","access_level":"closed","file_size":1830758,"file_name":"2410.09537v2.pdf"}],"date_created":"2025-05-05T09:25:28Z","type":"preprint","department":[{"_id":"636"}],"status":"public","year":"2025","title":"Adaptive higher order reversible integrators for memory efficient deep learning","author":[{"id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279"},{"full_name":"Singh, Pranav","first_name":"Pranav","last_name":"Singh"},{"full_name":"Wembe Moafo, Boris Edgar","first_name":"Boris Edgar","last_name":"Wembe Moafo","id":"95394"}],"date_updated":"2025-09-30T15:16:09Z","has_accepted_license":"1","_id":"59794","language":[{"iso":"eng"}],"ddc":["510"],"user_id":"85279"},{"language":[{"iso":"eng"}],"article_number":"8","doi":"10.1007/s13138-025-00259-7","publication_identifier":{"issn":["0173-5322","1869-2699"]},"author":[{"id":"93186","last_name":"Richter","first_name":"Alix","full_name":"Richter, Alix"},{"full_name":"Bruns, Julia","last_name":"Bruns","orcid":"https://orcid.org/0000-0002-6604-5864","first_name":"Julia","id":"72183"},{"first_name":"Hedwig","last_name":"Gasteiger","full_name":"Gasteiger, Hedwig"}],"year":"2025","title":"Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften","intvolume":"        46","date_updated":"2025-10-05T17:55:53Z","publication_status":"published","date_created":"2025-10-05T17:55:20Z","department":[{"_id":"611"}],"type":"journal_article","publication":"Journal für Mathematik-Didaktik","issue":"1","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>Teacher professional development (TPD) is a crucial support mechanism for mathematics teachers. Strategies for implementing TPD include disseminating educative curriculum materials or conducting TPD courses. However, it remains unclear whether different implementations of the same TPD support mathematics teachers in distinct ways. This study investigated two implementations of the TPD <jats:italic>EmMa-FS</jats:italic> which focuses early mathematics education (EME) for German vocational school (VS) teachers who instruct prospective early childhood (EC) educators. One group of teachers received an in-person TPD course along with educative curriculum materials (<jats:italic>n</jats:italic>\r\n            <jats:sub>\r\n              <jats:italic>PM</jats:italic>\r\n            </jats:sub> = 26), whereas the other received only the educative curriculum materials (<jats:italic>n</jats:italic>\r\n            <jats:sub>\r\n              <jats:italic>M</jats:italic>\r\n            </jats:sub> = 15). The effects on VS teachers’ beliefs and knowledge concerning EME were examined using a <jats:italic>t</jats:italic>-test and repeated measures ANOVA. To assess how teachers in the different implementation groups made use of the TPD in their lesson planning, participants submitted hypothetical lesson sequences on early numeracy, which were analysed for instructional quality, covered content, and the visible implementation of the provided educative curriculum materials using qualitative content analysis. The results indicated that both TPD implementations positively affected VS teachers’ knowledge related to EME but not their beliefs. While the instructional quality of the lesson sequences varied across both groups, participants who received the TPD course appeared to use the educative curriculum materials more often and to cover more content.</jats:p>"}],"_id":"61518","publisher":"Springer Science and Business Media LLC","volume":46,"user_id":"72183","status":"public","citation":{"chicago":"Richter, Alix, Julia Bruns, and Hedwig Gasteiger. “Interaction- or Material-Centred Implementation of Teacher Professional Development: A Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung Interaktions- Oder Materialzentriert Implementieren: Ein Vergleich Hinsichtlich Der Kompetenzentwicklung Sowie Der Potentiellen Unterrichtsplanung von Lehrkräften.” <i>Journal Für Mathematik-Didaktik</i> 46, no. 1 (2025). <a href=\"https://doi.org/10.1007/s13138-025-00259-7\">https://doi.org/10.1007/s13138-025-00259-7</a>.","short":"A. Richter, J. Bruns, H. Gasteiger, Journal Für Mathematik-Didaktik 46 (2025).","apa":"Richter, A., Bruns, J., &#38; Gasteiger, H. (2025). Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften. <i>Journal Für Mathematik-Didaktik</i>, <i>46</i>(1), Article 8. <a href=\"https://doi.org/10.1007/s13138-025-00259-7\">https://doi.org/10.1007/s13138-025-00259-7</a>","ieee":"A. Richter, J. Bruns, and H. Gasteiger, “Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften,” <i>Journal für Mathematik-Didaktik</i>, vol. 46, no. 1, Art. no. 8, 2025, doi: <a href=\"https://doi.org/10.1007/s13138-025-00259-7\">10.1007/s13138-025-00259-7</a>.","ama":"Richter A, Bruns J, Gasteiger H. Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften. <i>Journal für Mathematik-Didaktik</i>. 2025;46(1). doi:<a href=\"https://doi.org/10.1007/s13138-025-00259-7\">10.1007/s13138-025-00259-7</a>","bibtex":"@article{Richter_Bruns_Gasteiger_2025, title={Interaction- or Material-Centred Implementation of Teacher Professional Development: a Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung interaktions- oder materialzentriert implementieren: Ein Vergleich hinsichtlich der Kompetenzentwicklung sowie der potentiellen Unterrichtsplanung von Lehrkräften}, volume={46}, DOI={<a href=\"https://doi.org/10.1007/s13138-025-00259-7\">10.1007/s13138-025-00259-7</a>}, number={18}, journal={Journal für Mathematik-Didaktik}, publisher={Springer Science and Business Media LLC}, author={Richter, Alix and Bruns, Julia and Gasteiger, Hedwig}, year={2025} }","mla":"Richter, Alix, et al. “Interaction- or Material-Centred Implementation of Teacher Professional Development: A Comparison of Teachers’ Competence Development and Potential Lesson Planning Lehrkräftefortbildung Interaktions- Oder Materialzentriert Implementieren: Ein Vergleich Hinsichtlich Der Kompetenzentwicklung Sowie Der Potentiellen Unterrichtsplanung von Lehrkräften.” <i>Journal Für Mathematik-Didaktik</i>, vol. 46, no. 1, 8, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s13138-025-00259-7\">10.1007/s13138-025-00259-7</a>."}},{"status":"public","_id":"61519","publisher":"Hogrefe Publishing Group","page":"193-200","volume":14,"user_id":"72183","citation":{"mla":"Bruns, Julia, and Tessa Mette. “Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?” <i>Frühe Bildung</i>, vol. 14, no. 4, Hogrefe Publishing Group, 2025, pp. 193–200, doi:<a href=\"https://doi.org/10.1026/2191-9186/a000730\">10.1026/2191-9186/a000730</a>.","bibtex":"@article{Bruns_Mette_2025, title={Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?}, volume={14}, DOI={<a href=\"https://doi.org/10.1026/2191-9186/a000730\">10.1026/2191-9186/a000730</a>}, number={4}, journal={Frühe Bildung}, publisher={Hogrefe Publishing Group}, author={Bruns, Julia and Mette, Tessa}, year={2025}, pages={193–200} }","ama":"Bruns J, Mette T. Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden? <i>Frühe Bildung</i>. 2025;14(4):193-200. doi:<a href=\"https://doi.org/10.1026/2191-9186/a000730\">10.1026/2191-9186/a000730</a>","ieee":"J. Bruns and T. Mette, “Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?,” <i>Frühe Bildung</i>, vol. 14, no. 4, pp. 193–200, 2025, doi: <a href=\"https://doi.org/10.1026/2191-9186/a000730\">10.1026/2191-9186/a000730</a>.","apa":"Bruns, J., &#38; Mette, T. (2025). Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden? <i>Frühe Bildung</i>, <i>14</i>(4), 193–200. <a href=\"https://doi.org/10.1026/2191-9186/a000730\">https://doi.org/10.1026/2191-9186/a000730</a>","short":"J. Bruns, T. Mette, Frühe Bildung 14 (2025) 193–200.","chicago":"Bruns, Julia, and Tessa Mette. “Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?” <i>Frühe Bildung</i> 14, no. 4 (2025): 193–200. <a href=\"https://doi.org/10.1026/2191-9186/a000730\">https://doi.org/10.1026/2191-9186/a000730</a>."},"author":[{"full_name":"Bruns, Julia","last_name":"Bruns","orcid":"https://orcid.org/0000-0002-6604-5864","first_name":"Julia","id":"72183"},{"full_name":"Mette, Tessa","last_name":"Mette","first_name":"Tessa"}],"publication_identifier":{"issn":["2191-9186","2191-9194"]},"title":"Mathematik mit Kindern ausgehend von Spiel- und Routinesituationen in der Kindertagesstätte erkunden?","year":"2025","intvolume":"        14","date_updated":"2025-10-05T17:56:50Z","publication_status":"published","language":[{"iso":"ger"}],"alternative_title":["Analyse von Gelegenheiten zur frühen mathematischen Bildung im Alltag einer Kindertagesstätte"],"doi":"10.1026/2191-9186/a000730","publication":"Frühe Bildung","issue":"4","abstract":[{"lang":"eng","text":"<jats:p> Zusammenfassung: Frühe mathematische Bildung, die ihren Ausgangspunkt in den (Spiel-)Situationen der Kindertagesstätte nimmt, kann breite mathematische Erfahrungen ermöglichen, wenn die (Spiel-)Situationen entsprechende Möglichkeiten bieten. Erste Studien weisen darauf hin, dass in diesen Situationen verschiedene mathematische Inhalte angesprochen werden können. Allerdings konzentrieren sich bisherige Studien auf ausgewählte Kontexte oder Inhaltsbereiche. Diese Studie zielt daher auf eine vertiefte Analyse der Gelegenheiten für mathematische Erfahrungen, die in verschiedenen (Spiel-)Situationen im Alltag der Kindertagesstätte entstehen können. Dazu wurde eine videobasierte Beobachtungsstudie mittels einer Action-Kamera in einer Kindertagesstätte durchgeführt. Die Ergebnisse zeigen, dass eine Vielfalt von mathematischen Inhalten in (Spiel-)Situationen in der Kindertagesstätte beobachtet werden kann, einzelne Inhalte jedoch nur in formellen Lernsituationen auftreten. </jats:p>"}],"date_created":"2025-10-05T17:56:06Z","department":[{"_id":"611"}],"type":"journal_article"},{"oa":"1","external_id":{"arxiv":["2411.18422"]},"citation":{"ieee":"R. I. Bot and K. Sonntag, “Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization,” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","apa":"Bot, R. I., &#38; Sonntag, K. (2025). Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>.","chicago":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","short":"R.I. Bot, K. Sonntag, Journal of Mathematical Analysis and Applications (2025).","mla":"Bot, Radu Ioan, and Konstantin Sonntag. “Inertial Dynamics with Vanishing Tikhonov Regularization for Multobjective Optimization.” <i>Journal of Mathematical Analysis and Applications</i>, 2025.","bibtex":"@article{Bot_Sonntag_2025, title={Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization}, journal={Journal of Mathematical Analysis and Applications}, author={Bot, Radu Ioan and Sonntag, Konstantin}, year={2025} }","ama":"Bot RI, Sonntag K. Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization. <i>Journal of Mathematical Analysis and Applications</i>. Published online 2025."},"file_date_updated":"2024-11-28T08:58:00Z","user_id":"56399","ddc":["510"],"_id":"57472","has_accepted_license":"1","status":"public","department":[{"_id":"101"},{"_id":"530"},{"_id":"655"}],"keyword":["Pareto optimization","Lyapunov analysis","gradient-like dynamical systems","inertial dynamics","asymptotic vanishing damping","Tikhonov regularization","strong convergence"],"type":"journal_article","date_created":"2024-11-28T08:58:17Z","file":[{"date_updated":"2024-11-28T08:58:00Z","relation":"main_file","file_size":4291134,"access_level":"open_access","file_name":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization.pdf","content_type":"application/pdf","file_id":"57473","creator":"sonntagk","date_created":"2024-11-28T08:58:00Z"}],"abstract":[{"text":"In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting.","lang":"eng"}],"publication":"Journal of Mathematical Analysis and Applications","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/pdf/2411.18422"}],"date_updated":"2025-10-16T11:56:36Z","author":[{"full_name":"Bot, Radu Ioan","last_name":"Bot","first_name":"Radu Ioan"},{"full_name":"Sonntag, Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin","id":"56399"}],"title":"Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization","year":"2025"},{"citation":{"ieee":"S. Rezat and N. Doligkeit, “Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken,” <i>mathematik lehren</i>, no. 252, pp. 16–22, 2025.","apa":"Rezat, S., &#38; Doligkeit, N. (2025). Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken. <i>mathematik lehren</i>, <i>252</i>, 16–22.","short":"S. Rezat, N. Doligkeit, mathematik lehren (2025) 16–22.","chicago":"Rezat, Sebastian, and Nadja Doligkeit. “Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken.” <i>mathematik lehren</i>, no. 252 (2025): 16–22.","mla":"Rezat, Sebastian, and Nadja Doligkeit. “Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken.” <i>mathematik lehren</i>, no. 252, 2025, pp. 16–22.","bibtex":"@article{Rezat_Doligkeit_2025, title={Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken}, number={252}, journal={mathematik lehren}, author={Rezat, Sebastian and Doligkeit, Nadja}, year={2025}, pages={16–22} }","ama":"Rezat S, Doligkeit N. Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken. <i>mathematik lehren</i>. 2025;(252):16–22."},"issue":"252","publication":"mathematik lehren","date_created":"2025-11-21T16:25:49Z","department":[{"_id":"360"}],"type":"journal_article","author":[{"full_name":"Rezat, Sebastian","first_name":"Sebastian","last_name":"Rezat","id":"31132"},{"first_name":"Nadja","last_name":"Doligkeit","full_name":"Doligkeit, Nadja"}],"title":"Zahlenmuster und Brüche: Eine Lernumgebung zum algebraischen Denken","status":"public","year":"2025","publication_status":"published","date_updated":"2025-11-21T16:26:27Z","language":[{"iso":"ger"}],"_id":"62283","page":"16–22","user_id":"31132"},{"editor":[{"last_name":"Cramer","first_name":"C.","full_name":"Cramer, C."},{"full_name":"König, J.","last_name":"König","first_name":"J."},{"first_name":"M.","last_name":"Rothland","full_name":"Rothland, M."}],"doi":"10.35468/hblb2025-070","user_id":"44184","_id":"62645","language":[{"iso":"ger"}],"edition":"2","publisher":"Klinkhardt","page":"549-555","date_updated":"2025-11-27T10:53:52Z","author":[{"id":"60267","full_name":"Häsel-Weide, Uta","first_name":"Uta","orcid":"0000-0001-6278-4240","last_name":"Häsel-Weide"},{"full_name":"Nührenbörger, Marcus","first_name":"Marcus","last_name":"Nührenbörger"}],"year":"2025","status":"public","title":" Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule","department":[{"_id":"543"}],"type":"book_chapter","date_created":"2025-11-27T10:53:30Z","citation":{"mla":"Häsel-Weide, Uta, and Marcus Nührenbörger. “ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule.” <i>Handbuch Lehrerinnen- und Lehrerbildung</i>, edited by C. Cramer et al., 2nd ed., Klinkhardt, 2025, pp. 549–55, doi:<a href=\"https://doi.org/10.35468/hblb2025-070\">10.35468/hblb2025-070</a>.","bibtex":"@inbook{Häsel-Weide_Nührenbörger_2025, edition={2}, title={ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule}, DOI={<a href=\"https://doi.org/10.35468/hblb2025-070\">10.35468/hblb2025-070</a>}, booktitle={Handbuch Lehrerinnen- und Lehrerbildung}, publisher={Klinkhardt}, author={Häsel-Weide, Uta and Nührenbörger, Marcus}, editor={Cramer, C. and König, J. and Rothland, M.}, year={2025}, pages={549–555} }","ama":"Häsel-Weide U, Nührenbörger M.  Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule. In: Cramer C, König J, Rothland M, eds. <i>Handbuch Lehrerinnen- und Lehrerbildung</i>. 2nd ed. Klinkhardt; 2025:549-555. doi:<a href=\"https://doi.org/10.35468/hblb2025-070\">10.35468/hblb2025-070</a>","ieee":"U. Häsel-Weide and M. Nührenbörger, “ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule,” in <i>Handbuch Lehrerinnen- und Lehrerbildung</i>, 2nd ed., C. Cramer, J. König, and M. Rothland, Eds. Klinkhardt, 2025, pp. 549–555.","apa":"Häsel-Weide, U., &#38; Nührenbörger, M. (2025).  Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule. In C. Cramer, J. König, &#38; M. Rothland (Eds.), <i>Handbuch Lehrerinnen- und Lehrerbildung</i> (2nd ed., pp. 549–555). Klinkhardt. <a href=\"https://doi.org/10.35468/hblb2025-070\">https://doi.org/10.35468/hblb2025-070</a>","chicago":"Häsel-Weide, Uta, and Marcus Nührenbörger. “ Mathematik (Primarstufe) in der Lehrerinnen- und Lehrerbildung. Qualifizierung für das Lehren von Mathematik in der Grundschule.” In <i>Handbuch Lehrerinnen- und Lehrerbildung</i>, edited by C. Cramer, J. König, and M. Rothland, 2nd ed., 549–55. Klinkhardt, 2025. <a href=\"https://doi.org/10.35468/hblb2025-070\">https://doi.org/10.35468/hblb2025-070</a>.","short":"U. Häsel-Weide, M. Nührenbörger, in: C. Cramer, J. König, M. Rothland (Eds.), Handbuch Lehrerinnen- und Lehrerbildung, 2nd ed., Klinkhardt, 2025, pp. 549–555."},"publication":"Handbuch Lehrerinnen- und Lehrerbildung"},{"oa":"1","citation":{"apa":"Sonntag, K. (2025). <i>First-order methods and gradient dynamical systems for multiobjective optimization</i>. Paderborn University. <a href=\"https://doi.org/10.17619/UNIPB/1-2457\">https://doi.org/10.17619/UNIPB/1-2457</a>","ieee":"K. Sonntag, <i>First-order methods and gradient dynamical systems for multiobjective optimization</i>. Paderborn University, 2025.","chicago":"Sonntag, Konstantin. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University, 2025. <a href=\"https://doi.org/10.17619/UNIPB/1-2457\">https://doi.org/10.17619/UNIPB/1-2457</a>.","short":"K. Sonntag, First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization, Paderborn University, 2025.","mla":"Sonntag, Konstantin. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University, 2025, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>.","ama":"Sonntag K. <i>First-Order Methods and Gradient Dynamical Systems for Multiobjective Optimization</i>. Paderborn University; 2025. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>","bibtex":"@book{Sonntag_2025, title={First-order methods and gradient dynamical systems for multiobjective optimization}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-2457\">10.17619/UNIPB/1-2457</a>}, publisher={Paderborn University}, author={Sonntag, Konstantin}, year={2025} }"},"supervisor":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"user_id":"56399","ddc":["510"],"_id":"62750","publisher":"Paderborn University","has_accepted_license":"1","status":"public","type":"dissertation","department":[{"_id":"101"},{"_id":"530"}],"date_created":"2025-12-03T06:55:01Z","abstract":[{"text":"Diese Dissertation enthält Beiträge zum Bereich der Mehrzieloptimierung mit einem Fokus auf unbeschränkten Problemen, die auf einem allgemeinen Hilbertraum definiert sind. Für Mehrzieloptimierungsprobleme mit lokal Lipschitz-stetigen Zielfunktionen definieren wir ein multikriterielles Subdifferential, das wir erstmals im Kontext allgemeiner Hilberträume analysieren. Aufbauend auf diesen theoretischen Untersuchungen präsentieren wir ein Abstiegsverfahren, bei welchem in jeder Iteration eine Abstiegsrichtung mittels einer numerischen Approximation des multikriteriellen Subdifferentials bestimmt wird. Im Kontext konvexer, stetig differenzierbarer Zielfunktionen mit Lipschitz-stetigen Gradienten, führen wir eine Familie von dynamischen Gradientensystemen mit Trägheitsterm ein, die bekannte kontinuierliche Systeme aus der skalaren Optimierung verallgemeinern. Wir stellen drei neue Systeme vor: eines mit konstanter Dämpfung, eines mit asymptotisch abnehmender Dämpfung und eines, das zusätzlich eine zeitabhängige Tikhonov-Regularisierung beinhaltet. Aufbauend auf den Untersuchungen der neuen dynamischen Gradientensysteme, entwickeln wir ein beschleunigtes Gradientenverfahren zur Mehrzieloptimierung, das auf einer Diskretisierung des multikriteriellen Gradientensystems mit asymptotisch abnehmender Dämpfung beruht. Das hergeleitete Verfahren bewahrt die günstigen Konvergenzeigenschaften des kontinuierlichen Systems und erreicht eine schnellere Konvergenz als klassische Verfahren.","lang":"eng"},{"text":"This dissertation contributes to the field of multiobjective optimization, with a focus on unconstrained problems formulated in a general Hilbert space. For multiobjective optimization problems with locally Lipschitz continuous objective functions, we define a multiobjective subdifferential, which we analyze for the first time in the context of general Hilbert spaces. Building on these theoretical investigations, we present a descent method in which, at each iteration, a descent direction is determined via a numerical approximation of the multiobjective subdifferential. In the setting of convex, continuously differentiable objective functions with Lipschitz continuous gradients, we introduce a family of inertial gradient dynamical systems that generalize well-known continuous-time systems from scalar optimization. We present three novel systems: one with constant damping, one with asymptotic vanishing damping, and one combining vanishing damping with time-dependent Tikhonov regularization. Building on the investigation of the novel gradient dynamical systems, we develop an accelerated gradient method for multiobjective optimization via discretization of the multiobjective gradient system with asymptotic vanishing damping. The proposed method retains the favorable convergence properties of the continuous system while achieving faster convergence than standard approaches, such as classical methods.","lang":"eng"}],"doi":"10.17619/UNIPB/1-2457","main_file_link":[{"open_access":"1","url":"https://digital.ub.uni-paderborn.de/hs/download/pdf/8141881"}],"language":[{"iso":"eng"}],"date_updated":"2025-12-03T07:04:36Z","title":"First-order methods and gradient dynamical systems for multiobjective optimization","year":"2025","author":[{"id":"56399","full_name":"Sonntag, Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin"}]}]