[{"language":[{"iso":"eng"}],"_id":"63342","user_id":"31496","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>In a bounded planar domain <jats:inline-formula><jats:alternatives><jats:tex-math>$\\varOmega $</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Ω</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with smooth boundary, the initial-boundary value problem of homogeneous Neumann type for the Keller-Segel-fluid system \r\n\t\t\t<jats:disp-formula><jats:alternatives><jats:tex-math> $$\\begin{aligned} \\left \\{ \\textstyle\\begin{array}{l@{\\quad }l} n_{t} + \\nabla \\cdot (nu) = \\Delta n - \\nabla \\cdot (n\\nabla c), &amp; x\\in \\varOmega , \\ t&gt;0, \\\\ 0 = \\Delta c -c+n, &amp; x\\in \\varOmega , \\ t&gt;0, \\end{array}\\displaystyle \\right . \\end{aligned}$$ </jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mrow>\r\n                    <mml:mo>{</mml:mo>\r\n                    <mml:mtable>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:msub>\r\n                            <mml:mi>n</mml:mi>\r\n                            <mml:mi>t</mml:mi>\r\n                          </mml:msub>\r\n                          <mml:mo>+</mml:mo>\r\n                          <mml:mi>∇</mml:mi>\r\n                          <mml:mo>⋅</mml:mo>\r\n                          <mml:mo>(</mml:mo>\r\n                          <mml:mi>n</mml:mi>\r\n                          <mml:mi>u</mml:mi>\r\n                          <mml:mo>)</mml:mo>\r\n                          <mml:mo>=</mml:mo>\r\n                          <mml:mi>Δ</mml:mi>\r\n                          <mml:mi>n</mml:mi>\r\n                          <mml:mo>−</mml:mo>\r\n                          <mml:mi>∇</mml:mi>\r\n                          <mml:mo>⋅</mml:mo>\r\n                          <mml:mo>(</mml:mo>\r\n                          <mml:mi>n</mml:mi>\r\n                          <mml:mi>∇</mml:mi>\r\n                          <mml:mi>c</mml:mi>\r\n                          <mml:mo>)</mml:mo>\r\n                          <mml:mo>,</mml:mo>\r\n                        </mml:mtd>\r\n                        <mml:mtd>\r\n                          <mml:mi>x</mml:mi>\r\n                          <mml:mo>∈</mml:mo>\r\n                          <mml:mi>Ω</mml:mi>\r\n                          <mml:mo>,</mml:mo>\r\n                          <mml:mspace/>\r\n                          <mml:mi>t</mml:mi>\r\n                          <mml:mo>&gt;</mml:mo>\r\n                          <mml:mn>0</mml:mn>\r\n                          <mml:mo>,</mml:mo>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                      <mml:mtr>\r\n                        <mml:mtd>\r\n                          <mml:mn>0</mml:mn>\r\n                          <mml:mo>=</mml:mo>\r\n                          <mml:mi>Δ</mml:mi>\r\n                          <mml:mi>c</mml:mi>\r\n                          <mml:mo>−</mml:mo>\r\n                          <mml:mi>c</mml:mi>\r\n                          <mml:mo>+</mml:mo>\r\n                          <mml:mi>n</mml:mi>\r\n                          <mml:mo>,</mml:mo>\r\n                        </mml:mtd>\r\n                        <mml:mtd>\r\n                          <mml:mi>x</mml:mi>\r\n                          <mml:mo>∈</mml:mo>\r\n                          <mml:mi>Ω</mml:mi>\r\n                          <mml:mo>,</mml:mo>\r\n                          <mml:mspace/>\r\n                          <mml:mi>t</mml:mi>\r\n                          <mml:mo>&gt;</mml:mo>\r\n                          <mml:mn>0</mml:mn>\r\n                          <mml:mo>,</mml:mo>\r\n                        </mml:mtd>\r\n                      </mml:mtr>\r\n                    </mml:mtable>\r\n                  </mml:mrow>\r\n                </mml:math></jats:alternatives></jats:disp-formula> is considered, where <jats:inline-formula><jats:alternatives><jats:tex-math>$u$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>u</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> is a given sufficiently smooth velocity field on <jats:inline-formula><jats:alternatives><jats:tex-math>$\\overline {\\varOmega }\\times [0,\\infty )$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mover>\r\n                    <mml:mi>Ω</mml:mi>\r\n                    <mml:mo>‾</mml:mo>\r\n                  </mml:mover>\r\n                  <mml:mo>×</mml:mo>\r\n                  <mml:mo>[</mml:mo>\r\n                  <mml:mn>0</mml:mn>\r\n                  <mml:mo>,</mml:mo>\r\n                  <mml:mi>∞</mml:mi>\r\n                  <mml:mo>)</mml:mo>\r\n                </mml:math></jats:alternatives></jats:inline-formula> that is tangential on <jats:inline-formula><jats:alternatives><jats:tex-math>$\\partial \\varOmega $</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>∂</mml:mi>\r\n                  <mml:mi>Ω</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> but not necessarily solenoidal.</jats:p><jats:p>It is firstly shown that for any choice of <jats:inline-formula><jats:alternatives><jats:tex-math>$n_{0}\\in C^{0}(\\overline {\\varOmega })$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:msub>\r\n                  <mml:mo>∈</mml:mo>\r\n                  <mml:msup>\r\n                    <mml:mi>C</mml:mi>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:msup>\r\n                  <mml:mo>(</mml:mo>\r\n                  <mml:mover>\r\n                    <mml:mi>Ω</mml:mi>\r\n                    <mml:mo>‾</mml:mo>\r\n                  </mml:mover>\r\n                  <mml:mo>)</mml:mo>\r\n                </mml:math></jats:alternatives></jats:inline-formula> with <jats:inline-formula><jats:alternatives><jats:tex-math>$\\int _{\\varOmega}n_{0}&lt;4\\pi $</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n                    <mml:mo>∫</mml:mo>\r\n                    <mml:mi>Ω</mml:mi>\r\n                  </mml:msub>\r\n                  <mml:msub>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:msub>\r\n                  <mml:mo>&lt;</mml:mo>\r\n                  <mml:mn>4</mml:mn>\r\n                  <mml:mi>π</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, this problem admits a global classical solution with <jats:inline-formula><jats:alternatives><jats:tex-math>$n(\\cdot ,0)=n_{0}$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>n</mml:mi>\r\n                  <mml:mo>(</mml:mo>\r\n                  <mml:mo>⋅</mml:mo>\r\n                  <mml:mo>,</mml:mo>\r\n                  <mml:mn>0</mml:mn>\r\n                  <mml:mo>)</mml:mo>\r\n                  <mml:mo>=</mml:mo>\r\n                  <mml:msub>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:msub>\r\n                </mml:math></jats:alternatives></jats:inline-formula>, and that this solution is even bounded whenever <jats:inline-formula><jats:alternatives><jats:tex-math>$u$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>u</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> is bounded and <jats:inline-formula><jats:alternatives><jats:tex-math>$\\int _{\\varOmega}n_{0}&lt;2\\pi $</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n                    <mml:mo>∫</mml:mo>\r\n                    <mml:mi>Ω</mml:mi>\r\n                  </mml:msub>\r\n                  <mml:msub>\r\n                    <mml:mi>n</mml:mi>\r\n                    <mml:mn>0</mml:mn>\r\n                  </mml:msub>\r\n                  <mml:mo>&lt;</mml:mo>\r\n                  <mml:mn>2</mml:mn>\r\n                  <mml:mi>π</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula>. Secondly, it is seen that for each <jats:inline-formula><jats:alternatives><jats:tex-math>$m&gt;4\\pi $</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>m</mml:mi>\r\n                  <mml:mo>&gt;</mml:mo>\r\n                  <mml:mn>4</mml:mn>\r\n                  <mml:mi>π</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> one can find a classical solution with <jats:inline-formula><jats:alternatives><jats:tex-math>$\\int _{\\varOmega}n(\\cdot ,0)=m$</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:msub>\r\n                    <mml:mo>∫</mml:mo>\r\n                    <mml:mi>Ω</mml:mi>\r\n                  </mml:msub>\r\n                  <mml:mi>n</mml:mi>\r\n                  <mml:mo>(</mml:mo>\r\n                  <mml:mo>⋅</mml:mo>\r\n                  <mml:mo>,</mml:mo>\r\n                  <mml:mn>0</mml:mn>\r\n                  <mml:mo>)</mml:mo>\r\n                  <mml:mo>=</mml:mo>\r\n                  <mml:mi>m</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> which blows up in finite time, provided that <jats:inline-formula><jats:alternatives><jats:tex-math>$\\varOmega $</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>Ω</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> satisfies a technical assumption requiring <jats:inline-formula><jats:alternatives><jats:tex-math>$\\partial \\varOmega $</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mi>∂</mml:mi>\r\n                  <mml:mi>Ω</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> to contain a line segment.</jats:p><jats:p>In particular, this indicates that the value <jats:inline-formula><jats:alternatives><jats:tex-math>$4\\pi $</jats:tex-math><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                  <mml:mn>4</mml:mn>\r\n                  <mml:mi>π</mml:mi>\r\n                </mml:math></jats:alternatives></jats:inline-formula> of the critical mass for the corresponding fluid-free Keller-Segel system is left unchanged by any fluid interaction of the considered type, thus marking a considerable contrast to a recent result revealing some fluid-induced increase of critical blow-up masses in a related Cauchy problem in the entire plane.</jats:p>","lang":"eng"}],"status":"public","type":"journal_article","publication":"Acta Applicandae Mathematicae","title":"Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?","doi":"10.1007/s10440-020-00312-2","date_updated":"2025-12-18T19:57:40Z","publisher":"Springer Science and Business Media LLC","author":[{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-18T19:47:51Z","volume":169,"year":"2020","citation":{"mla":"Winkler, Michael. “Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?” <i>Acta Applicandae Mathematicae</i>, vol. 169, no. 1, Springer Science and Business Media LLC, 2020, pp. 577–91, doi:<a href=\"https://doi.org/10.1007/s10440-020-00312-2\">10.1007/s10440-020-00312-2</a>.","short":"M. Winkler, Acta Applicandae Mathematicae 169 (2020) 577–591.","bibtex":"@article{Winkler_2020, title={Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?}, volume={169}, DOI={<a href=\"https://doi.org/10.1007/s10440-020-00312-2\">10.1007/s10440-020-00312-2</a>}, number={1}, journal={Acta Applicandae Mathematicae}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2020}, pages={577–591} }","apa":"Winkler, M. (2020). Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains? <i>Acta Applicandae Mathematicae</i>, <i>169</i>(1), 577–591. <a href=\"https://doi.org/10.1007/s10440-020-00312-2\">https://doi.org/10.1007/s10440-020-00312-2</a>","ama":"Winkler M. Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains? <i>Acta Applicandae Mathematicae</i>. 2020;169(1):577-591. doi:<a href=\"https://doi.org/10.1007/s10440-020-00312-2\">10.1007/s10440-020-00312-2</a>","ieee":"M. Winkler, “Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?,” <i>Acta Applicandae Mathematicae</i>, vol. 169, no. 1, pp. 577–591, 2020, doi: <a href=\"https://doi.org/10.1007/s10440-020-00312-2\">10.1007/s10440-020-00312-2</a>.","chicago":"Winkler, Michael. “Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?” <i>Acta Applicandae Mathematicae</i> 169, no. 1 (2020): 577–91. <a href=\"https://doi.org/10.1007/s10440-020-00312-2\">https://doi.org/10.1007/s10440-020-00312-2</a>."},"page":"577-591","intvolume":"       169","publication_status":"published","publication_identifier":{"issn":["0167-8019","1572-9036"]},"issue":"1"},{"year":"2018","citation":{"apa":"Peitz, S., Ober-Blöbaum, S., &#38; Dellnitz, M. (2018). Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. <i>Acta Applicandae Mathematicae</i>, <i>161</i>(1), 171–199. <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">https://doi.org/10.1007/s10440-018-0209-7</a>","short":"S. Peitz, S. Ober-Blöbaum, M. Dellnitz, Acta Applicandae Mathematicae 161 (2018) 171–199.","bibtex":"@article{Peitz_Ober-Blöbaum_Dellnitz_2018, title={Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling}, volume={161}, DOI={<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>}, number={1}, journal={Acta Applicandae Mathematicae}, author={Peitz, Sebastian and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2018}, pages={171–199} }","mla":"Peitz, Sebastian, et al. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” <i>Acta Applicandae Mathematicae</i>, vol. 161, no. 1, 2018, pp. 171–199, doi:<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>.","chicago":"Peitz, Sebastian, Sina Ober-Blöbaum, and Michael Dellnitz. “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.” <i>Acta Applicandae Mathematicae</i> 161, no. 1 (2018): 171–199. <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">https://doi.org/10.1007/s10440-018-0209-7</a>.","ieee":"S. Peitz, S. Ober-Blöbaum, and M. Dellnitz, “Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling,” <i>Acta Applicandae Mathematicae</i>, vol. 161, no. 1, pp. 171–199, 2018, doi: <a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>.","ama":"Peitz S, Ober-Blöbaum S, Dellnitz M. Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling. <i>Acta Applicandae Mathematicae</i>. 2018;161(1):171–199. doi:<a href=\"https://doi.org/10.1007/s10440-018-0209-7\">10.1007/s10440-018-0209-7</a>"},"page":"171–199","intvolume":"       161","publication_status":"published","publication_identifier":{"issn":["0167-8019","1572-9036"]},"issue":"1","title":"Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling","doi":"10.1007/s10440-018-0209-7","date_updated":"2022-01-21T10:01:41Z","author":[{"id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","first_name":"Sebastian"},{"first_name":"Sina","id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_created":"2019-03-29T13:30:41Z","volume":161,"abstract":[{"text":"In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When the problem under consideration is described by a partial differential equation (PDE), as is the case for fluid flow, the computational cost rapidly increases and makes its direct treatment infeasible. Reduced order modeling is a very popular method to reduce the computational cost, in particular in a multi query context such as uncertainty quantification, parameter estimation or optimization. In this article, we show how to combine reduced order modeling and multiobjective optimal control techniques in order to efficiently solve multiobjective optimal control problems constrained by PDEs. We consider a global, derivative free optimization method as well as a local, gradient-based approach for which the optimality system is derived in two different ways. The methods are compared with regard to the solution quality as well as the computational effort and they are illustrated using the example of the flow around a cylinder and a backward-facing-step channel flow.","lang":"eng"}],"status":"public","type":"journal_article","publication":"Acta Applicandae Mathematicae","language":[{"iso":"eng"}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"_id":"8753","user_id":"15694","department":[{"_id":"101"}]},{"status":"public","publication":"Acta Applicandae Mathematicae","type":"journal_article","language":[{"iso":"eng"}],"_id":"63368","user_id":"31496","year":"2018","page":"1-17","intvolume":"       163","citation":{"ieee":"M. Winkler, “Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity,” <i>Acta Applicandae Mathematicae</i>, vol. 163, no. 1, pp. 1–17, 2018, doi: <a href=\"https://doi.org/10.1007/s10440-018-0211-0\">10.1007/s10440-018-0211-0</a>.","chicago":"Winkler, Michael. “Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity.” <i>Acta Applicandae Mathematicae</i> 163, no. 1 (2018): 1–17. <a href=\"https://doi.org/10.1007/s10440-018-0211-0\">https://doi.org/10.1007/s10440-018-0211-0</a>.","ama":"Winkler M. Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity. <i>Acta Applicandae Mathematicae</i>. 2018;163(1):1-17. doi:<a href=\"https://doi.org/10.1007/s10440-018-0211-0\">10.1007/s10440-018-0211-0</a>","mla":"Winkler, Michael. “Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity.” <i>Acta Applicandae Mathematicae</i>, vol. 163, no. 1, Springer Science and Business Media LLC, 2018, pp. 1–17, doi:<a href=\"https://doi.org/10.1007/s10440-018-0211-0\">10.1007/s10440-018-0211-0</a>.","bibtex":"@article{Winkler_2018, title={Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity}, volume={163}, DOI={<a href=\"https://doi.org/10.1007/s10440-018-0211-0\">10.1007/s10440-018-0211-0</a>}, number={1}, journal={Acta Applicandae Mathematicae}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2018}, pages={1–17} }","short":"M. Winkler, Acta Applicandae Mathematicae 163 (2018) 1–17.","apa":"Winkler, M. (2018). Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity. <i>Acta Applicandae Mathematicae</i>, <i>163</i>(1), 1–17. <a href=\"https://doi.org/10.1007/s10440-018-0211-0\">https://doi.org/10.1007/s10440-018-0211-0</a>"},"publication_identifier":{"issn":["0167-8019","1572-9036"]},"publication_status":"published","issue":"1","title":"Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity","doi":"10.1007/s10440-018-0211-0","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-19T11:02:21Z","volume":163,"date_created":"2025-12-19T11:02:13Z","author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}]},{"year":"2006","issue":"1-2","title":"SU(d)-Biinvariant Random Walks on SL(d,C) and their Euclidean Counterparts","date_created":"2023-01-25T09:57:30Z","publisher":"Springer Science and Business Media LLC","publication":"Acta Applicandae Mathematicae","language":[{"iso":"eng"}],"keyword":["Applied Mathematics"],"intvolume":"        90","page":"179-195","citation":{"ama":"Rösler M, Voit M. SU(d)-Biinvariant Random Walks on SL(d,C) and their Euclidean Counterparts. <i>Acta Applicandae Mathematicae</i>. 2006;90(1-2):179-195. doi:<a href=\"https://doi.org/10.1007/s10440-006-9035-4\">10.1007/s10440-006-9035-4</a>","ieee":"M. Rösler and M. Voit, “SU(d)-Biinvariant Random Walks on SL(d,C) and their Euclidean Counterparts,” <i>Acta Applicandae Mathematicae</i>, vol. 90, no. 1–2, pp. 179–195, 2006, doi: <a href=\"https://doi.org/10.1007/s10440-006-9035-4\">10.1007/s10440-006-9035-4</a>.","chicago":"Rösler, Margit, and Michael Voit. “SU(d)-Biinvariant Random Walks on SL(d,C) and Their Euclidean Counterparts.” <i>Acta Applicandae Mathematicae</i> 90, no. 1–2 (2006): 179–95. <a href=\"https://doi.org/10.1007/s10440-006-9035-4\">https://doi.org/10.1007/s10440-006-9035-4</a>.","mla":"Rösler, Margit, and Michael Voit. “SU(d)-Biinvariant Random Walks on SL(d,C) and Their Euclidean Counterparts.” <i>Acta Applicandae Mathematicae</i>, vol. 90, no. 1–2, Springer Science and Business Media LLC, 2006, pp. 179–95, doi:<a href=\"https://doi.org/10.1007/s10440-006-9035-4\">10.1007/s10440-006-9035-4</a>.","bibtex":"@article{Rösler_Voit_2006, title={SU(d)-Biinvariant Random Walks on SL(d,C) and their Euclidean Counterparts}, volume={90}, DOI={<a href=\"https://doi.org/10.1007/s10440-006-9035-4\">10.1007/s10440-006-9035-4</a>}, number={1–2}, journal={Acta Applicandae Mathematicae}, publisher={Springer Science and Business Media LLC}, author={Rösler, Margit and Voit, Michael}, year={2006}, pages={179–195} }","short":"M. Rösler, M. Voit, Acta Applicandae Mathematicae 90 (2006) 179–195.","apa":"Rösler, M., &#38; Voit, M. (2006). SU(d)-Biinvariant Random Walks on SL(d,C) and their Euclidean Counterparts. <i>Acta Applicandae Mathematicae</i>, <i>90</i>(1–2), 179–195. <a href=\"https://doi.org/10.1007/s10440-006-9035-4\">https://doi.org/10.1007/s10440-006-9035-4</a>"},"publication_identifier":{"issn":["0167-8019","1572-9036"]},"publication_status":"published","doi":"10.1007/s10440-006-9035-4","volume":90,"author":[{"id":"37390","full_name":"Rösler, Margit","last_name":"Rösler","first_name":"Margit"},{"first_name":"Michael","last_name":"Voit","full_name":"Voit, Michael"}],"date_updated":"2023-01-26T17:47:14Z","status":"public","type":"journal_article","extern":"1","department":[{"_id":"555"}],"user_id":"37390","_id":"39948"}]