%0 Journal Article %1 fern2020construction %A Fernández, Mauricio %A Fritzen, Felix %D 2020 %J Journal of Applied Mathematics %K EXC2075 from:simtechpuma pn3 %P 18 %T Construction of a Class of Sharp L&#xf6;wner Majorants for a Set of Symmetric Matrices %U https://doi.org/10.1155/2020/9091387 %V 2020 %X The L&amp;#xf6;wner partial order is taken into consideration in order to define L&amp;#xf6;wner majorants for a given finite set of symmetric matrices. A special class of L&amp;#xf6;wner majorants is analyzed based on two specific matrix parametrizations: a two-parametric form and a four-parametric form, which arise in the context of so-called zeroth-order bounds of the effective linear behavior in the field of solid mechanics in engineering. The condensed explicit conditions defining the convex parameter sets of L&amp;#xf6;wner majorants are derived. Examples are provided, and potential application to semidefinite programming problems is discussed. Open-source MATLAB software is provided to support the theoretical findings and for reproduction of the presented results. The results of the present work offer in combination with the theory of zeroth-order bounds of mechanics a highly efficient approach for the automated material selection for future engineering applications."/><meta name="citation_fulltext_html_url" content="https://www.hindawi.com/journals/jam/2020/9091387/"/><meta name="citation_pdf_url" content="https://downloads.hindawi.com/journals/jam/2020/9091387.pdf"/><meta name="citation_xml_url" content="https://downloads.hindawi.com/journals/jam/2020/9091387.xml"/><meta name="dc.creator" content="Fernández, Mauricio"/><meta name="dc.creator" content="Fritzen, Felix"/><meta name="dc.title" content="Construction of a Class of Sharp Löwner Majorants for a Set of Symmetric Matrices"/><meta name="dc.description" content="The L&amp;#xf6;wner partial order is taken into consideration in order to define L&amp;#xf6;wner majorants for a given finite set of symmetric matrices. A special class of L&amp;#xf6;wner majorants is analyzed based on two specific matrix parametrizations: a two-parametric form and a four-parametric form, which arise in the context of so-called zeroth-order bounds of the effective linear behavior in the field of solid mechanics in engineering. The condensed explicit conditions defining the convex parameter sets of L&amp;#xf6;wner majorants are derived. Examples are provided, and potential application to semidefinite programming problems is discussed. Open-source MATLAB software is provided to support the theoretical findings and for reproduction of the presented results. The results of the present work offer in combination with the theory of zeroth-order bounds of mechanics a highly efficient approach for the automated material selection for future engineering applications."/><meta name="dc.publisher" content="Hindawi"/><meta name="dc.format" content="text/html"/><meta name="dc.language" content="en"/><meta name="dc.identifier" content="https://doi.org/10.1155/2020/9091387"/><meta name="dc.type" content="Research Article"/><meta name="dc.date" content="2020/06/11"/><meta name="dcterms.issued" content="2020/06/11"/><meta name="prism.publicationDate" content="2020/06/11"/><meta name="prism.volume" content="2020"/><meta name="prism.section" content="Research Article"/><meta name="prism.doi" content="https://doi.org/10.1155/2020/9091387"/><meta name="prism.issn" content="1110-757X"/><meta name="dc.source" content="Journal of Applied Mathematics"/><meta name="prism.publicationName" content="Journal of Applied Mathematics"/><meta name=äuthors" content="Mauricio Fernández | Felix Fritzen"/><meta name=Äuthor" content="Hindawi"/><meta name="robots" content="index"/><meta name="google-site-verification" content=ÄxEuDsL7vXGOxRe53-uFhOk2ODN0bbXMeuBy6Pfq4ww"/><script src="https://cdn.cookielaw.org/scripttemplates/otSDKStub.js" type="text/javascript" charset=ÜTF-8" data-domain-script="fbafd62a-0a4e-4f7b-a04d-56f57fa3d716"></script><link href="https://static-01.hindawi.com/articles/jam/volume-2020/9091387/9091387-style.css" rel="stylesheet" class="next-head"/><link href="https://static-01.hindawi.com/next_assets/YOfauMIWzCyU57PCScyHn/static/lib/basictable.css" rel="stylesheet" media="none" class="next-head"/><link rel="stylesheet" href="https://static-01.hindawi.com/next_assets/YOfauMIWzCyU57PCScyHn/static/lib/owl.carousel.min.css" media="none" class="next-head"/><link rel="stylesheet" href="https://static-01.hindawi.com/next_assets/YOfauMIWzCyU57PCScyHn/static/lib/owl.theme.default.min.css" media="none" class="next-head"/><script src="https://static-01.hindawi.com/next_assets/YOfauMIWzCyU57PCScyHn/static/lib/jquery.js" class="next-head"></script><link rel="preload" type="text/css" href="https://cdn.bibblio.org/rcm/4.24/bib-related-content.min.css" as="style" class="next-head"/><link rel="preload" type="text/css" href="https://cdn.bibblio.org/rcm/4.24/bib-related-content.min.css" as="style" class="next-head

@article{fern2020construction, abstract = {The L&amp;#xf6;wner partial order is taken into consideration in order to define L&amp;#xf6;wner majorants for a given finite set of symmetric matrices. A special class of L&amp;#xf6;wner majorants is analyzed based on two specific matrix parametrizations: a two-parametric form and a four-parametric form, which arise in the context of so-called zeroth-order bounds of the effective linear behavior in the field of solid mechanics in engineering. The condensed explicit conditions defining the convex parameter sets of L&amp;#xf6;wner majorants are derived. Examples are provided, and potential application to semidefinite programming problems is discussed. Open-source MATLAB software is provided to support the theoretical findings and for reproduction of the presented results. The results of the present work offer in combination with the theory of zeroth-order bounds of mechanics a highly efficient approach for the automated material selection for future engineering applications."/><meta name="citation_fulltext_html_url" content="https://www.hindawi.com/journals/jam/2020/9091387/"/><meta name="citation_pdf_url" content="https://downloads.hindawi.com/journals/jam/2020/9091387.pdf"/><meta name="citation_xml_url" content="https://downloads.hindawi.com/journals/jam/2020/9091387.xml"/><meta name="dc.creator" content="Fernández, Mauricio"/><meta name="dc.creator" content="Fritzen, Felix"/><meta name="dc.title" content="Construction of a Class of Sharp Löwner Majorants for a Set of Symmetric Matrices"/><meta name="dc.description" content="The L&amp;#xf6;wner partial order is taken into consideration in order to define L&amp;#xf6;wner majorants for a given finite set of symmetric matrices. A special class of L&amp;#xf6;wner majorants is analyzed based on two specific matrix parametrizations: a two-parametric form and a four-parametric form, which arise in the context of so-called zeroth-order bounds of the effective linear behavior in the field of solid mechanics in engineering. The condensed explicit conditions defining the convex parameter sets of L&amp;#xf6;wner majorants are derived. Examples are provided, and potential application to semidefinite programming problems is discussed. Open-source MATLAB software is provided to support the theoretical findings and for reproduction of the presented results. The results of the present work offer in combination with the theory of zeroth-order bounds of mechanics a highly efficient approach for the automated material selection for future engineering applications."/><meta name="dc.publisher" content="Hindawi"/><meta name="dc.format" content="text/html"/><meta name="dc.language" content="en"/><meta name="dc.identifier" content="https://doi.org/10.1155/2020/9091387"/><meta name="dc.type" content="Research Article"/><meta name="dc.date" content="2020/06/11"/><meta name="dcterms.issued" content="2020/06/11"/><meta name="prism.publicationDate" content="2020/06/11"/><meta name="prism.volume" content="2020"/><meta name="prism.section" content="Research Article"/><meta name="prism.doi" content="https://doi.org/10.1155/2020/9091387"/><meta name="prism.issn" content="1110-757X"/><meta name="dc.source" content="Journal of Applied Mathematics"/><meta name="prism.publicationName" content="Journal of Applied Mathematics"/><meta name="authors" content="Mauricio Fernández | Felix Fritzen"/><meta name="Author" content="Hindawi"/><meta name="robots" content="index"/><meta name="google-site-verification" content="AxEuDsL7vXGOxRe53-uFhOk2ODN0bbXMeuBy6Pfq4ww"/><script src="https://cdn.cookielaw.org/scripttemplates/otSDKStub.js" type="text/javascript" charset="UTF-8" data-domain-script="fbafd62a-0a4e-4f7b-a04d-56f57fa3d716"></script><link href="https://static-01.hindawi.com/articles/jam/volume-2020/9091387/9091387-style.css" rel="stylesheet" class="next-head"/><link href="https://static-01.hindawi.com/next_assets/YOfauMIWzCyU57PCScyHn/static/lib/basictable.css" rel="stylesheet" media="none" class="next-head"/><link rel="stylesheet" href="https://static-01.hindawi.com/next_assets/YOfauMIWzCyU57PCScyHn/static/lib/owl.carousel.min.css" media="none" class="next-head"/><link rel="stylesheet" href="https://static-01.hindawi.com/next_assets/YOfauMIWzCyU57PCScyHn/static/lib/owl.theme.default.min.css" media="none" class="next-head"/><script src="https://static-01.hindawi.com/next_assets/YOfauMIWzCyU57PCScyHn/static/lib/jquery.js" class="next-head"></script><link rel="preload" type="text/css" href="https://cdn.bibblio.org/rcm/4.24/bib-related-content.min.css" as="style" class="next-head"/><link rel="preload" type="text/css" href="https://cdn.bibblio.org/rcm/4.24/bib-related-content.min.css" as="style" class="next-head}, added-at = {2021-12-08T17:10:08.000+0100}, author = {Fernández, Mauricio and Fritzen, Felix}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/29e07e9ebc1a055e8badbe56cea96ef78/katharinafuchs}, interhash = {b8fb0aafaac7fbc2ba5db574b0508367}, intrahash = {9e07e9ebc1a055e8badbe56cea96ef78}, journal = {Journal of Applied Mathematics}, keywords = {EXC2075 from:simtechpuma pn3}, pages = 18, timestamp = {2021-12-08T16:10:08.000+0100}, title = {Construction of a Class of Sharp L&#xf6;wner Majorants for a Set of Symmetric Matrices}, url = {https://doi.org/10.1155/2020/9091387}, volume = 2020, year = 2020 }