{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,5]],"date-time":"2025-12-05T12:22:34Z","timestamp":1764937354333},"reference-count":21,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["NHM"],"published-print":{"date-parts":[[2022]]},"abstract":"<p style='text-indent:20px;'>Hyperbolic systems on networks often can be written as systems of first order equations on an interval, coupled by transmission conditions at the endpoints, also called port-Hamiltonians. However, general results for the latter have been difficult to interpret in the network language. The aim of this paper is to derive conditions under which a port-Hamiltonian with general linear Kirchhoff's boundary conditions can be written as a system of <inline-formula><tex-math id=\"M1\">\\begin{document}$ 2\\times 2 $\\end{document}<\/tex-math><\/inline-formula> hyperbolic equations on a metric graph <inline-formula><tex-math id=\"M2\">\\begin{document}$ \\Gamma $\\end{document}<\/tex-math><\/inline-formula>. This is achieved by interpreting the matrix of the boundary conditions as a potential map of vertex connections of <inline-formula><tex-math id=\"M3\">\\begin{document}$ \\Gamma $\\end{document}<\/tex-math><\/inline-formula> and then showing that, under the derived assumptions, that matrix can be used to determine the adjacency matrix of <inline-formula><tex-math id=\"M4\">\\begin{document}$ \\Gamma $\\end{document}<\/tex-math><\/inline-formula>.<\/p><\/jats:p>","DOI":"10.3934\/nhm.2021024","type":"journal-article","created":{"date-parts":[[2021,12,28]],"date-time":"2021-12-28T11:54:34Z","timestamp":1640692474000},"page":"73","source":"Crossref","is-referenced-by-count":3,"title":["Telegraph systems on networks and port-Hamiltonians. \u2161. Network realizability"],"prefix":"10.3934","volume":"17","author":[{"given":"Jacek","family":"Banasiak","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa \n\t\t\t\t\t\t\t\t\t \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \t\t\t\t\t\t\t\t\t Institute of Mathematics, L\u00f3d\u017a University of Technology L\u00f3d\u017a, Poland \n\t\t\t\t\t\t\t\t\t \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \t\t\t\t\t\t\t\t\t International Scientific Laboratory of Applied Semigroup Research South Ural State University, Chelyabinsk, Russia"}]},{"given":"Adam","family":"B\u0142och","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, L\u00f3d\u017a University of Technology L\u00f3d\u017a, Poland"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2021024-1","unstructured":"F. 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