1. The liberation set in the inverse eigenvalue problem of a graphJephian C.-H. Lin, Polona Oblak, Helena Šmigoc, 2023, original scientific article Abstract: The inverse eigenvalue problem of a graph $G$ is the problem of characterizing all lists of eigenvalues of real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of $G$. The strong spectral property is a powerful tool in this problem, which identifies matrices whose entries can be perturbed while controlling the pattern and preserving the eigenvalues. The Matrix Liberation Lemma introduced by Barrett et al. in 2020 advances the notion to a more general setting. In this paper we revisit the Matrix Liberation Lemma and prove an equivalent statement, that reduces some of the technical difficulties in applying the result. We test our method on matrices of the form $M=A \oplus B$ and show how this new approach supplements the results that can be obtained from the strong spectral property only. While extending this notion to the direct sums of graphs, we discover a surprising connection with the zero forcing game on Cartesian products of graphs. Throughout the paper we apply our results to resolve a selection of open cases for the inverse eigenvalue problem of a graph on six vertices.
Keywords: symmetric matrix, inverse eigenvalue problem, strong spectral property, Matrix Liberation Lemma, zero forcing
Published in DiRROS: 14.03.2024; Views: 87; Downloads: 47
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2. Effects of Zr doping into ceria for the dry reforming of methane over ▫$Ni/CeZrO_2$▫ catalysts ein situ studies with XRD, XAFS, and AP-XPS : in situ studies with XRD, XAFS, and AP-XPSFeng Zhang, Zenghui Liu, Xiaobo Chen, Ning Rui, Luis E. Betancourt, Lili Lin, Wenqian Xu, Cheng-jun Sun, A. M. Milinda Abeykoon, José A. Rodriguez, Janvit Teržan, Kristijan Lorber, Petar Djinović, Sanjaya D. Senanayake, 2020, original scientific article Keywords: nickel, ceria, zirconia, ▫$CeZrO_2$▫ solid solution, XRD, XAFS, AP-XPS, dry reforming of methane
Published in DiRROS: 13.03.2023; Views: 494; Downloads: 336
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4. In-situ regeneration of Au nanocatalysts by atmospheric-pressure air plasma : significant contribution of water vaporBin Zhu, Xiao-Song Li, Jing-Lin Liu, Jin-Bao Liu, Xiaobing Zhu, Ai-Min Zhu, 2015, original scientific article Keywords: Au catalyst, air plasma, in-situ regeneration, water vapor, CO oxidation
Published in DiRROS: 07.04.2016; Views: 4423; Downloads: 978
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5. In-situ plasma regeneration of deactivated Au/TiO [sub] 2 nanocatalysts during CO oxidation and effect of N [sub] 2 contentHong-Yu Fan, Chuan Shi, Xiao-Song Li, Shuo Zhang, Jing-Lin Liu, Ai-Min Zhu, 2012, original scientific article Keywords: gold catalyst, deactivation, plasma regeneration, N [sub] 2 content, CO oxidation
Published in DiRROS: 07.04.2016; Views: 5781; Downloads: 821
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