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1.
Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size
Duško Bogdanić, Alen Ðurić, Sara Koljančić, Polona Oblak, Klemen Šivic, 2024, original scientific article

Abstract: In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix $B$ consisting of two Jordan blocks of the same size. We list all the possible Jordan canonical forms of the nilpotent matrices that commute with $B$ by characterizing the corresponding partitions.
Keywords: nilpotent matrix, centralizer, nilpotent orbit
Published in DiRROS: 26.03.2024; Views: 34; Downloads: 14
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2.
Seismogenic depth and seismic coupling estimation in the transition zone between Alps, Dinarides and Pannonian Basin for the new Slovenian seismic hazard model
Polona Zupančič, Barbara Šket Motnikar, Michele M. C. Carafa, Petra Jamšek Rupnik, Mladen Živčić, Vanja Kastelic, Gregor Rajh, Martina Čarman, Jure Atanackov, Andrej Gosar, 2024, original scientific article

Abstract: Seismogenic depth and seismic coupling are important inputs into seismic hazard estimates. Although the importance of seismic coupling is often overlooked, it significantly impacts seismic hazard results. We present an estimation of upper and lower seismogenic depth and expected hypocentral depth and seismic coupling in the transition zone between the Alps, Dinarides and Pannonian Basin, characterized by a complex deformation pattern, highly variable crustal thickness, and moderate seismic hazard, supporting the development of the 2021 seismic hazard model of Slovenia. The hazard model was based on three seismic source models: area source model, fault source model and smoothed seismicity (point) source model. We estimated the lower seismogenic depth using seismological and geological data and compared them. The seismological estimate was based on two regional earthquake catalogues prepared for this study. In the area source model, estimates of lower seismogenic depth from seismological data are deeper or equal to the ones derived from geological data, except in one case. In the fault source model, we analysed each fault individually and chose seismological lower depth estimates in 12 among 89 faults as more representative. The seismogenic thickness for each individual fault source was determined for seismic coupling determination. The seismic coupling was assessed by two approaches, i.e. we chose the most trusted value from the literature, and the value determined for each fault individually by using the approach based on the updated regional fault and earthquake data sets. The final estimate of seismic coupling ranges from 0.77 to 0.38. We compared the tectonic moment rate based on long-term slip rate using different values of seismic coupling with the seismic moment rate obtained from the earthquake catalogue. The analysis is done for the whole area, as well as for the individual area zones. The analysis of N–S components of estimated slip for the largest faults in the area of west Slovenia shows that the regional geological and geodetic shortening rates are comparable. The total activity rate of three global seismic source models is compared, which gives up to a 10 % difference. Our results contribute to a better understanding of the seismic activity in the region. The presented approach for seismic coupling estimation can be applied in cases where the total slip rate is given instead of its seismic part and can be used at regional or national level. The approach is also suitable for the cross-border harmonization of the European seismic hazard modelling data.
Keywords: seismic hazard, modeling, Slovenia
Published in DiRROS: 18.03.2024; Views: 68; Downloads: 41
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3.
4.
The liberation set in the inverse eigenvalue problem of a graph
Jephian 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: 59; Downloads: 34
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5.
Cryogenic transmission electron images of Phaeodactylum tricornutum isolates of small cellular particles
Apolonija Bedina Zavec, Darja Božič, Matej Hočevar, Aleš Iglič, Marko Jeran, Veronika Kralj-Iglič, Anna Romolo, 2024, published scientific conference contribution

Published in DiRROS: 08.03.2024; Views: 57; Downloads: 41
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7.
Scanning electron microscope images of Phaeodactylum tricornutum culture
Apolonija Bedina Zavec, Darja Božič, Matej Hočevar, Aleš Iglič, Marko Jeran, Veronika Kralj-Iglič, Anna Romolo, 2024, published scientific conference contribution

Published in DiRROS: 08.03.2024; Views: 61; Downloads: 45
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Scanning electron microscope images of Dunaliella tertiolecta isolates of small cellular particles
Apolonija Bedina Zavec, Darja Božič, Matej Hočevar, Aleš Iglič, Marko Jeran, Anna Romolo, Veronika Kralj-Iglič, 2024, published scientific conference contribution

Published in DiRROS: 08.03.2024; Views: 53; Downloads: 25
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10.
Scanning electron microscope images of Dunaliella tertiolecta culture
Apolonija Bedina Zavec, Darja Božič, Matej Hočevar, Aleš Iglič, Marko Jeran, Veronika Kralj-Iglič, Anna Romolo, 2024, published scientific conference contribution

Published in DiRROS: 08.03.2024; Views: 59; Downloads: 33
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