761. Positive self-commutators of positive operatorsRoman Drnovšek, Marko Kandić, 2025, original scientific article Abstract: We consider a positive operator $A$ on a Hilbert lattice such that its self-commutator $C = A^* A - A A^*$ is positive. If $A$ is also idempotent, then it is an orthogonal projection, and so $C = 0$. Similarly, if $A$ is power compact, then $C = 0$ as well. We prove that every positive compact central operator on a separable infinite-dimensional Hilbert lattice ${\mathcal H}$ is a self-commutator of a positive operator. We also show that every positive central operator on ${\mathcal H}$ is a sum of two positive self-commutators of positive operators.
Keywords: Banach lattices, positive operators, commutators
Published in DiRROS: 20.10.2025; Views: 244; Downloads: 94
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762. Maker-Breaker resolving game played on corona products of graphsTijo James, Sandi Klavžar, Dorota Kuziak, K. S. Savitha, Ambat Vijayakumar, 2025, original scientific article Abstract: The Maker-Breaker resolving game is a game played on a graph $G$ by Resolver and Spoiler. The players taking turns alternately in which each player selects a not yet played vertex of $G$. The goal of Resolver is to select all the vertices in a resolving set of $G$, while that of Spoiler is to prevent this from happening. The outcome $o(G)$ of the game played is one of $\mathcal{R}$, $\mathcal{S}$, and $\mathcal{N}$, where $o(G)=\mathcal{R}$ (resp. $o(G)=\mathcal{S}$), if Resolver (resp. Spoiler) has a winning strategy no matter who starts the game, and $o(G)=\mathcal{N}$, if the first player has a winning strategy. In this paper, the game is investigated on corona products $G\odot H$ of graphs $G$ and $H$. It is proved that if $o(H)\in\{\mathcal{N}, \mathcal{S}\}$, then $o(G\odot H) = \mathcal{S}$. No such result is possible under the assumption $o(H) = \mathcal{R}$. It is proved that $o(G\odot P_k) = \mathcal{S}$ if $k=5$, otherwise $o(G\odot P_k) = \mathcal{R}$, and that $o(G\odot C_k) = \mathcal{S}$ if $k=3$, otherwise $o(G\odot C_k) = \mathcal{R}$. Several results are also given on corona products in which the second factor is of diameter at most $2$.
Keywords: Maker-Breaker game, resolving set, Maker-Breaker resolving game, Maker-Breaker resolving number, corona product of graphs
Published in DiRROS: 20.10.2025; Views: 178; Downloads: 105
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764. Two-generation of traceless matrices over finite fieldsOmer Cantor, Urban Jezernik, Andoni Zozaya, 2025, original scientific article Abstract: We prove that the Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ of traceless matrices over a finite field of characteristic ▫$p$▫ can be generated by $2$ elements with exceptions when $(n, p)$ is $(3, 3)$ or $(4,2)$. In the latter cases, we establish curious identities that obstruct $2$-generation.
Keywords: generation, simple Lie algebras, finite fields
Published in DiRROS: 20.10.2025; Views: 209; Downloads: 105
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765. Connected matchingsOswin Aichholzer, Sergio Cabello, Viola Mészáros, Patrick Schnider, Jan Soukup, 2025, original scientific article Abstract: We show that each set of $n\ge 2$ points in the plane in general position has a straight-line matching with at least $(5n+1)/27$ edges whose segments form a connected set, and such a matching can be computed in $O(n \log n)$ time. As an upper bound, we show that for some planar point sets in general position the largest matching whose segments form a connected set has $\lceil \frac{n-1}{3}\rceil$ edges. We also consider a colored version, where each edge of the matching should connect points with different colors.
Keywords: point sets, matchings for point sets, intersection graph
Published in DiRROS: 20.10.2025; Views: 198; Downloads: 110
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766. Rezultati ankete "ChatGPT pri delu poljskih in slovenskih visokošolskih učiteljev in učiteljic"Valerija Vendramin, Sabina Autor, Janja Žmavc, Lucija Zala Bezlaj, Igor Bijuklič, Krzysztof Skonieczny, Kamil Wielecki, 2025, complete scientific database of research data Abstract: Datoteki vsebujeta odgovore slovenskih in poljskih visokošolskih učiteljev in učiteljic v anketi, katere namen je bil oceniti vpliv ChatGPT-ja in podobnih tehnologij umetne inteligence na izobraževalne prakse. Hkrati je bil namen tudi razumeti strategije, ki jih visokošolski učitelji in učiteljice uporabljajo, ko se soočajo z novimi tehnologijami, ki bi lahko motile učni proces.
Keywords: vzgoja in izobraževanje, podatkovne baze, EDUCATHUM, ChatGPT, raziskovalni podatki, anketa, izobraževanje na mejah človeškega, visokošolski učitelji/-ice, Poljska, Slovenija
Published in DiRROS: 20.10.2025; Views: 241; Downloads: 63
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767. Weighted Padovan graphsVesna Iršič Chenoweth, Sandi Klavžar, Gregor Rus, Elif Tan, 2025, original scientific article Abstract: Weighted Padovan graphs $\Phi^{n}_{k}$, $n \geq 1$, $\lfloor \frac{n}{2} \rfloor \leq k \leq \lfloor \frac{2n-2}{3} \rfloor$, are introduced as the graphs whose vertices are all Padovan words of length $n$ with $k$ $1$s, two vertices being adjacent if one can be obtained from the other by replacing exactly one $01$ with a $10$. By definition, $\sum_k |V(\Phi^{n}_{k})|=P_{n+2}$, where $P_n$ is the $n$th Padovan number. Two families of graphs isomorphic to weighted Padovan graphs are presented. The order, the size, the degree, the diameter, the cube polynomial, and the automorphism group of weighted Padovan graphs are determined. It is also proved that they are median graphs.
Keywords: Padovan sequence, weighted Padovan graph, integer partition, median graphs
Published in DiRROS: 20.10.2025; Views: 158; Downloads: 66
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768. A model theoretic perspective on matrix ringsIgor Klep, Marcus Tressl, 2025, original scientific article Abstract: In this paper natural necessary and sufficient conditions for quantifier elimination of matrix rings $M_n(K)$ in the language of rings expanded by two unary functions, naming the trace and transposition, are identified. This is used together with invariant theory to prove quantifier elimination when $K$ is an intersection of real closed fields. On the other hand, it is shown that finding a natural definable expansion with quantifier elimination of the theory of $M_n({\mathbb C})$ is closely related to the infamous simultaneous conjugacy problem in matrix theory. Finally, for various natural structures describing dimension-free matrices it is shown that no such elimination results can hold by establishing undecidability results.
Keywords: model theory, quantifier elimination, matrix rings, trace, decidability, free analysis, simultaneous conjugacy problem
Published in DiRROS: 20.10.2025; Views: 192; Downloads: 87
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769. Advanced Monte Carlo analysis of ex-vessel neutron dosimetry for cycle 25 of Krško nuclear power plantTanja Goričanec, Benjamin Barbarič, Vladimir Radulović, Dušan Čalič, Luka Snoj, Marjan Kromar, 2026, original scientific article Abstract: This paper presents the results of Monte Carlo neutron transport calculations performed for the containment building of the Krško Nuclear Power Plant. The calculations were performed using the Monte Carlo N-Particle Transport Code (MCNP) in combination with the ADVANTG hybrid code to speed up the convergence of the results outside the reactor core. The paper focuses on the analysis of the Ex-Vessel Neutron Dosimetry (EVND) program conducted during the 25th fuel cycle at the Krško nuclear power plant with the irradiation of gradient chains and multiple foil sensor sets. The calculated reaction rates at the dosimeter locations are in good agreement with the measured values. However, deviations were observed in the thermal part of the neutron energy spectrum which cannot be neglected, and investigated were some possible reasons for the deviations: nuclear data, concrete material composition, concrete geometry, sensor position and impurities in sample.
Keywords: neutron transport, ex-vessel neutron dosimeters, neutron
Published in DiRROS: 20.10.2025; Views: 174; Downloads: 72
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770. Agro-morphological characteristics of selected sweet potato (Ipomoea batatas L.) varieties from organic farming and their genetic backgroundNataša Kunstelj, Lovro Sinkovič, Barbara Pipan, Mohamed Neji, Vladimir Meglič, 2025, original scientific article Keywords: allele polymorphisms, genetic diversity, organic farming, plant descriptor, SSR marker
Published in DiRROS: 18.10.2025; Views: 210; Downloads: 100
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