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Povzetek: 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.
Ključne besede: Banach lattices, positive operators, commutators
Objavljeno v DiRROS: 20.10.2025; Ogledov: 244; Prenosov: 93
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Ključne besede: traffic management, fleet management, trafic simulation, mobility
Objavljeno v DiRROS: 20.10.2025; Ogledov: 208; Prenosov: 114
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Povzetek: 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.
Ključne besede: point sets, matchings for point sets, intersection graph
Objavljeno v DiRROS: 20.10.2025; Ogledov: 197; Prenosov: 109
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Povzetek: 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.
Ključne besede: Padovan sequence, weighted Padovan graph, integer partition, median graphs
Objavljeno v DiRROS: 20.10.2025; Ogledov: 158; Prenosov: 66
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Povzetek: 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.
Ključne besede: neutron transport, ex-vessel neutron dosimeters, neutron
Objavljeno v DiRROS: 20.10.2025; Ogledov: 167; Prenosov: 70
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