1981. Wandering domains arising from Lavaurs maps with Siegel disksMatthieu Astorg, Luka Boc Thaler, Han Peters, 2023, original scientific article Abstract: The first example of polynomial maps with wandering domains was constructed in 2016 by the first and last authors, together with Buff, Dujardin and Raissy. In this paper, we construct a second example with different dynamics, using a Lavaurs map with a Siegel disk instead of an attracting fixed point. We prove a general necessary and sufficient condition for the existence of a trapping domain for nonautonomous compositions of maps converging parabolically towards a Siegel-type limit map. Constructing a skew-product satisfying this condition requires precise estimates on the convergence to the Lavaurs map, which we obtain by a new approach. We also give a self-contained construction of parabolic curves, which are integral to this new method.
Keywords: Fatou sets, holomorphic dynamics, parabolic implosion, polynomial mappings, skew-products, wandering Fatou components, parabolic curves, nonautonomous dynamics
Published in DiRROS: 09.04.2024; Views: 656; Downloads: 198
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1982. Depth of SCUBA diving affects cardiac autonomic nervous systemMarina Vulić, Branislav Milovanovic, Ante Obad, Duška Glavaš, Igor Glavičič, Damir Zubac, Maja Valic, Zoran Valić, 2024, review article Abstract: The present study investigated the influence of SCUBA dives with compressed air at depths of 10 and 20 m on ECG-derived HRV parameters in apparently healthy individuals. We hypothesized that cardiac sympathetic activity (measured by HRV parameters) adapts proportionally to diving depth, and that both time- and frequency-domain parameters are sensitive enough to track changes in cardiac ANS function during diving activities and subsequently during the recovery period. Eleven healthy middle-aged recreational divers (nine men and two women, age 43 ± 8, all nonsmokers) volunteered to participate in the present study. The participants (all open-circuit divers) were equipped with dry suits and ECG Holter devices and were later randomly assigned to dive pairs and depths (10 m vs. 20 m), and each participant served as his or her own control. No interaction effects (diving depth x time epoch) were found for the most commonly used HRV markers. More precisely, in response to two different diving protocols, a significant post hoc effect of time was observed for HR and SDNN, as these parameters transiently decreased during the dives and returned to baseline after ascent (p < 0.001). The ULF, VLF (p < 0.003), TP, and LF parameters decreased significantly during the dives, while HF significantly increased (p < 0.003). SCUBA diving apparently challenges the cardiac ANS, even in healthy individuals. The observed changes reveal possible underwater methods of influencing the parasympathetic activity of the heart depending on the depth of the dive. These results identify autonomic nervous system markers to track the cardiovascular risk related to diving and point to the possibility of tracking cardiovascular system benefits during underwater activities in selected patients
Keywords: autonomic nervous system, diving, parasympathicus, cardiovascular risk
Published in DiRROS: 09.04.2024; Views: 496; Downloads: 256
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1983. |
1984. Injective coloring of graphs revisitedBoštjan Brešar, Babak Samadi, Ismael G. Yero, 2023, original scientific article Abstract: An open packing in a graph $G$ is a set $S$ of vertices in $G$ such that no two vertices in $S$ have a common neighbor in $G$. The injective chromatic number $\chi_i(G)$ of $G$ is the smallest number of colors assigned to vertices of ▫$G$▫ such that each color class is an open packing. Alternatively, the injective chromatic number of $G$ is the chromatic number of the two-step graph of $G$, which is the graph with the same vertex set as $G$ in which two vertices are adjacent if they have a common neighbor. The concept of injective coloring has been studied by many authors, while in the present paper we approach it from two novel perspectives, related to open packings and the two-step graph operation. We prove several general bounds on the injective chromatic number expressed in terms of the open packing number. In particular, we prove that $\chi_i(G) \ge \frac{1}{2}\sqrt{\frac{1}{4}+\frac{2m-n}{\rho^{o}}}$ holds for any connected graph $G$ of order $n\ge 2$, size $m$, and the open packing number ${\rho^{o}}$, and characterize the class of graphs attaining the bound. Regarding the well known bound $\chi_i(G)\ge \Delta(G)$, we describe the family of extremal graphs and prove that deciding when the equality holds (even for regular graphs) is NP-complete, solving an open problem from an earlier paper. Next, we consider the chromatic number of the two-step graph of a graph, and compare it with the clique number and the maximum degree of the graph. We present two large families of graphs in which $\chi_i(G)$ equals the cardinality of a largest clique of the two-step graph of $G$. Finally, we consider classes of graphs that admit an injective coloring in which all color classes are maximal open packings. We give characterizations of three subclasses of these graphs among graphs with diameter 2, and find a partial characterization of hypercubes with this property.
Keywords: two-step graph of a graph, injective coloring, open packing, hypercubes
Published in DiRROS: 09.04.2024; Views: 464; Downloads: 188
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1985. The core of a vertex-transitive complementary prismMarko Orel, 2023, original scientific article Abstract: The complementary prism $\Gamma \overline{\Gamma}$ is obtained from the union of a graph $\Gamma$ and its complement $\overline{\Gamma}$ where each pair of identical vertices in $\Gamma$ and $\overline{\Gamma}$ is joined by an edge. It generalizes the Petersen graph, which is the complementary prism of the pentagon. The core of a vertex-transitive complementary prism is studied. In particular, it is shown that a vertex-transitive complementary prism $\Gamma \overline{\Gamma}$ is a core, i.e. all its endomorphisms are automorphisms, whenever $\Gamma$ is a core or its core is a complete graph.
Keywords: graph homomorphism, complementary prism, self-complementary graph, vertex-transitive graph, core
Published in DiRROS: 09.04.2024; Views: 457; Downloads: 155
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1986. Domination and independence numbers of large 2-crossing-critical graphsVesna Iršič, Maruša Lekše, Miha Pačnik, Petra Podlogar, Martin Praček, 2023, original scientific article Abstract: After 2-crossing-critical graphs were characterized in 2016, their most general subfamily, large 3-connected 2-crossing-critical graphs, has attracted separate attention. This paper presents sharp upper and lower bounds for their domination and independence number.
Keywords: crossing-critical graphs, domination number, independence number
Published in DiRROS: 09.04.2024; Views: 438; Downloads: 198
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1987. |
1988. Sliding wear behaviour of conventional and cryotreated PM Cr-V (Vanadis 6) ledeburitic tool steelVenu Yarasu, Peter Jurči, Peter Gogola, Bojan Podgornik, Marko Sedlaček, 2023, original scientific article Keywords: cold work tool steel, conventional treatment, cryogenic treatment, hardness, reciprocal sliding, wear
Published in DiRROS: 08.04.2024; Views: 558; Downloads: 78
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1989. Maximum matchings in geometric intersection graphsÉdouard Bonnet, Sergio Cabello, Wolfgang Mulzer, 2023, original scientific article Abstract: Let $G$ be an intersection graph of $n$ geometric objects in the plane. We show that a maximum matching in $G$ can be found in $O(\rho^{3\omega/2}n^{\omega/2})$ time with high probability, where $\rho$ is the density of the geometric objects and $\omega>2$ is a constant such that $n \times n$ matrices can be multiplied in $O(n^\omega)$ time. The same result holds for any subgraph of $G$, as long as a geometric representation is at hand. For this, we combine algebraic methods, namely computing the rank of a matrix via Gaussian elimination, with the fact that geometric intersection graphs have small separators. We also show that in many interesting cases, the maximum matching problem in a general geometric intersection graph can be reduced to the case of bounded density. In particular, a maximum matching in the intersection graph of any family of translates of a convex object in the plane can be found in $O(n^{\omega/2})$ time with high probability, and a maximum matching in the intersection graph of a family of planar disks with radii in $[1, \Psi]$ can be found in $O(\Psi^6\log^{11} n + \Psi^{12 \omega} n^{\omega/2})$ time with high probability.
Keywords: computational geometry, geometric intersection graphs, disk graphs, unit-disk graphs, matchings
Published in DiRROS: 08.04.2024; Views: 442; Downloads: 209
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1990. Maker-Breaker domination game on trees when Staller winsCsilla Bujtás, Pakanun Dokyeesun, Sandi Klavžar, 2023, original scientific article Abstract: In the Maker-Breaker domination game played on a graph $G$, Dominator's goal is to select a dominating set and Staller's goal is to claim a closed neighborhood of some vertex. We study the cases when Staller can win the game. If Dominator (resp., Staller) starts the game, then $\gamma_{\rm SMB}(G)$ (resp., $\gamma_{\rm SMB}'(G)$) denotes the minimum number of moves Staller needs to win. For every positive integer $k$, trees $T$ with $\gamma_{\rm SMB}'(T)=k$ are characterized and a general upper bound on $\gamma_{\rm SMB}'$ is proved. Let $S = S(n_1,\dots, n_\ell)$ be the subdivided star obtained from the star with $\ell$ edges by subdividing its edges $n_1-1, \ldots, n_\ell-1$ times, respectively. Then $\gamma_{\rm SMB}'(S)$ is determined in all the cases except when $\ell\ge 4$ and each $n_i$ is even. The simplest formula is obtained when there are at least two odd $n_i$s. If ▫$n_1$▫ and $n_2$ are the two smallest such numbers, then $\gamma_{\rm SMB}'(S(n_1,\dots, n_\ell))=\lceil \log_2(n_1+n_2+1)\rceil$▫. For caterpillars, exact formulas for $\gamma_{\rm SMB}$ and for $\gamma_{\rm SMB}'$ are established.
Keywords: domination game, Maker-Breaker game, Maker-Breaker domination game, hypergraphs, trees, subdivided stars, caterpillars
Published in DiRROS: 08.04.2024; Views: 601; Downloads: 240
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