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163. On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applicationsNabil Chems Eddine, Maria Alessandra Ragusa, Dušan Repovš, 2024, original scientific article Abstract: We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there is potential for future extensions, particularly in extending the concentration-compactness principle to anisotropic fractional order Sobolev spaces with variable exponents in bounded domains. This extension could find applications in solving the generalized fractional Brezis–Nirenberg problem.
Keywords: Sobolev embeddings, concentration-compactness principle, anisotropic variable exponent Sobolev spaces, p(x)-Laplacian, fractional Brezis-Nirenberg problem
Published in DiRROS: 20.03.2024; Views: 67; Downloads: 26
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165. Additive and lithographic manufacturing of biomedical scaffold structures using a versatile thiol-ene photocurable resinMichael Kainz, Stjepan Perak, Gerald Stubauer, Sonja Kopp, Sebastian Kauscheder, Julia Hemetzberger, Adrián Martínez Cendrero, Andrés Díaz Lantada, Disha Tupe, Zoltan Major, Darja Marolt Presen, 2024, original scientific article Published in DiRROS: 20.03.2024; Views: 82; Downloads: 39
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167. Moss as a biomonitor to identify atmospheric deposition of minor and trace elements in MacedoniaRobert Šajn, Katerina Bačeva Andronovska, Trajče Stafilov, Lambe Barandovski, 2024, original scientific article Abstract: The present work was carried out to obtain and highlight the fifth comprehensive baseline dataset on atmospheric deposition of trace elements and to assess air quality in Macedonia. In the period from August to September 2020, a total of 72 moss samples were collected in accessible areas in the country. The content of 28 elements (Ag, Al, B, Ba, Ca, Cd, Co, Cr, Cu, Fe, Ga, Hg, K, La, Mg, Mn, Mo, Na, Ni, P, Pb, S, Sb, Sc, Sr, Ti, U, and Zn) was determined using inductively coupled plasma–mass spectrometry. Based on the data obtained on the content of the elements, a factor analysis was carried out to identify and characterise different sources of pollution. In addition, distribution maps were created for all elements to show the regions most affected by anthropogenic activities. The survey conducted in 2020 has shown that air pollution with potentially toxic elements (PTEs) has slightly decreased compared to the results of the previous survey from 2015. This is due to the fact that, despite the operation of all mining and smelting facilities with the same capacity, government regulations for the installation of cleaning systems and additional regulations to reduce pollution have been introduced in the last five years. Nevertheless, the fact remains that the highest anthropogenic air pollution with PTEs is still caused by the operation of the ferronickel smelter in Kavadarci (Ni and Cr) in the southern part and by the lead and zinc mines in Probištip, Makedonska Kamenica, and Kriva Palanka in the eastern part of the country (Cd, Pb, and Zn).
Keywords: moss, atmospheric deposition, trace elements, air quality, Macedonia
Published in DiRROS: 20.03.2024; Views: 76; Downloads: 30
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168. The Sierpiński product of graphsJurij Kovič, Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik, 2023, original scientific article Abstract: In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let $G$, $H$ be graphs and let $f: V(G) \to V(H)$ be a function. Then the Sierpiński product of graphs $G$ and $H$ with respect to $f$, denoted by $G\otimes_f H$, is defined as the graph on the vertex set $V(G) \times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $\{g, g'\}$ of $G$ there is an edge between copies $gH$ and $g'H$ of form $\{(g, f(g'), (g', f(g))\}$. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph $G\otimes_f H$ is connected if and only if both graphs $G$ and $H$ are connected and we present some conditions that $G, \, H$ must fulfill for $G\otimes_f H$ to be planar. As for symmetry properties, we show which automorphisms of $G$ and $H$ extend to automorphisms of $G\otimes_f H$. In several cases we can also describe the whole automorphism group of the graph $G\otimes_f H$. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation $n$ times to the same graph we obtain an alternative approach to the well-known $n$-th generalized Sierpiński graph.
Keywords: Sierpiński graphs, graph products, connectivity, planarity, symmetry
Published in DiRROS: 19.03.2024; Views: 99; Downloads: 40
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170. On metric dimensions of hypercubesAleksander Kelenc, Aoden Teo Masa Toshi, Riste Škrekovski, Ismael G. Yero, 2023, original scientific article Abstract: In this note we show two unexpected results concerning the metric, the edge metric and the mixed metric dimensions of hypercube graphs. First, we show that the metric and the edge metric dimensions of $Q_d$ differ by at most one for every integer $d$. In particular, if $d$ is odd, then the metric and the edge metric dimensions of $Q_d$ are equal. Second, we prove that the metric and the mixed metric dimensions of the hypercube $Q_d$ are equal for every $d \ge 3$. We conclude the paper by conjecturing that all these three types of metric dimensions of $Q_d$ are equal when d is large enough.
Keywords: edge metric dimension, mixed metric dimension, metric dimension, hypercubes
Published in DiRROS: 19.03.2024; Views: 87; Downloads: 30
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