381. Generalized cut method for computing Szeged-like polynomials with applications to polyphenyls and carbon nanoconesSimon Brezovnik, Niko Tratnik, 2023, original scientific article Abstract: Szeged, Padmakar-Ivan (PI), and Mostar indices are some of the most investigated distance-based Szeged-like topological indices. On the other hand, the polynomials related to these topological indices were also introduced, for example the Szeged polynomial, the edge- Szeged polynomial, the PI polynomial, the Mostar polynomial, etc. In this paper, we introduce a concept of the general Szeged-like polynomial for a connected strength-weighted graph. It turns out that this concept includes all the above mentioned polynomials and also infinitely many other graph polynomials. As the main result of the paper, we prove a cut method which enables us to efficiently calculate a Szeged-like polynomial by using the corresponding polynomials of strength-weighted quotient graphs obtained by a partition of the edge set that is coarser than ▫$\Theta^*$▫-partition. To the best of our knowledge, this represents the first implementation of the famous cut method to graph polynomials. Finally, we show how the deduced cut method can be applied to calculate some Szeged-like polynomials and corresponding topological indices of para-polyphenyl chains and carbon nanocones.
Keywords: graph theory, carbon nanocone, topological indices
Published in DiRROS: 20.03.2024; Views: 109; Downloads: 34
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382. Arc length preserving $G^2$ Hermite interpolation of circular arcsEmil Žagar, 2023, original scientific article Abstract: In this paper, the problem of interpolation of two points, two corresponding tangent directions and curvatures, and the arc length sampled from a circular arc (circular arc data) is considered. Planar Pythagorean–hodograph (PH) curves of degree seven are used since they possess enough free parameters and are capable of interpolating the arc length in an easy way. A general approach using the complex representation of PH curves is presented first and the strong dependence of the solution on the general data is demonstrated. For circular arc data, a complicated system of nonlinear equations is reduced to a numerical solution of only one algebraic equation of degree 6 and a detailed analysis of the existence of admissible solutions is provided. In the case of several solutions, some criteria for selecting the most appropriate one are described and an asymptotic analysis is given. Numerical examples are included which confirm theoretical results.
Keywords: geometric interpolation, circular arc, arc length, Pythagorean-hodograph curve, solution selection
Published in DiRROS: 20.03.2024; Views: 110; Downloads: 53
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383. Orientable domination in product-like graphsSarah Anderson, Boštjan Brešar, Sandi Klavžar, Kirsti Kuenzel, Douglas F. Rall, 2023, original scientific article Abstract: The orientable domination number, ${\rm DOM}(G)$, of a graph $G$ is the largest domination number over all orientations of $G$. In this paper, ${\rm DOM}$ is studied on different product graphs and related graph operations. The orientable domination number of arbitrary corona products is determined, while sharp lower and upper bounds are proved for Cartesian and lexicographic products. A result of Chartrand et al. from 1996 is extended by establishing the values of ${\rm DOM}(K_{n_1,n_2,n_3})$ for arbitrary positive integers $n_1,n_2$ and $n_3$. While considering the orientable domination number of lexicographic product graphs, we answer in the negative a question concerning domination and packing numbers in acyclic digraphs posed in [Domination in digraphs and their direct and Cartesian products, J. Graph Theory 99 (2022) 359-377].
Keywords: digraph, domination, orientable domination number, packing, graph product, corona graph
Published in DiRROS: 20.03.2024; Views: 118; Downloads: 53
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386. 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: 289; Downloads: 405
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388. 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: 191; Downloads: 261
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390. 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: 286; Downloads: 306
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