1681. Recent developments on Oka manifoldsFranc Forstnerič, 2023, review article Abstract: In this paper we present the main developments in Oka theory since the publication of my book "Stein Manifolds and Holomorphic Mappings (The Homotopy Principle in Complex Analysis)", 2nd ed., Springer, 2017. We also give several new results, examples and constructions of Oka domains in Euclidean and projective spaces. Furthermore, we show that for $n > 1$ the fibre $\mathbb C^n$ in a Stein family can degenerate to a non-Oka fibre, thereby answering a question of Takeo Ohsawa. Several open problems are discussed. Keywords: Oka manifold, Oka map, Stein manifold, elliptic manifold, algebraically subelliptic manifold, Calabi–Yau manifold, density property Published in DiRROS: 14.03.2024; Views: 691; Downloads: 574
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1682. Optimal approximation of spherical squares by tensor product quadratic Bézier patchesAleš Vavpetič, Emil Žagar, 2023, original scientific article Abstract: In cited article E. F. Eisele considered the problem of the optimal approximation of symmetric surfaces by biquadratic Bézier patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal approximation of spherical squares. A detailed analysis and a numerical algorithm are given, providing the best approximant according to the (simplified) radial error, which differs from the one obtained mentioned article. The sphere is then approximated by the continuous spline of two and six tensor product quadratic Bézier patches. It is further shown that the $G^1$ smooth spline of six patches approximating the sphere exists, but it is not a good approximation. The problem of an approximation of spherical rectangles is also addressed and numerical examples indicate that several optimal approximants might exist in some cases, making the problem extremely difficult to handle. Finally, numerical examples are provided that confirm the theoretical results. Keywords: Bézier patches, spherical squares, optimal approximation, sphere approximation Published in DiRROS: 14.03.2024; Views: 398; Downloads: 174
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1683. Resolving a structural issue in cerium-nickel-based oxide : single compound or a two-phase system?Jelena Kojčinović, Dalibor Tatar, Stjepan Šarić, Cora Pravda Bartus, Andraž Mavrič, Iztok Arčon, Zvonko Jagličić, Maximilian Mellin, Marcus Einert, Angela Altomare, Rocco Caliandro, 2024, original scientific article Keywords: cerium oxide, nickel oxide, crystallography Published in DiRROS: 13.03.2024; Views: 648; Downloads: 577
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1684. Coherence and avoidance of sure loss for standardized functions and semicopulasErich Peter Klement, Damjana Kokol-Bukovšek, Blaž Mojškerc, Matjaž Omladič, Susanne Saminger, Nik Stopar, 2024, original scientific article Abstract: We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, $1$-increasing functions with value $1$ at $(1, 1, \ldots , 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A \le C \le B$ for standardized $n$-variate functions $A$, $B$ and discuss methods for constructing such functions. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when $A$ respectively $B$ coincides with the pointwise infimum respectively supremum of the set of all $k$-increasing $n$-variate functions $C$ fulfilling $A \le C \le B$. Keywords: copulas, quasi-copulas, semicopulas, standardized function, coherence, avoidance of sure loss, k-increasing function Published in DiRROS: 13.03.2024; Views: 299; Downloads: 158
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1685. Outerplane bipartite graphs with isomorphic resonance graphsSimon Brezovnik, Zhongyuan Che, Niko Tratnik, Petra Žigert Pleteršek, 2024, original scientific article Abstract: We present novel results related to isomorphic resonance graphs of 2-connected outerplane bipartite graphs. As the main result, we provide a structure characterization for 2-connected outerplane bipartite graphs with isomorphic resonance graphs. Three additional characterizations are expressed in terms of resonance digraphs, via local structures of inner duals, as well as using distributive lattices on the set of order ideals of posets defined on inner faces of 2-connected outerplane bipartite graphs. Keywords: distributive lattice, inner dual, isomorphic resonance graphs, order ideal, 2-connected outerplane bipartite graph Published in DiRROS: 13.03.2024; Views: 358; Downloads: 174
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1686. On the structure of consistent cycles in cubic symmetric graphsKlavdija Kutnar, Dragan Marušič, Štefko Miklavič, Primož Šparl, 2024, original scientific article Keywords: 1/2-consistent cycles, automorphisms, consistent cycles, cubic symmetric graphs, shunt, s-regular graphs Published in DiRROS: 13.03.2024; Views: 313; Downloads: 166
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1687. On the exact region determined by Spearman's rho and Spearman's footruleDamjana Kokol-Bukovšek, Nik Stopar, 2024, original scientific article Abstract: We determine the lower bound for possible values of Spearman’s rho of a bivariate copula given that the value of its Spearman's footrule is known and show that this bound is always attained. We also give an estimate for the exact upper bound and prove that the estimate is exact for some but not all values of Spearman's footrule. Nevertheless, we show that the estimate is quite tight. Keywords: copula, dependence concepts, supremum and infimum of a set of copulas, measures of concordance, quasi-copula, local bounds Published in DiRROS: 13.03.2024; Views: 357; Downloads: 153
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1688. Minimal surfaces with symmetriesFranc Forstnerič, 2024, original scientific article Abstract: Let $G$ be a finite group acting on a connected open Riemann surface $X$ by holomorphic automorphisms and acting on a Euclidean space ${\mathbb R}^n$ $(n\ge 3)$ by orthogonal transformations. We identify a necessary and sufficient condition for the existence of a $G$-equivariant conformal minimal immersion $F:X\to{\mathbb R}^n$. We show in particular that such a map $F$ always exists if $G$ acts without fixed points on $X$. Furthermore, every finite group $G$ arises in this way for some open Riemann surface $X$ and $n=2|G|$. We obtain an analogous result for minimal surfaces having complete ends with finite total Gaussian curvature, and for discrete infinite groups acting on $X$ properly discontinuously and acting on ${\mathbb R}^n$ by rigid transformations. Keywords: Riemann surfaces, minimal surfaces, G-equivariant conformal minimal immersion Published in DiRROS: 13.03.2024; Views: 378; Downloads: 144
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1690. Weathering effects on cellulose acetate microplastics from discarded cigarette buttsBranka Mušič, Andrijana Sever Škapin, 2024, published scientific conference contribution (invited lecture) Abstract: Cellulose acetate, commonly used in cigarette filters, poses environmental concerns due to its questionable (bio)degradability and prevalent presence in nature. This study compares the weathering effects on two types of cigarette filters: traditional and newer filters used in heated tobacco devices (HTP). Microplastics were derived from used cigarette parts and then subjected to artificial aging. Analytical techniques (Thermogravimetry-Differential Scanning Calorimetry TG/DSC, Fourier-Transform Infrared Spectroscopic Analysis (FTIR)) and loose bulk density measurements were employed pre- and post-aging cellulose acetate of both types of samples. Despite increasing evidence influencing European Union (EU) directives on tobacco product disposal, there's a lack of systematic analysis on the weathering impact, especially concerning the touted environmental benefits of newer filters. Results indicate decreased particle size in cellulose acetate filters post-aging. Variances were observed in thermal behavior, yet FTIR spectra remained unchanged. Keywords: cellulose acetate, cigarette filters, microplastics, artificial weathering, polymer degradation Published in DiRROS: 12.03.2024; Views: 472; Downloads: 428
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