1981. Proper holomorphic maps in Euclidean spaces avoiding unbounded convex setsBarbara Drinovec-Drnovšek, Franc Forstnerič, 2023, izvirni znanstveni članek Povzetek: We show that if $E$ is a closed convex set in $\mathbb C^n$, $n>1$ contained in a closed halfspace $H$ such that ▫$E\cap bH$▫ is nonempty and bounded, then the concave domain $\Omega=\mathbb C^n\setminus E$ contains images of proper holomorphicmaps $f : X \to \mathbb C^n$ from any Stein manifold $X$ of dimension $< n$, with approximation of a givenmap on closed compact subsets of $X$. If in addition $2 {\rm dim} X+1 \le n$ then $f$ can be chosen an embedding, and if $2 {\rm dim} X = n$, then it can be chosen an immersion. Under a stronger condition on $E$, we also obtain the interpolation property for such maps on closed complex subvarieties. Ključne besede: Stein manifolds, holomorphic embeddings, Oka manifold, minimal surfaces, convexity Objavljeno v DiRROS: 15.03.2024; Ogledov: 393; Prenosov: 189 Celotno besedilo (441,34 KB) Gradivo ima več datotek! Več... |
1982. Computational complexity aspects of super dominationCsilla Bujtás, Nima Ghanbari, Sandi Klavžar, 2023, izvirni znanstveni članek Povzetek: Let ▫$G$▫ be a graph. A dominating set ▫$D\subseteq V(G)$▫ is a super dominating set if for every vertex ▫$x\in V(G) \setminus D$▫ there exists ▫$y\in D$▫ such that ▫$N_G(y)\cap (V(G)\setminus D)) = \{x\}$▫. The cardinality of a smallest super dominating set of ▫$G$▫ is the super domination number of ▫$G$▫. An exact formula for the super domination number of a tree ▫$T$▫ is obtained, and it is demonstrated that a smallest super dominating set of ▫$T$▫ can be computed in linear time. It is proved that it is NP-complete to decide whether the super domination number of a graph ▫$G$▫ is at most a given integer if ▫$G$▫ is a bipartite graph of girth at least ▫$8$▫. The super domination number is determined for all ▫$k$▫-subdivisions of graphs. Interestingly, in half of the cases the exact value can be efficiently computed from the obtained formulas, while in the other cases the computation is hard. While obtaining these formulas, II-matching numbers are introduced and proved that they are computationally hard to determine. Ključne besede: super domination number, trees, bipartite graphs, k-subdivision of a graph, computational complexity, matching, II-matching number Objavljeno v DiRROS: 14.03.2024; Ogledov: 463; Prenosov: 177 Celotno besedilo (453,39 KB) Gradivo ima več datotek! Več... |
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1984. The liberation set in the inverse eigenvalue problem of a graphJephian C.-H. Lin, Polona Oblak, Helena Šmigoc, 2023, izvirni znanstveni članek Povzetek: The inverse eigenvalue problem of a graph $G$ is the problem of characterizing all lists of eigenvalues of real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of $G$. The strong spectral property is a powerful tool in this problem, which identifies matrices whose entries can be perturbed while controlling the pattern and preserving the eigenvalues. The Matrix Liberation Lemma introduced by Barrett et al. in 2020 advances the notion to a more general setting. In this paper we revisit the Matrix Liberation Lemma and prove an equivalent statement, that reduces some of the technical difficulties in applying the result. We test our method on matrices of the form $M=A \oplus B$ and show how this new approach supplements the results that can be obtained from the strong spectral property only. While extending this notion to the direct sums of graphs, we discover a surprising connection with the zero forcing game on Cartesian products of graphs. Throughout the paper we apply our results to resolve a selection of open cases for the inverse eigenvalue problem of a graph on six vertices. Ključne besede: symmetric matrix, inverse eigenvalue problem, strong spectral property, Matrix Liberation Lemma, zero forcing Objavljeno v DiRROS: 14.03.2024; Ogledov: 402; Prenosov: 188 Celotno besedilo (626,24 KB) Gradivo ima več datotek! Več... |
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1987. On the Schrödinger-Poisson system with $(p,q)$-LaplacianYueqiang Song, Yuanyuan Huo, Dušan Repovš, 2023, izvirni znanstveni članek Povzetek: We study a class of Schrödinger-Poisson systems with $(p,q)$-Laplacian. Using fixed point theory, we obtain a new existence result for nontrivial solutions. The main novelty of the paper is the combination of a double phase operator and the nonlocal term. Our results generalize some known results. Ključne besede: double phase operator, Schrödinger-Poisson systems, (p, q)–Laplacian, fixed point theory Objavljeno v DiRROS: 14.03.2024; Ogledov: 421; Prenosov: 225 Celotno besedilo (686,98 KB) Gradivo ima več datotek! Več... |
1988. Recent developments on Oka manifoldsFranc Forstnerič, 2023, pregledni znanstveni članek Povzetek: 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. Ključne besede: Oka manifold, Oka map, Stein manifold, elliptic manifold, algebraically subelliptic manifold, Calabi–Yau manifold, density property Objavljeno v DiRROS: 14.03.2024; Ogledov: 801; Prenosov: 639 Celotno besedilo (1014,41 KB) Gradivo ima več datotek! Več... |
1989. Optimal approximation of spherical squares by tensor product quadratic Bézier patchesAleš Vavpetič, Emil Žagar, 2023, izvirni znanstveni članek Povzetek: 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. Ključne besede: Bézier patches, spherical squares, optimal approximation, sphere approximation Objavljeno v DiRROS: 14.03.2024; Ogledov: 489; Prenosov: 207 Celotno besedilo (1,59 MB) Gradivo ima več datotek! Več... |
1990. 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, izvirni znanstveni članek Ključne besede: cerium oxide, nickel oxide, crystallography Objavljeno v DiRROS: 13.03.2024; Ogledov: 766; Prenosov: 615 Celotno besedilo (4,01 MB) Gradivo ima več datotek! Več... |