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1662. Trilinear embedding for divergence-form operators with complex coefficientsAndrea Carbonaro, Oliver Dragičević, Vjekoslav Kovač, Kristina Ana Škreb, 2023, izvirni znanstveni članek Povzetek: We prove a dimension-free $L^p(\Omega)\times L^q(\Omega)\times L^r(\Omega)\rightarrow L^1(\Omega\times (0,\infty))$ embedding for triples of elliptic operators in divergence form with complex coefficients and subject to mixed boundary conditions on $\Omega$, and for triples of exponents $p,q,r \in (1,\infty)$ mutually related by the identity $1/p+1/q+1/r=1$. Here $\Omega$ is allowed to be an arbitrary open subset of $\mathbb{R}^d$. Our assumptions involving the exponents and coefficient matrices are expressed in terms of a condition known as $p$-ellipticity. The proof utilizes the method of Bellman functions and heat flows. As a corollary, we give applications to (i) paraproducts and (ii) square functions associated with the corresponding operator semigroups, moreover, we prove (iii) inequalities of Kato-Ponce type for elliptic operators with complex coefficients. All the above results are the first of their kind for elliptic divergence-form operators with complex coefficients on arbitrary open sets. Furthermore, the approach to (ii),(iii) through trilinear embeddings seems to be new. Ključne besede: elliptic differential operator, p-ellipticity, operator semigroup, multilinear estimate Objavljeno v DiRROS: 15.03.2024; Ogledov: 306; Prenosov: 172
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1663. A comparative analysis among quenched, tempered, and stepped cooled TIG welded SS-304 plates based on tensile strength, hardness, and microstructural appearanceSaurabh Dewangan, Saksham Saksham, Adhir Chandra Paul, Jaka Burja, 2023, izvirni znanstveni članek Ključne besede: welding, austenitic stainless steel, heat affected zone, mechanical properties Objavljeno v DiRROS: 15.03.2024; Ogledov: 311; Prenosov: 147
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1664. The cut method on hypergraphs for the Wiener indexSandi Klavžar, Gašper Domen Romih, 2023, izvirni znanstveni članek Povzetek: The cut method has been proved to be extremely useful in chemical graph theory. In this paper the cut method is extended to hypergraphs. More precisely, the method is developed for the Wiener index of $k$-uniform partial cube-hypergraphs. The method is applied to cube-hypergraphs and hypertrees. Extensions of the method to hypergraphs arising in chemistry which are not necessary $k$-uniform and/or not necessary linear are also developed. Ključne besede: hypergraphs, Wiener index, cut method, partial cube-hypergraphs, hypertrees, phenylene, Clar structures Objavljeno v DiRROS: 15.03.2024; Ogledov: 374; Prenosov: 146
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1665. Faster distance-based representative skyline and k-center along pareto front in the planeSergio Cabello, 2023, izvirni znanstveni članek Povzetek: We consider the problem of computing the distance-based representative skyline in the plane, a problem introduced by Tao, Ding, Lin and Pei and independently considered by Dupin, Nielsen and Talbi in the context of multi-objective optimization. Given a set $P$ of $n$ points in the plane and a parameter $k$, the task is to select $k$ points of the skyline defined by $P$ (also known as Pareto front for $P$) to minimize the maximum distance from the points of the skyline to the selected points. We show that the problem can be solved in $O(n \log h)$ time, where $h$ is the number of points in the skyline of $P$. We also show that the decision problem can be solved in $O(n \log k)$ time and the optimization problem can be solved in $O(n \log k + n \log\log n)$ time. This improves previous algorithms and is optimal for a large range of values of $k$. Ključne besede: geometric optimization, skyline, pareto front, clustering, k-center Objavljeno v DiRROS: 15.03.2024; Ogledov: 331; Prenosov: 166
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1666. 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: 278; Prenosov: 141
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1667. 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: 350; Prenosov: 143
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1669. 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: 285; Prenosov: 156
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