1. On $L^2$ approximation by spatial Pythagorean-hodograph curvesRida T. Farouki, Marjetka Knez, Vito Vitrih, Emil Žagar, 2027, izvirni znanstveni članek Povzetek: Two methods for the $L^2$ approximation of smooth space curves by spatial Pythagorean-hodograph (PH) curves are considered. The first method employs direct approximation in ${\mathbb R}^3$, which results in a non-linear system of equations that may be solved by a numerical iteration or optimization scheme. The second method performs the optimization in the quaternion preimage space of PH curves, which results in a linear system of equations. The preimage of a curve in ${\mathbb R}^3$ is a surface in the quaternion space, and an appropriate locus on this surface must be identified for the given space curve. This is accomplished by observing that PH curves equipped with a rational rotation-minimizing frame (RMF) have preimages that are geodesic loci on the surface, and computing a discretized approximation to the RMF on the given curve. The methods are also extended to the approximation of spatial B-spline curves. Detailed algorithm descriptions are provided for both methods, and several computed examples illustrate their performance.
Ključne besede: $L^2$ approximation, quaternions, Pythagorean-hodograph curves, B-splines, preimage
Objavljeno v DiRROS: 31.07.2026; Ogledov: 73; Prenosov: 74
 Celotno besedilo (5,65 MB)
Gradivo ima več datotek! Več... |
2. Constructive approach to the truncated moment problem on reducible cubic curves: hyperbolic-type relationsSeonguk Yoo, Aljaž Zalar, 2026, izvirni znanstveni članek Povzetek: In this paper, we solve constructively the bivariate truncated moment problem (TMP) of even degree on reducible cubic curves, where the conic part is a hyperbola. According to the classification from our previous work, these represent three out of nine possible canonical forms of reducible cubic curves after applying an affine linear transformation. Constructive solutions to the TMP on the union of three parallel lines and to the circular- and parabolic-type cases of the TMP are known, while in this paper we consider three hyperbolic-type cases, namely, a type without real self-intersection points, a type with a simple real self-intersection point, and a type with a double real self-intersection point. In all cases, we also establish bounds on the number of atoms in a minimal representing measure.
Ključne besede: truncated moment problems, K-moment problems, K-representing measure, minimal measure, moment matrix extensions
Objavljeno v DiRROS: 29.07.2026; Ogledov: 87; Prenosov: 67
Celotno besedilo (943,64 KB)
Gradivo ima več datotek! Več... |
3. Runge and Mergelyan theorems on families of open Riemann surfacesFranc Forstnerič, 2026, izvirni znanstveni članek Povzetek: Given a smooth open oriented surface $X$, endowed with a family of complex structures $\{J_b\}_{b\in B}$ of some Hölder class and depending continuously or smoothly on the parameter $b$ in a suitable topological space $B$, we construct continuous or smooth families $F_b:X\to Y$, $b\in B$ of $J_b$-holomorphic maps to any Oka manifold $Y$, with approximation on a suitable family of compact Runge sets in $X$. Along the way, we prove Runge and Mergelyan approximation theorems and Weierstrass interpolation theorem for functions on such families. We include applications to the construction of families of directed holomorphic immersions and conformal minimal immersions to Euclidean spaces.
Ključne besede: Riemann surfaces, Runge theorem, Mergelyan theorem, Oka manifold, Stein manifold, minimal surfaces
Objavljeno v DiRROS: 24.07.2026; Ogledov: 100; Prenosov: 113
Celotno besedilo (2,51 MB)
Gradivo ima več datotek! Več... |
4. Isotopies of complete minimal surfaces of finite total curvatureAntonio Alarcón, Franc Forstnerič, Finnur Lárusson, 2026, izvirni znanstveni članek Povzetek: Let $M$ be a Riemann surface biholomorphic to an affine algebraic curve. We show that the inclusion of the space $\Re {\mathrm {NC}}_*(M,{\mathbb C}^n)$ of real parts of nonflat proper algebraic null immersions $M\to{\mathbb C}^n$, $n\ge 3$, into the space ${\mathrm {CMI}}_*(M,{\mathbb R}^n)$ of complete nonflat conformal minimal immersions $M\to{\mathbb R}^n$ of finite total curvature is a weak homotopy equivalence. We also show that the $(1,0)$-differential $\partial$, mapping ${\mathrm {CMI}}_*(M,{\mathbb R}^n)$ or $\Re{\mathrm {NC}}_*(M,{\mathbb C}^n)$ to the space ${\mathcal A}^1(M, {\mathbf A})$ of algebraic $1$-forms on $M$ with values in the punctured null quadric $\mathbf {A}\subset {\mathbb C}^n\setminus \{0\}$, is a weak homotopy equivalence. Analogous results are obtained for proper algebraic immersions $M\to{\mathbb C}^n$, $n\ge 2$, directed by a flexible or algebraically elliptic punctured cone in ${\mathbb C}^n \setminus \{0\}$.
Ključne besede: Riemann surfaces, minimal surface, algebraic immersions, directed immersions, algebraically elliptic manifold, flexible manifold, Oka manifold
Objavljeno v DiRROS: 23.07.2026; Ogledov: 121; Prenosov: 105
Celotno besedilo (539,47 KB)
Gradivo ima več datotek! Več... |
5. Separating subsets from their imagesMarco Barbieri, Maruša Lekše, Primož Potočnik, Kamilla Rekvényi, 2026, izvirni znanstveni članek Povzetek: Let $G$ be a transitive permutation group acting on $\Omega$. In this paper, we introduce and study the parameter ${\mathrm {sep}}(G)$, which denotes the size of the smallest set of points $A$ such that, for every permutation $g\in G$, $A \cap A^g$ is nonempty. In particular, we focus on deriving general bounds for arbitrary transitive groups, and on the asymptotic behaviour of certain families of primitive groups. We also provide a classification of transitive groups with ${\mathrm {sep}}(G)$ largest possible, namely with ${\mathrm {sep}}(G)=\lceil (|\Omega |+1) / 2 \rceil$.
Ključne besede: permutation groups, transitive groups, primitive groups, self-separable set
Objavljeno v DiRROS: 23.07.2026; Ogledov: 153; Prenosov: 106
Celotno besedilo (681,64 KB)
Gradivo ima več datotek! Več... |
6. Transforming solutions for the Oberwolfach problem into solutions for the spouse-loving variantMaruša Lekše, Mateja Šajna, 2026, izvirni znanstveni članek Povzetek: The Oberwolfach problem ${\mathrm {OP}}(F)$, for a $2$-factor $F$ of $K_n$, asks whether there exists a $2$-factorization of $K_n$ (if $n$ is odd) or $K_n-I$ (if $n$ is even) where each $2$-factor is isomorphic to $F$. Here, $I$ denotes any $1$-factor of $K_n$. For even $n$, the problem ${\mathrm {OP}}(F)$ may also be denoted ${\mathrm {OP}}^-(F)$, and has been nicknamed the spouse-avoiding variant. Similarly, the spouse-loving variant is denoted ${\mathrm {OP}}^+(F)$ and asks for a $2$-factorization of $K_n + I$ (the complete graph with the edges of a $1$-factor $I$ duplicated, rather than deleted) in which each $2$-factor is isomorphic to $F$. To date, many more infinite families of cases of ${\mathrm {OP}}$ and ${\mathrm {OP}}^-$ have been solved than of ${\mathrm {OP}}^+(F)$. In this paper, we show how certain solutions to ${\mathrm {OP}}^-(F)$ can be used to construct solutions to ${\mathrm {OP}}^+(F)$; in particular, when the number of odd cycles in the $2$-factor $F$ is not too large. Our technique of setups also allows us to completely solve the two-table ${\mathrm {OP}}^+$; that is, ${\mathrm {OP}}^+(F)$, where $F$ has exactly two components.
Ključne besede: 1‐rotational solution, 12‐setup, 2‐factorization, 2‐starter, 6‐setup, complete graph plus a 1‐factor, Oberwolfach problem, spouse‐loving variant
Objavljeno v DiRROS: 23.07.2026; Ogledov: 124; Prenosov: 104
Celotno besedilo (4,34 MB)
Gradivo ima več datotek! Več... |
7. Core-EP decomposition and related relations revisitedGregor Dolinar, Janko Marovt, Dijana Mosić, 2026, izvirni znanstveni članek Povzetek: We study relations that are induced by the core-EP decomposition. We revisit the core-EP preorder and extend the concepts of the core-minus, the c-minus, and the c-star partial orders from the set of all $n \times n$ complex matrices to the set of all core-EP invertible elements in a $\ast$-ring. Several characterizations of these relations are presented and thus some known results are generalized.
Ključne besede: core-EP decomposition, ∗-ring, partial order, core order, minus order, star order
Objavljeno v DiRROS: 23.07.2026; Ogledov: 123; Prenosov: 76
Celotno besedilo (418,71 KB)
Gradivo ima več datotek! Več... |
8. Varieties of mutual-visibility and general position on Sierpiński graphsDhanya Roy, Sandi Klavžar, Aparna Lakshmanan S., Jing Tian, 2026, izvirni znanstveni članek Povzetek: The variety of mutual-visibility problems contains four members, as does the variety of general position problems. The basic problem is to determine the cardinality of the largest such sets. In this paper, these eight invariants are investigated on Sierpiński graphs $S_p^n$. They are determined for the Sierpiński graphs $S_p^2$, $p\ge 3$. All, but the outer mutual-visibility number and the outer general position number, are also determined for $S_3^n$, $n\ge 3$. In many of the cases the corresponding extremal sets are enumerated.
Ključne besede: mutual-visibility set, general position set, Sierpiński graph
Objavljeno v DiRROS: 17.07.2026; Ogledov: 191; Prenosov: 100
Celotno besedilo (262,67 KB)
Gradivo ima več datotek! Več... |
9. The Oka principle for tame families of Stein manifoldsFranc Forstnerič, Álfheiður Edda Sigurðardóttir, 2026, izvirni znanstveni članek Povzetek: Let $X$ be a smooth open manifold of even dimension, $T$ be a topological space, and ${\mathscr J}=\{J_t\}_{t\in T}$ be a continuous family of smooth integrable Stein structures on $X$. Under suitable additional assumptions on $T$ and ${\mathscr J}$, we prove an Oka principle for continuous families of maps from the family of Stein manifolds $(X,J_t)$, $t\in T$, to any Oka manifold, showing that every family of continuous maps is homotopic to a family of $J_t$-holomorphic maps depending continuously on $t$. We also prove the Oka-Weil theorem for sections of ${\mathscr J}$-holomorphic vector bundles on $Z = T \times X$ and the Oka principle for isomorphism classes of such bundles. The assumption on the family ${\mathscr J}$ is that the $J_t$-convex hulls of any compact set in $X$ are upper semicontinuous with respect to $t \in T$; such a family is said to be tame. For suitable parameter spaces $T$, we characterise tameness by the existence of a continuous family $\rho_t:X\to {\mathbb R}_+ = [0,+\infty)$, $t\in T$, of strongly $J_t$-plurisubharmonic exhaustion functions on $X$. Every family of complex structures on an open orientable surface is tame. We give an example of a nontame smooth family of Stein structures $J_t$ on ${\mathbb R}^{2n} (t \in {\mathbb R}, n > 1)$ such that $({\mathbb R}^{2n}, J_t)$ is biholomorphic to ${\mathbb C}^n$ for every $t\in{\mathbb R}$. We show that the Oka principle fails on any nontame family.
Ključne besede: Stein manifold, Oka principle, Oka manifold, vector bundle
Objavljeno v DiRROS: 17.07.2026; Ogledov: 182; Prenosov: 103
Celotno besedilo (537,43 KB)
Gradivo ima več datotek! Več... |
10. New approach for constructing edge B-spline-like basis functions for $C^1$ and $C^2$ splines over triangulationsMarjetka Knez, Matija Šteblaj, 2027, izvirni znanstveni članek Povzetek: Splines over triangulations provide a flexible and efficient way to approximate bivariate functions defined over domains, partitioned by triangles. One of the important challenges is the construction of locally supported non-negative basis functions that form a partition of unity, i.e., B-spline-like basis functions. Due to smoothness conditions that depend on the geometry of the triangulation, spline basis functions are typically divided into three groups: triangle, vertex, and edge functions. While the construction of triangle and vertex basis splines is well developed, the computation of non-negative edge basis splines of general degree that form a partition of unity has so far been addressed only for $C^1$ continuous splines, using a completely algebraic approach, with no explicit geometric interpretation ([7]). In this paper a novel approach is presented that extends the control-triangle-based idea known for vertex basis splines and can be geometrically explained and generalized to splines of a higher order of smoothness. The construction is developed on pairs of adjacent triangles forming a strictly convex quadrilateral. Since each smoothness order requires a separate analysis, a detailed study is provided for the $C^1$ and $C^2$ continuous splines of degrees $d \ge 2$ and $d \ge 4$, respectively. Numerical examples are provided to confirm the effectiveness and applicability of the derived construction.
Ključne besede: Bernstein-Bézier form, ▫$C^r$▫ splines over triangulations, B-spline-like basis, control triangles, subdivision
Objavljeno v DiRROS: 01.07.2026; Ogledov: 151; Prenosov: 130
Celotno besedilo (9,42 MB)
Gradivo ima več datotek! Več... |
