811. An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary mapsIsabel Hubard, Primož Potočnik, Primož Šparl, 2026, original scientific article Abstract: In this paper, we provide the first known infinite family of simple graphs, each of which is the skeleton of a chiral map, a skeleton of a reflexible map on an orientable surface, as well as a skeleton of a reflexible map on a non-orientable surface. This family consists of all lexicographic products $C_n[mK_1]$, where $m \ge 3, n=sm$, with $s$ an integer not divisible by $4$. This answers a question posed by Wilson in 2002.
Keywords: rotary maps, chiral maps, orientable reflexible maps, non-orientable rotary maps
Published in DiRROS: 17.10.2025; Views: 186; Downloads: 87
 Full text (895,56 KB)
This document has many files! More... |
812. Cross-positive linear maps, positive polynomials and sums of squaresIgor Klep, Klemen Šivic, Aljaž Zalar, 2026, original scientific article Abstract: A $\ast$-linear map $\Phi$ between matrix spaces is cross-positive if it is positive on orthogonal pairs $(U,V)$ of positive semidefinite matrices in the sense that $\langle U,V \rangle:={\rm tr}(UV)=0$ implies $\langle\Phi (U),V \rangle \ge 0$, and is completely cross-positive if all its ampliations $I_n \otimes \Phi$ are cross-positive. (Completely) cross-positive maps arise in the theory of operator semigroups, where they are sometimes called exponentially-positive maps, and are also important in the theory of affine processes on symmetric cones in mathematical finance. To each $\Phi$ as above a bihomogeneous form is associated by $p_\Phi (x,y)=y^T\Phi (xx^T)y$. Then $\Phi$ is cross-positive if and only if $p_\Phi$ is nonnegative on the variety of pairs of orthogonal vectors $\{(x,y) | x^Ty = 0\}$. Moreover, $\Phi$ is shown to be completely cross-positive if and only if $p_\Phi$ is a sum of squares modulo the principal ideal $(x^Ty)$. These observations bring the study of cross-positive maps into the powerful setting of real algebraic geometry. Here this interplay is exploited to prove quantitative bounds on the fraction of cross-positive maps that are completely cross-positive. Detailed results about cross-positive maps $\Phi$ mapping between $3\times3$ matrices are given. Finally, an algorithm to produce cross-positive maps that are not completely cross-positive is presented.
Keywords: positive polynomials, sum of squares, positive maps, completely positive maps, one-parameter semigroups, convex cones
Published in DiRROS: 17.10.2025; Views: 176; Downloads: 94
Full text (1,67 MB)
This document has many files! More... |
813. |
814. |
815. |
816. A contribution to the vascular and bryophyte flora of the upper Neretva and Zalomka river valleys (Bosnia and Herzegovina)Đorđije Milanović, Simona Strgulc Krajšek, Jugoslav Brujić, Valentin Heimer, Dragan Koljanin, Marija Kravanja, Ivana Rešetnik, Vladimir Stupar, Peter Schönswetter, Božo Frajman, 2025, original scientific article Abstract: etween 1st and 6th June 2023, we conducted floristic research on sev-eral sites in the upper Neretva River valley and along Zalomka River at Nevesinjsko Polje. We recorded 933 taxa in total; 897 plant taxa including 125 bryophytes were found at 51 localities in the upper Neretva River val-ley, and 200 plant taxa, including 32 bryophytes, were found at 11 sites in the Zalomka River valley. Among the registered taxa, 39 taxa are endemic to the Balkan Peninsula, 56 are listed in the List of endangered and rare taxa of Bosnia and Herzegovina, 27 are on the Red List of the Federation of Bosnia and Herzegovina, and 95 taxa are protected in the Republic of Srpska. We also registered several species new to the flora of Bosnia and Herzegovina. Among Angiosperms these were Barbarea intermedia, Lamium hybridum, Myosotis sicula and Poa ursina, and among bryophytes Fissidens gracilifolius, Grimmia dissimulata, Plagiomnium ellipticum, Schistidium robustum, Sphenolobus minutus, Tortella fasciculata and T. pseudofragilis. Our study reveals the high nature conservation value of the upper Neretva and Zalomka River valleys that should be protected for future generations. In addition, further systematic research of the flora of Bosnia and Herzegovina is needed
Keywords: angiosperms, mosses, nature conservation, Neretva River, vegetation, are species
Published in DiRROS: 16.10.2025; Views: 236; Downloads: 105
Full text (1,26 MB)
This document has many files! More... |
817. Optimal version of the fundamental theorem of chronogeometryMichiya Mori, Peter Šemrl, 2025, original scientific article Abstract: We study lightlikeness preserving mappings from the $4$-dimensional Minkowski spacetime $\mathcal{M}_4$ to itself under no additional regularity assumptions like continuity, surjectivity, or injectivity. We prove that such a mapping $\phi$ satisfies one of the following three conditions. (1) The mapping $\phi$ can be written as a composition of a Lorentz transformation, a multiplication by a positive scalar, and a translation. (2) There is an event $r\in \mathcal{M}_4$ such that $\phi(\mathcal{M}_4\setminus\{r\})$ is contained in one light cone. (3) There is a lightlike line $\ell$ such that $\phi(\mathcal{M}_4\setminus \ell)$ is contained in another lightlike line. Here, a line that is contained in some light cone in $\mathcal{M}_4$ is called a lightlike line. We also give several similar results on mappings defined on a certain subset of $\mathcal{M}_4$ or the compactification of $\mathcal{M}_4$.
Keywords: fundamental theorem of chronogeometry, special relativity, coherency preserving mapping
Published in DiRROS: 16.10.2025; Views: 209; Downloads: 94
Full text (2,86 MB)
This document has many files! More... |
818. Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root findingHaoze He, Daniel Kressner, Bor Plestenjak, 2025, original scientific article Abstract: It is well known that a family of $n \times n$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the $n$ joint eigenvalues of the family. In this work, we consider the task of numerically computing approximations to such joint eigenvalues for a family of (nearly) commuting matrices. This task arises, for example, in solvers for multiparameter eigenvalue problems and systems of multivariate polynomials, which are our main motivations. We propose and analyze a simple approach that computes eigenvalues as one-sided or two-sided Rayleigh quotients from eigenvectors of a random linear combination of the matrices in the family. We provide some analysis and numerous numerical examples, showing that such randomized approaches can compute semisimple joint eigenvalues accurately and lead to improved performance of existing solvers.
Keywords: commuting matrices, joint eigenvalues, Rayleigh quotient, randomized numerical linear algebra, multiparameter eigenvalue problems, polynomial systems
Published in DiRROS: 16.10.2025; Views: 220; Downloads: 119
Full text (3,88 MB)
This document has many files! More... |
819. |
820. Effect of hardening on the magnetic behavior of AISI 1045 steelMario Vukotić, Damijan Miljavec, Jaka Burja, 2025, original scientific article Abstract: Hardening is an effective method to improve the hardness of the steel construction elements of an electric machine, such as rotor shaft. Surface hardening is typically employed for shafts as it provides a material with hard wear-resistant surface (martensite) and tough and ductile core (ferrite and pearlite), with the transitional zone between them (martensite, ferrite, and pearlite). The investigations were performed on the specimens of AISI 1045 steel, which is commonly used in electric machines. There were three categories of specimens, each of them representing a region in a surface hardened shaft – normalized specimens found in as-delivered steel (core), partially hardened specimens obtained by partial hardening of normalized specimens (transitional zone), and fully hardened specimens (hardened surface), also obtained from the normalized steel. Comparison of the magnetization curves showed that partially and fully hardened specimens exhibited a decrease of saturation magnetic flux density for about 11% and 7%, respectively, compared to the normalized specimens. The magnetizing curves from this study can be directly used in the magnetic simulations of a surface-hardened shaft. This allows more accurate electromagnetic design of electric machines, in which the shaft represents an important part of the magnetic circuit, e.g. two-pole wound-rotor synchronous machine.
Keywords: electric machine, hardening, hysteresis loop, magnetic properties, magnetizing curve, microstructure, shaft
Published in DiRROS: 16.10.2025; Views: 234; Downloads: 132
Full text (2,71 MB)
This document has many files! More... |
