31. High order parametric polynomial approximation of quadrics in R [sup] dGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2012, original scientific article Abstract: In this paper an approximation of implicitly defined quadrics in ▫${\mathbb R}^d$▫ by parametric polynomial hypersurfaces is considered. The construction of the approximants provides the polynomial hypersurface in a closed form, and it is based on the minimization of the error term arising from the implicit equation of a quadric. It is shown that this approach also minimizes the normal distance between the quadric and the polynomial hypersurface. Furthermore, the asymptotic analysis confirms that the distance decreases at least exponentially as the polynomial degree grows. Numerical experiments for spatial quadrics illustrate the obtained theoretical results.
Keywords: mathematics, quadric hypersurface, conic section, polynomial approximation, approximation order, normal distance
Published in RUP: 03.04.2017; Views: 2115; Downloads: 32
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32. On maximal distances in a commuting graphGregor Dolinar, Bojan Kuzma, Polona Oblak, 2012, original scientific article Abstract: It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.
Keywords: matematika, linearna algebra, teorija grafov, komutirajoči grafi, matrična algebra, algebraično zaprt obseg, centralizator, razdalja v grafih, mathematics, linear algebra, graph theory, commuting graph, matrix algebra, algebraically closed field, centralizer, distance in graphs
Published in RUP: 03.04.2017; Views: 2318; Downloads: 256
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35. Distance deviation measure of contouring variabilityPeter Rogelj, Robert Hudej, Primož Petrič, 2013, original scientific article Abstract: Background. Several methods that are currently used for contouring analysis have problems providing reliable and/ or meaningful results. In this paper a solution to these problems is proposed in a form of a novel measure, which was developed based on requirements defined for contouring studies. Materials and methods. The proposed distance deviation measure can be understood as an extension of the closest point measures in such a way that it does not measure only distances between points on contours but rather analyse deviation of distances to both/all contours from each image point/voxel. The obtained result is information rich, reliable and provided in a form of an image, enabling detailed topographic analysis. In addition to image representation, results can be further processed into angular representation for compact topographic analysis or into overall scalar estimates for quick assessment of contour disagreement. Results. Distance deviation method is demonstrated on a multi observer contouring example with complex contour shapes, i.e., with pronounced extremes and void interior. The results are presented using the three proposed methods. Conclusions. The proposed method can detect and measure contour variation irrespective of contour complexity and number of contour segments, while the obtained results are easy to interpret. It can be used in various situations, regarding the presence of reference contour or multiple test contours.
Keywords: contouring, contour comparison, distance transform
Published in RUP: 21.12.2015; Views: 2782; Downloads: 123
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37. Patterns of plastid DNA differentiation in Erythronium (Liliaceae) are consistent with allopatric lineage divergence in Europe across longitude and latitudeLázsló Bartha, Gábor Sramkó, Polina A. Volkova, Boštjan Surina, Alexander L. Ivanov, Horia Banciu, 2015, original scientific article Keywords: Karpati, kriptični refugiji, disperzija, kontinentalno-oceanski gradient, Carpathian Basin, cryptic northern refugia, long distance dispersal, ocenic-continental gradient, phylogeography, temperate species
Published in RUP: 15.10.2015; Views: 3196; Downloads: 155
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38. eMIPS - A step closer to outsource the front end of innovation processKlemen Širok, Borut Likar, Katarina Košmrlj Muha, 2015, published scientific conference contribution abstract Keywords: inoviranje, problemi, učenje na daljavo, zunanje izvajanje dejavnosti, front end, innovation, problem, distance learning, eCoaching, outsourcing
Published in RUP: 14.10.2015; Views: 3045; Downloads: 72
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40. Distance-regular Cayley graphs on dihedral groupsŠtefko Miklavič, Primož Potočnik, 2005, original scientific article Abstract: The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every non-trivial distance-regular Cayley graph on a dihedral group is bipartite, non-antipodal, has diameter 3 and arises either from a cyclic di#erence set, or possibly (if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all distance-transitive Cayley graphs on dihedral groups are determined. It transpires that a Cayley graph on a dihedral group is distance-transitive if and only if it is trivial, or isomorphic to the incidence or to the non-incidence graph of a projective space ▫$\mathrm{PG}_{d-1} (d,q)$▫, ▫$d \ge 2$▫, or the unique pair of complementary symmetric designs on 11 vertices.
Keywords: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Published in RUP: 10.07.2015; Views: 2582; Downloads: 90
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