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No-hole λ-L (k, k – 1, …, 2,1)-labeling for square grid
Soumen Atta, Stanisław Goldstein, Priya Ranjan Sinha Mahapatra, 2017, original scientific article

Abstract: Motivated by a frequency assignment problem, we demonstrate, for a fixed positive integer k, how to label an infinite square grid with a possibly small number of integer labels, ranging from 0 to λ −1, in such a way that labels of adjacent vertices differ by at least k, vertices connected by a path of length two receive values which differ by at least k − 1, and so on. The vertices which are at least k + 1 distance apart may receive the same label. By finding a lower bound for λ, we prove that the solution is close to optimal, with approximation ratio at most 9/8. The labeling presented is a no-hole one, i.e., it uses each of the allowed labels at least once.
Keywords: graph labeling, labeling number, no-hole labeling, square grid, frequency assignment problem, approximation ratio
Published in RUNG: 17.04.2023; Views: 725; Downloads: 0
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Estensioni di Stone del teorema di approssimazione di Weierstrass
Federico Mangano, undergraduate thesis

Keywords: Function approximation, geometry
Published in RUNG: 23.11.2022; Views: 928; Downloads: 0
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Blaž Winkler, 2019, doctoral dissertation

Abstract: This work is primarily focused on application of standard first-principle computational approaches to model oxygen excess related point defects in amorphous silica. Atomic models with their respective electronic and optical properties are explored together with some conversion mechanisms between defect models. The first chapter overviews extensive literature about the already known properties of oxygen related defects. Second chapter briefly introduces main methods that have been used in this research, in particular Density Functional Theory (DFT) as energy and force engine with short description of minimal energy path (MEP) algorithm used for modeling chemical/migration reactions, GW approximation for charged electronic excitations (band structure) and Bethe-Salpeter Equation (BSE) for neutral excitations (optical absorption and excitonic structure including electron hole interaction). The third chapter is devoted to the presentation of results. Thanks to the calculation of optical properties of peroxy bridge (POL), a correlation has been found between structural disorder, specifically dihedral angle dispersion, and low coupling with light, which has been identified as main reason why no clear absorption bands have been assigned to the POL. Structure and stability of some other defects, like interstitial ozone molecule (ozonyl) and dioxasilirane (silicon analogy of dioxirane), have been studied. These defects are usually not considered as most important species, however their calculated formation energies are lower compared to some known defects, which indicates they might be present in silica. From a detailed study on possible reaction mechanisms, it has been found that ozonyl might be one of the most important intermediate steps for oxygen exchange reactions. Results also show that dioxasilirane can be spontaneously created during the interaction of oxygen with lone pair defects. By exploring different reactions between oxygen and pre-existing oxygen deficiency centers (ODCs), calculations predict two kinds of passivation behaviors: single-barrier reversible mechanisms with the formation of dioxasilirane-like groups, for which the network keeps the memory of the precursory lone pair defects, and single or multiple-barrier mechanisms, for which the network loses its memory, either because of the high reverse barrier or because of a reconstruction. Final part of this research has been devoted to experimental characterization of the response and tolerance of optical fibers loaded with oxygen under irradiation. These include experiments on commercial fiber along with canonical samples (Optical fibers developed with the intention of studying correlations between different fabrication parameters, dopant/impurity concentration and doping concentrations). Studied fibers also include rare-earth doped fibers.
Keywords: Silica, DFT, GW-approximation, Bethe-Salpeter equation, NEB, defect, oxygen, oxygen excess centers, oxygen deficiency centers, optical absorption, optical fibers, radiation induced attenuation.
Published in RUNG: 07.05.2019; Views: 4368; Downloads: 199
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Accelerating GW calculations with optimal polarizability basis
Paolo Umari, X Qian, Nicola Marzari, G Stenuit, Luigi Giacomazzi, Stefano Baroni, 2011, original scientific article

Keywords: GW approximation, silicon nitride, silica, DFT
Published in RUNG: 16.10.2018; Views: 3339; Downloads: 0
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NAZIA TALAT, 2018, doctoral dissertation

Keywords: Two-phase flow, free and moving boundaries, computational fluid dynamics, phasefield formulation, 2D problems, axisymmetric problems, diffuse approximate meshless method, Rayleigh-Taylor instability, Boussinesq approximation, variable density and viscosity, flow focusing, dripping, jetting
Published in RUNG: 11.09.2018; Views: 5088; Downloads: 178  (1 vote)
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