Search results for "Geometry"

showing 10 items of 4487 documents

Imposing tree-based topologies onto self organizing maps

2011

Accepted version of an article from the journal Information Sciences. Definitive published version available on Elsevier Science Direct: http://dx.doi.org/10.1016/j.ins.2011.04.038 The beauty of the Kohonen map is that it has the property of organizing the codebook vectors, which represent the data points, both with respect to the underlying distribution and topologically. This topology is traditionally linear, even though the underlying lattice could be a grid, and this has been used in a variety of applications [23,35,40]. The most prominent efforts to render the topology to be structured involves the Evolving Tree (ET) due to Pakkanen et al. [36], and the Self-Organizing Tree Maps (SOTM)…

VDP::Mathematics and natural science: 400::Information and communication science: 420::Algorithms and computability theory: 422VDP::Mathematics and natural science: 400::Mathematics: 410::Topology/geometry: 415
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A theoretical study of the electronic spectrum of bithiophene

1995

The electronic spectrum of bithiophene in the energy range up to 6.0 eV has been studied using multiconfigurational second order perturbation theory (CASPT2) and a basis set of ANO type, with split valence quality and including polarization functions on all heavy atoms. Calculations were performed at a planar (trans) and twisted geometry. The calculated ordering of the excited singlet states is 1Bu, 1Bu, 1Ag, 1Ag, and 1Bu with 0–0 transition energies: 3.88, 4.15, 4.40, 4.71, and 5.53 eV, respectively. The first Rydberg transition (3s) has been found at 5.27 eV. The results have been used in aiding the interpretation of the experimental spectra, and in cases where a direct comparison is poss…

Valence (chemistry)Electron spectraChemistryGeneral Physics and AstronomyGeometryExcited StatesSpectral lineUNESCO::FÍSICA::Química físicasymbols.namesakePlanarElectron SpectraThiopheneRydberg StatesExcited stateRydberg formulasymbolsPerturbation TheoryThiophene ; Electron Spectra ; Perturbation Theory ; Geometry ; Excited States ; Rydberg StatesPhysical and Theoretical ChemistryAtomic physics:FÍSICA::Química física [UNESCO]Excited singletBasis set
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Stability of Rare-Earth Oxychloride Phases: Bond Valence Study

2002

Abstract The crystal structures of the tetragonal rare earth ( RE ) oxychlorides, RE OCl ( RE =La–Nd, Sm–Ho, and Y) were studied by X-ray powder diffraction measurements, Rietveld analyses, and bond valence calculations. The tetragonal structure (space group P 4/ nmm , No. 129, Z =2) is stable for all but Er–Lu oxychlorides, which possess a hexagonal structure. The tetragonal structure consists of alternating layers of ( RE O) n n + complex cations and X n − anions, where the rare earth is coordinated to four oxygens and four plus one chlorines in a monocapped tetragonal antiprism arrangement. The Rietveld analyses yielded a coherent series of structural parameters. Preferred orientation an…

Valence (chemistry)Ionic radiusRietveld refinementChemistryStereochemistryCrystal structureCondensed Matter PhysicsElectronic Optical and Magnetic MaterialsInorganic ChemistryTetragonal crystal systemCrystallographyMolecular geometryCovalent bondMaterials ChemistryCeramics and CompositesPhysical and Theoretical ChemistryPowder diffractionJournal of Solid State Chemistry
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Oxovanadium(V) complexes with tripodal bisphenolate and monophenolate ligands: Syntheses, structures and catalytic activities

2019

Abstract The reactions between [VO(acac)2] (acac– = acetylacetonate) and the tripodal amino bisphenols 6,6′-(((2-morpholinoethyl)azanediyl)bis(methylene))bis(2,4-di-tert-butylphenol) (H2L1) and 6,6′-(((thiophen-2-ylmethyl)azanediyl)bis(methylene))bis(2,4-di-tert-butylphenol) (H2L2) as well as the tetradentate amino phenol 2,2′-((3,5-di-tert-butyl-2-hydroxybenzyl)azanediyl)bis(ethan-1-ol) (H3L3) afford the complexes [VO(L1)(OMe)] (1), [VO(L2)(acac)] (2) and [VO(L3)] (3), correspondingly. Complexes 1 and 3 can also be prepared using VOSO4·xH2O or [VO(OPr)3] as vanadium precursors. When [VO(acac)2] or VOSO4·xH2O is used, mononuclear oxovanadium(V) complexes are formed upon oxidation of the met…

Vanadiumchemistry.chemical_element010402 general chemistry01 natural sciencesMedicinal chemistrysulfoxidationCatalysisInorganic ChemistryMetalchemistry.chemical_compoundepoxidationcalculationsMaterials ChemistryPhysical and Theoretical ChemistryMethyleneta116Vanadium (V) complexes010405 organic chemistryChemistryThioanisolekompleksiyhdisteet0104 chemical sciencesTrigonal bipyramidal molecular geometryOctahedronvisual_artvisual_art.visual_art_mediumSingle crystalInorganica Chimica Acta
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Qualitative models of equipment units and their use in automatic HAZOP analysis

2000

Abstract The use of qualitative models in a support system for HAZOP analyses, in connection with an algorithm for finding the causes and the consequences of variable deviations, is described. The models use several representation structures among which mini-trees constitute the most important from the logical-functional point of view. The models are conceived both for continuous and batch plants. For the latter procedures, regulating the use of equipment units are also modelled using similar structures while equipment units are considered in various phases of their functioning. A brief description of the prototype support system, in which the models are implemented, is also given.

Variable (computer science)EngineeringProcess safetyHazard and operability studybusiness.industryPoint (geometry)Support systemSafety Risk Reliability and QualityRepresentation (mathematics)businessIndustrial and Manufacturing EngineeringReliability engineeringReliability Engineering & System Safety
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On double Veronese embeddings in the Grassmannian G(1,N)

2004

We classify all the embeddings of P^n in a Grassmannian of lines G(1,N) such that the composition with Pl\"ucker is given by a linear system of quadrics of P^n.

Veronese embeddingsGeneral MathematicsLinear systemComposition (combinatorics)CombinatoricsAlgebra14M15 (Primary) 14M07 (Secondary)rank-2 bundlesMathematics - Algebraic GeometryGrassmannianFOS: MathematicsSettore MAT/03 - GeometriaGrassmanniansPluckerAlgebraic Geometry (math.AG)Mathematics
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Automorphisms and abstract commensurators of 2-dimensional Artin groups

2004

In this paper we consider the class of 2-dimensional Artin groups with connected, large type, triangle-free defining graphs (type CLTTF). We classify these groups up to isomorphism, and describe a generating set for the automorphism group of each such Artin group. In the case where the defining graph has no separating edge or vertex we show that the Artin group is not abstractly commensurable to any other CLTTF Artin group. If, moreover, the defining graph satisfies a further `vertex rigidity' condition, then the abstract commensurator group of the Artin group is isomorphic to its automorphism group and generated by inner automorphisms, graph automorphisms (induced from automorphisms of the…

Vertex (graph theory)20F67CommensuratorCoxeter groupCoxeter group20F36InverseGroup Theory (math.GR)Automorphism2–dimensional Artin group20F36 20F55 20F65 20F67CombinatoricsMathematics::Group Theorytriangle freeGenerating set of a groupFOS: Mathematicscommensurator groupArtin groupGeometry and TopologyIsomorphism20F5520F65graph automorphismsMathematics - Group TheoryMathematics
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Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta

2017

We determine the non-Abelian version of the four longitudinal form factors of the quark-gluon vertex, using exact expressions derived from the Slavnov-Taylor identity that this vertex satisfies. In addition to the quark and ghost propagators, a key ingredient of the present approach is the quark-ghost scattering kernel, which is computed within the one-loop dressed approximation. The vertex form factors obtained from this procedure are evaluated for arbitrary Euclidean momenta, and display features not captured by the well-known Ball-Chiu vertex, deduced from the Abelian (ghost-free) Ward identity. The potential phenomenological impact of these results is evaluated through the study of spec…

Vertex (graph theory)PhysicsHigh Energy Physics - Theory010308 nuclear & particles physicsHigh Energy Physics::LatticeHigh Energy Physics - Lattice (hep-lat)High Energy Physics::PhenomenologyForm factor (quantum field theory)PropagatorFOS: Physical sciences01 natural sciencesHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)High Energy Physics - LatticeHigh Energy Physics - Theory (hep-th)Quantum mechanics0103 physical sciencesEuclidean geometryVertex modelTensorBall (mathematics)Abelian group010306 general physicsMathematical physics
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Prediction of Molecular Volume and Surface of Alkanes by Molecular Topology.

2003

Molecular volume and molecular surface are expressed as a function of topological degree in alkane graphs. This allows not only a straightforward approach to calculate such physicochemical magnitudes but also an interpretation of the role of the local vertex invariant (LOVI) or valence degree, delta, as well as the connectivity indices in the prediction of physicochemical properties. The interpretation is based on the concept of molecular accessibility (as introduced by Estrada, J. Phys. Chem. A 2002, 106, 9085) for which precise mathematical definitions are provided.

Vertex (graph theory)Surface (mathematics)Alkanechemistry.chemical_classificationValence (chemistry)Degree (graph theory)ChemistryGeometryGeneral ChemistryGeneral MedicineFunction (mathematics)Computer Science ApplicationsInterpretation (model theory)Computational Theory and MathematicsStatistical physicsMolecular topologyInvariant (mathematics)Information SystemsMathematicsChemInform
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UV Index experimental values on vertical surfaces

2011

UV erythemal irradiance (UVER) has been studied on a horizontal plane and on vertical surfaces with different orientations in Valencia, Spain. The evolution of the solar noon value and the maximum daily value over a year has been analysed from the instantaneous UVER taken every five minutes on the horizontal plane and on vertical surfaces with north, south, east and west orientations. The annual evolution of these values shows a sinusoidal form for all planes except for the vertical south plane with maxima in spring and autumn. The UV Index (UVI) on these planes was also determined. The percentage of coincidence of the UVI at solar noon and of the maximum daily UVER values, considering diff…

Vertical surfacesAtmospheric ScienceMeteorologyHorizontal and verticalPlane (geometry)ClimatologyIrradianceVertical planeNoonGeodesyMaximaHorizontal planeGeologyInternational Journal of Climatology
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