Search results for " Geometry"

showing 10 items of 2294 documents

Spacelike energy of timelike unit vector fields on a Lorentzian manifold

2004

On a Lorentzian manifold, we define a new functional on the space of unit timelike vector fields given by the L2 norm of the restriction of the covariant derivative of the vector field to its orthogonal complement. This spacelike energy is related with the energy of the vector field as a map on the tangent bundle endowed with the Kaluza–Klein metric, but it is more adapted to the situation. We compute the first and second variation of the functional and we exhibit several examples of critical points on cosmological models as generalized Robertson–Walker spaces and Godel universe, on Einstein and contact manifolds and on Lorentzian Berger’s spheres. For these critical points we have also stu…

Tangent bundleMathematical analysisGeneral Physics and AstronomyOrthogonal complementCongruence (general relativity)ManifoldCovariant derivativeGeneral Relativity and Quantum CosmologyDifferential geometryUnit vectorVector fieldMathematics::Differential GeometryGeometry and TopologyMathematical PhysicsMathematicsMathematical physicsJournal of Geometry and Physics
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A historical account on characterizations ofC1-manifolds in Euclidean spaces by tangent cones

2014

Abstract A historical account on characterizations of C 1 -manifolds in Euclidean spaces by tangent cones is provided. Old characterizations of smooth manifold (by tangent cones), due to Valiron (1926, 1927) and Severi (1929, 1934) are recovered; modern characterizations, due to Gluck (1966, 1968) and Tierno (1997) are restated. All these results are consequences of the Four-cones coincidence theorem due to [1] .

Tangent bundlePure mathematicsApplied MathematicsMathematical analysisTangent coneTangentManifoldVertical tangentTangent spacePushforward (differential)Mathematics::Differential GeometryTangent vectorAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Kähler manifolds with split tangent bundle

2006

( Varietes kahleriennes a fibre tangent scinde). - On etudie dans cet article les varietes kahleriennes compactes dont le fibre tangent se decompose en somme directe de sous-fibres. En particulier, on montre que si le fibre tangent se decompose en somme directe de sous-fibres en droites, alors la variete est uniformisee par un produit de courbes. Les methodes sont issues de la theorie des feuilletages de (co)dimension 1.

Tangent bundlekähler manifoldsPure mathematicsGeneral Mathematics32Q15 ; 53C15010102 general mathematicsGeometry01 natural sciences[ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG]010101 applied mathematics[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Mathematics::Differential Geometry0101 mathematics[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Mathematics::Symplectic GeometryMathematics
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Tangent Measures, Densities, and Singular Integrals

1995

We introduce tangent measures in the sense of David Preiss. We discuss their applications to the density and rectifiability properties of general Borel measures in ℝ n as well as to the behaviour of certain singular integrals with respect to such measures.

Tangent measureMathematical analysisMathematics::General TopologyMathematics::Metric GeometrySingular integralMathematics
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Study of High-Temperature Behaviour of ZnO by Ab Initio Molecular Dynamics Simulations and X-ray Absorption Spectroscopy

2021

Wurtzite-type zinc oxide (w-ZnO) is a widely used material with a pronounced structural anisotropy along the c axis, which affects its lattice dynamics and represents a difficulty for its accurate description using classical models of interatomic interactions. In this study, ab initio molecular dynamics (AIMD) was employed to simulate a bulk w-ZnO phase in the NpT ensemble in the high-temperature range from 300 K to 1200 K. The results of the simulations were validated by comparison with the experimental Zn K-edge extended X-ray absorption fine structure (EXAFS) spectra and known diffraction data. AIMD NpT simulations reproduced well the thermal expansion of the lattice, and the pronounced …

TechnologyMaterials science02 engineering and technology01 natural sciencesMolecular physicsThermal expansionArticleCondensed Matter::Materials Science0103 physical sciencesAtomGeneral Materials Science010306 general physicsAnisotropyAbsorption (electromagnetic radiation)MicroscopyQC120-168.85X-ray absorption spectroscopyExtended X-ray absorption fine structureTab initio molecular dynamicsQH201-278.5Anharmonicityzinc oxideEngineering (General). Civil engineering (General)021001 nanoscience & nanotechnologyTK1-9971Molecular geometryDescriptive and experimental mechanicsZnOElectrical engineering. Electronics. Nuclear engineeringTA1-20400210 nano-technologyextended X-ray absorption fine structureMaterials
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3D visualization of sheath folds in Ancient Roman marble wall coverings from Ephesos, Turkey

2014

Abstract Archaeological excavations and restoration of a palatial Roman housing complex in Ephesos, Turkey yielded 40 wall-decorating plates of folded mylonitic marble (Cipollino verde), derived from the internal Hellenides near Karystos, Greece. Cipollino verde was commonly used for decoration purposes in Roman buildings. The plates were serial-sectioned from a single quarried block of 1,25 m3 and provided a research opportunity for detailed reconstruction of the 3D geometry of meterscale folds in mylonitized marble. A GOCAD model is used to visualize the internal fold structures of the marble, comprising curtain folds and multilayered sheath folds. The sheath folds are unusual in that the…

TectonicsOutcropMineralogyGeologyGeometryFold (geology)3d geometryLayeringGeologyMyloniteJournal of Structural Geology
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Abelian varieties and theta functions associated to compact Riemannian manifolds; constructions inspired by superstring theory

2012

We look into a construction of principal abelian varieties attached to certain spin manifolds, due to Witten and Moore-Witten around 2000 and try to place it in a broader framework. This is related to Weil intermediate Jacobians but it also suggests to associate abelian varieties to polarized even weight Hodge structures. The latter construction can also be explained in terms of algebraic groups which might be useful from the point of view of Tannakian categories. The constructions depend on moduli much as in Teichm\"uller theory although the period maps in general are only real analytic. One of the nice features is how the index for certain differential operators canonically associated to …

Teichmüller spaceMathematics - Differential GeometryPure mathematicsMathematics(all)Intermediate JacobianGeneral MathematicsFOS: Physical sciencesTheta functionDirac operatorModulisymbols.namesakeMathematics - Algebraic GeometryMathematics::Algebraic Geometry14K10 14C30 19K56FOS: MathematicsAbelian groupAlgebraic Geometry (math.AG)Mathematical PhysicsMathematicsApplied MathematicsSuperstring theoryMathematical Physics (math-ph)AlgebraDifferential Geometry (math.DG)symbolsAtiyah–Singer index theoremJournal de Mathématiques Pures et Appliquées
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Aromatic dicarboxylate incorporated new di- and tetranuclear cobalt(II) complexes: Synthetic and structural aspects, and evaluation of properties and…

2020

Abstract The synthetic and structural aspects as well as evaluation of magnetic properties and catalytic activity toward aerial oxidation of 3,5-di-tert-butylcatechol to 3,5-di-tert-butylbenzoquinone of three new, two di- and one tetranuclear cobalt(II) complexes, [Co2(cpdp)(Hphth)]∙5H2O (1), [Co2(cpdp)(Hisophth)] (2) and [Co4(cpdp)2(terephth)]∙4.5CH3OH·5.5H2O (3), based on a symmetrical multidentate ligand, N,N'-Bis[2-carboxybenzomethyl]-N,N'-Bis[2-pyridylmethyl]-1,3-diaminopropan-2-ol (H3cpdp) in combination with exogeneous aromatic dicarboxylic acids, such as phthalic acid (H2phth), isophthalic acid (H2isophth) and terephthalic acid (H2terephth) are reported. All three coordination compl…

Terephthalic acidDenticity010405 organic chemistryLigandchemistry.chemical_element010402 general chemistry01 natural sciencesSquare pyramidal molecular geometry0104 chemical sciencesInorganic ChemistryIsophthalic acidchemistry.chemical_compoundTrigonal bipyramidal molecular geometryCrystallographyPhthalic acidchemistryMaterials ChemistryPhysical and Theoretical ChemistryCobaltInorganica Chimica Acta
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The ionic tin(IV) complex tri-μ2-methoxy-μ3-oxo-tris[di-tert-butyltin(IV)] tri-μ2-methoxy-bis[tert-butyldimethoxystannate(IV)]

2004

The solid-state of the title compound, [Sn3(C4H9)6(CH3O)3O][Sn2(C4H9)2(CH3O)7], consists of distinct [tBu6Sn3(μ-OCH3)3(μ3-O)]+ cations and [tBu2Sn2(OCH3)4(μ-OCH3)3]− anions, apparently formed as a result of slow hydro­lysis of pure di(tert-butyl)­di­methoxy­stannane, tBu2Sn(OCH3)2. In the monocation, the coordin­ation about the Sn atoms is distorted trigonal bipyramidal, and, in the monoanion, distorted octahedral. The trigonal bipyramidal arrangement induces planarity of the Sn3O4 motif.

Tert butylTrisStannateStereochemistryIonic bondingchemistry.chemical_elementGeneral ChemistryCondensed Matter PhysicsMedicinal chemistryTrigonal bipyramidal molecular geometrychemistry.chemical_compoundchemistryOctahedronSN2 reactionGeneral Materials ScienceTinActa Crystallographica Section E Structure Reports Online
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Synthesis, characterization, crystal structures and magnetic exchange in dinuclear copper complexes with 3-amino-1-propanol as terminal and bridging …

1990

Abstract The synthesis, X-ray structures and spectroscopic and magnetic properties are described for two groups of dinuclear Cu(II) compounds with the ligand 3-amino-1-propanol (Hap). The formulae of the compounds are for group A: [Cu(ap)(anion)]2, in which ap is the dehydronated Hap and the anions are formate, nitrate, chloride and bromide and for group B: [Cu(ap)(Hap)]2(anion)2, with anion = iodide, bromide, chloride, nitrate and tetrafluoroborate. The structure of group A compounds consists of dinuclear units with the co-planar centrosymmetric chromophore ANCuOO′CuNA, in which the A ligands (anions) bridge to neighbouring units as axial ligands, thereby forming infinite chains. Dimer Cu……

TetrafluoroborateCoordination sphereChemistryHydrogen bondStereochemistryLigandDimerBridging ligandCrystal structureSquare pyramidal molecular geometryInorganic Chemistrychemistry.chemical_compoundCrystallographyMaterials ChemistryPhysical and Theoretical ChemistryInorganica Chimica Acta
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