Search results for " Geometry."

showing 10 items of 2189 documents

Historical Origins of the nine-point conic -- The Contribution of Eugenio Beltrami

2020

In this paper, we examine the evolution of a specific mathematical problem, i.e. the nine-point conic, a generalisation of the nine-point circle due to Steiner. We will follow this evolution from Steiner to the Neapolitan school (Trudi and Battaglini) and finally to the contribution of Beltrami that closed this journey, at least from a mathematical point of view (scholars of elementary geometry, in fact, will continue to resume the problem from the second half of the 19th to the beginning of the 20th century). We believe that such evolution may indicate the steady development of the mathematical methods from Euclidean metric to projective, and finally, with Beltrami, with the use of quadrat…

HistoryMathematical problemMathematics - History and OverviewGeneral MathematicsHistory and Overview (math.HO)06 humanities and the artsAlgebraic geometrySettore MAT/04 - Matematiche Complementari01A55 51-03AlgebraEuclidean distanceEugenio Beltrami060105 history of science technology & medicineConic sectionQuadratic transformationsNine-point conicFOS: Mathematics0601 history and archaeologyNine-point conicPoint (geometry)Development (differential geometry)Period (music)Mathematics
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From the theory of “congeneric surd equations” to “Segre's bicomplex numbers”

2015

We will study the historical pathway of the emergence of Tessarines or Bicomplex numbers, from their origin as "imaginary" solutions of irrational equations, to their insertion in the context of study of the algebras of hypercomplex numbers.

HistoryPure mathematicsGeneral MathematicsHistory and Overview (math.HO)Context (language use)01 natural sciencesCorrado SegreBiquaternionJames CockleStoria dell'Algebra BicomplessiFOS: MathematicsBiquaternion0601 history and archaeology0101 mathematics01A55 08-03 51-03The ImaginaryMathematicsHypercomplex numberTessarineMathematics::Complex VariablesMathematics - History and Overview010102 general mathematics06 humanities and the artsSettore MAT/04 - Matematiche Complementari060105 history of science technology & medicineIrrational numberBicomplex numberMathematics::Differential GeometryWilliam Rowan Hamilton
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On Hodge theory for the generalized geometry (I)

2013

Abstract We first investigate the linear Dirac structure from the viewpoint of a mixed Hodge structure. Then we discuss a Hodge-decomposition-type theorem for the generalized Kahler manifold and study the moduli space of a generalized weak Calabi–Yau manifold. We present a holomorphic anomaly equation and a one-loop partition function in a topological B-model under the generalized geometric context.

Hodge theoryHolomorphic functionGeneral Physics and AstronomyComplex differential formGeometryKähler manifoldModuli spaceMathematics::Algebraic GeometryMathematics::Differential GeometryGeometry and TopologyComplex manifoldHodge dualMathematics::Symplectic GeometryMathematical PhysicsHodge structureMathematicsJournal of Geometry and Physics
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Review of Some Development of the Hole Drilling Method

1990

This paper contains a survey of some developments of the hole drilling method. It is mainly based on the research work carried out at the University of Palermo in the years from 1978 to 1989. The paper considers the relationship between the relaxed strain and the residual stresses for a rosette with an off-centre hole, the influence of hole eccentricity on the determination of residual stresses and of rosette calibration constants, the sensitivity of strain relaxation.

Hole drilling methodEngineeringbusiness.industrymedia_common.quotation_subjectMechanicsStructural engineeringDeep hole drillingResidual stressCalibrationRelaxation (physics)Development (differential geometry)Eccentricity (behavior)businessBlind holemedia_common
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Monte carlo methods in quantum many-body theories

2008

This is an introduction of Monte Carlo methods for beginners and their application to some quantum many-body problems. Special emphasis is done on the methodology and the general characteristics of Monte Carlo calculations. An introduction to the applications to many-body physics, specifically the Variational Monte Carlo and the Green Function Monte Carlo, is also included.

Hybrid Monte CarloComputer scienceQuantum Monte CarloMonte Carlo methodDynamic Monte Carlo methodMathematics::Metric GeometryMonte Carlo method in statistical physicsMonte Carlo integrationStatistical physicsVariational Monte CarloMonte Carlo molecular modeling
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Structural characterization of β-2′-pyridylaminocrotonoyl-2-pyridylamide by ESI-MS, NMR, single crystal X-ray analysis and ab initio methods

2003

Abstract In contradiction with earlier reports 1H, 13C and 15N NMR spectra show that β-2′-pyridylaminocrotonoyl-2-pyridylamide is the only form present in chloroform solution. According to the X-ray data the same tautomer exists also in the crystal state. The studied amide has a dimeric form where the monomer molecules are held together by two intermolecular hydrogen bonds. The NMR spectral data show that there is also an intramolecular hydrogen bond in each monomer subunit. The dilution experiments and variable-temperature 1H NMR runs show that β-2′-pyridylaminocrotonoyl-2-pyridylamide tends to form the dimers also in chloroform solution at higher concentrations. The ESI-TOF MS measurement…

Hydrogen bondChemistryOrganic ChemistryIntermolecular forceAb initioTautomerAnalytical ChemistryInorganic ChemistryNMR spectra databaseCrystallographyMolecular geometryIntramolecular forceProton NMRSpectroscopyJournal of Molecular Structure
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The preparation, IR spectrum and structure of the Di-μ3-hydroxo-μ-sulphatotetrakis-μ-(isonicotinato-N-oxide)tetraaqua-tetracopper(II)

1982

Abstract A very unusual new copper(II) complex with isonicotinate N-oxide (N-inicO), Cu4(N-inicO)4SO4(OH)2(H2O)4 has been prepared and its crystal and molecular structure determined from three dimensional X-ray diffraction data. The crystals belong to the monoclinic space group C2. The cell parameters are a = 19.089(8), b = 6.884(3), c = 19.533(12) A, β = 140.9(3)°, dobs = 1.99, dcalc = 2.01 and Z = 2. The structure was refined to a final R-value of 0.062. The monomeric tetranuclear complex resembles a space ship with the sulphate group at its top and pyridine rings as wings. Two copper atoms are very close to each other in the molecule; the Cu1Cu1′ distance is 2.885 A. The coordination ar…

Hydrogen bondInorganic chemistrychemistry.chemical_elementBridging ligandCopperSquare pyramidal molecular geometryInorganic ChemistryCrystallographychemistry.chemical_compoundchemistryPyridineMaterials ChemistryMoleculeCarboxylatePhysical and Theoretical ChemistryMonoclinic crystal systemInorganica Chimica Acta
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The key role of hydrogen bonding in the nuclearity of three copper(II) complexes with hydrazone-derived ligands and nitrogen donor heterocycles

2011

International audience; Three new Cu(II) complexes of formula [Cu(L1)(pyz)(CH3OH)]ClO4 (1), [Cu(L1)(4,4′-bpy)(ClO4)]·0.5H2O (2) and [{Cu(L2)(ClO4)}2(μ-4,4′-bpy)] (3) have been synthesised by using pyrazine (pyz) and 4,4′-bipyridine (4,4′-bpy) and tridentate O,N,O-donor hydrazone ligands, L1H and L2H, obtained by the condensation of 1,1,1-trifluoro-2,4-pentanedione with salicyloylhydrazide and benzhydrazide, respectively. The ligands and their complexes have been characterized by elemental analyses, FT-IR, and UV–Vis spectroscopies. Single crystal X-ray structure analysis evidences the metal ion in a slightly deformed square pyramidal geometry in all the complexes. However complexes 1 and 2 …

Hydrogen bondingDenticityPyrazineStereochemistryHydrazonechemistry.chemical_elementAntiferromagnetic couplingCrystal structure[CHIM.INOR]Chemical Sciences/Inorganic chemistry010402 general chemistry010403 inorganic & nuclear chemistry01 natural sciencesInorganic Chemistrychemistry.chemical_compoundMaterials Chemistry[CHIM.CRIS]Chemical Sciences/Cristallography[CHIM]Chemical SciencesMonodentate pyz and 4Physical and Theoretical ChemistryCu(II) hydrazone complexescopper complexhydrazone ligandchemistry.chemical_classificationhydrogen bondHydrogen bondSelf assemblyCopperSquare pyramidal molecular geometry0104 chemical sciencesCrystallographychemistryCrystal structures4′-bpySingle crystalhydrogen bond; copper complex; hydrazone ligand
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"Comment on ""Non-symmetric substituted ureas locked in an (E,Z) conformation: an unusual anion binding via supramolecular assembly"" by M. Olivari, …

2014

We propose another point of view on the type of hydrogen bonded complexes that were described in this journal (M. Olivari et al., New J. Chem., 2013, 37, 663). The main difference is the molecular geometry and breakage of the intramolecular hydrogen bond during association. The current comment is to highlight mentioned aspects and to point out that in some cases the interpretation may not be straightforward due to the simultaneous effects associated with complexation.

HydrogenHydrogen bondStereochemistryChemistrychemistry.chemical_elementGeneral ChemistryType (model theory)CatalysisSupramolecular assemblyInterpretation (model theory)Molecular geometryIntramolecular forceMaterials ChemistryAnion bindingta116New Journal of Chemistry
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Morphological Similarity of Channels: From Linear Erosional Features (Rill, Gully) to Alpine Rivers

2017

Hydrologygeographygeography.geographical_feature_category010504 meteorology & atmospheric sciencesMorphological similarity0208 environmental biotechnologySoil Science02 engineering and technologyDevelopmentChannel geometry01 natural sciences020801 environmental engineeringRillEnvironmental ChemistryGeomorphologyGeology0105 earth and related environmental sciencesGeneral Environmental ScienceLand Degradation & Development
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