Search results for " geometry"

showing 10 items of 2294 documents

An axiomatic treatment of ratios in an affine plane

1967

Affine geometryPure mathematicsAffine geometry of curvesPlane curveGeneral MathematicsAffine groupAffine spaceAffine planeAxiomMathematicsArchiv der Mathematik
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Hydroxo Hydrido Complexes of Iron and Cobalt (Sn−Fe−Sn, Sn−Co−Sn): Probing Agostic Sn⋅⋅⋅H−M Interactions in Solution and in the Solid State

2000

Bis(toluene)iron 9 reacts with Lappert's stannylene [Sn[CH(SiMe3)2]2] (4) to form the paramagnetic bis-stannylene complex [[(eta6-toluene)Fe-Sn-[CH(SiMe3)2]2]2] (10). Compound 10 reacts with H2O to form the hydroxo hydrido complex [(eta6-C7H8)(mu-OH)(H)-Fe-[Sn[CH(SiMe3)2]2]2] (12) in high yield; its solid-state structure has been elucidated by X-ray and neutron diffraction analysis. In agreement with the 1H NMR results, 12 contains a hydridic ligand whose exact coordination geometry could be determined by neutron diffraction. The 1H and 119Sn NMR analysis of 12 suggested a multicenter Sn/Sn/H/Fe bonding interaction in solution, based on significantly large values of J(Sn,H,Fe) = 640+/-30 Hz…

Agostic interactionChemistryLigandHydrideOrganic ChemistryInorganic chemistryNeutron diffractionIsolobal principleGeneral ChemistryCatalysisCrystallographySingle bondIsostructuralCoordination geometryChemistry - A European Journal
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Products of snowflaked Euclidean lines are not minimal for looking down

2017

We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance $d$ such that the product of snowflaked Euclidean lines looks down on $(\mathbb R^N,d)$, but not vice versa.

Ahlfors-regularity26B05 (Primary) 28A80 (Secondary)01 natural sciences010104 statistics & probabilityFractalMathematics - Metric GeometryEuclidean geometryClassical Analysis and ODEs (math.CA)FOS: MathematicsHeisenberg groupMathematics::Metric GeometryBPI-spacesbpi-spacessecondary 28a800101 mathematicsbilipschitz piecesMathematicsDiscrete mathematicsQA299.6-433ahlfors-regularityApplied Mathematics010102 general mathematicsprimary 26b05Metric Geometry (math.MG)biLipschitz piecesMathematics - Classical Analysis and ODEsProduct (mathematics)Geometry and TopologyAnalysis
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Adaptive BEM for Low Noise Propeller Design

2009

A potential-based Boundary Element Method is presented for the aerodynamic and acoustic design of propel- lers at on- and off-design point conditions. Using an adaptive method, a family of airfoil sections is selected to produce the required performance (thrust, torque and efficiency versus advance ratio) at different cruise flight levels. Climb condi- tions are also considered in order to check the off-design point performance. Once the available airfoil data have been stored in a database, the code processes the families of airfoils to generate a complete geometry for a propeller of the specified performance with an optimized noise emission. The computational scheme adjusts the blade geom…

AirfoilChord (geometry)Ffowcs Williams-Hawkings equationComputer scienceAcousticspropeller designPropellerBlade geometryAerodynamicsboundary element methodPhysics::Fluid DynamicsNoiseAeroacoustic optimizationClimbAdvance ratio
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DFT study of N–H···O hydrogen bond between model dehydropeptides and water molecule

2013

The strength of the hydrogen bond formed between a water molecule and two α,β-dehydroalanine derivatives including Ac-ΔAla-NMe2 (1) and Ac-ΔAla-NHMe (2) in comparison with standard amino acid Ac-Ala-NMe2 (3) is studied by density functional theory (with M06-2X and B3LYP functionals). Calculations were conducted for two different conformations of the peptides: extended (C5) and bent (β) with polyproline II backbone dihedral angles. The obtained results show that both dehydro and standard peptides in bent conformation form stronger hydrogen bonds with water than in the extended ones. Moreover, due to higher polarity of the N–H group of α,β-dehydroalanine residues, the H-bond in their complexe…

Alaninehydrogen bondB3LYPHydrogen bondStereochemistryChemistryBent molecular geometryLow-barrier hydrogen bonddehydroamino acidsBiophysicsDihedral angleCondensed Matter PhysicsDFTM06-2XMoleculeDensity functional theoryPhysical and Theoretical ChemistryMolecular BiologyPolyproline helixMolecular Physics
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Theozyme for antibody aldolases. Characterization of the transition-state analogueElectronic supplementary information (ESI) available: MP2/6-31G** e…

2003

A theozyme for antibody aldolases has been studied at the MP2/6-31G** computational level. Formation of two cooperative hydrogen-bonds between the acidic hydrogen atoms of the enamine and of a methanol molecule with the oxygen atom of the aldol acceptor markedly favors the C–C bond-formation associated with the aldol reaction. A comparative analysis of the geometry, the charge distribution and the shape of the molecular electrostatic potential of the transition structure (TS) with the covalent adduct, resulting from the reaction of methylamine and the β-diketone used as a hapten allows us to characterize the transition-state analogue (TSA) generated at immunization. This finding allows us t…

Aldol reactionCovalent bondStereochemistryTransition state analogChemistryOrganic ChemistryMoleculeTetrahedral molecular geometryPhysical and Theoretical ChemistryBiochemistryHaptenAcceptorAdductOrganic & Biomolecular Chemistry
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RELATIONSHIPS BETWEEN PLASMA ALDOSTERONE LEVELS AND LEFT VENTRICULAR MASS AND GEOMETRY IN ESSENTIAL HYPERTENSIVE PATIENTS: DOES SEX MATTER?

2019

Introduction: Experimental evidence suggested that aldosterone can cause myocardial hypertrophy and fibrosis. However, previous studies on the association between plasma aldosterone concentration (PAC) and left ventricular (LV) mass (LVM) and geometry, in subjects without primary aldosteronism yielded conflicting results. Aim: To evaluate the relationships of PAC with LV mass and geometry in patients with essential hypertension (EH), and to assess the influence of gender on these relationships. Methods: We enrolled 478 subjects (men: 63%; mean age 44 ± 12 years) with untreated EH. The measurements included 24-h blood pressures, plasma renin activity (PRA) and PAC, obtained by radioimmunoass…

Aldosterone - Left ventricular mass - Left ventricular geometry - Remodelling
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A descendent tropical Landau–Ginzburg potential for $\mathbb{P}^2$

2016

Algebra and Number Theory010102 general mathematicsTropical geometryGeneral Physics and AstronomyGeometry0101 mathematicsMirror symmetry01 natural sciencesDescendentMathematical PhysicsMathematical physicsMathematicsCommunications in Number Theory and Physics
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Bhabha Scattering and a special pencil of K3 surfaces

2018

We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Ap\'ery--Fermi pencil, that was related to Ap\'ery's proof of the irrationality of $\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.

Algebra and Number Theory14C22 14J28 34L25 14J81010308 nuclear & particles physicsPhysics::Medical PhysicsGeneral Physics and Astronomy01 natural sciencesApéry's constantLattice (module)Theoretical physicsMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: Mathematics010306 general physicsAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryMathematical PhysicsPencil (mathematics)Bhabha scatteringMathematics
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Rank two aCM bundles on the del Pezzo fourfold of degree 6 and its general hyperplane section

2018

International audience; In the present paper we completely classify locally free sheaves of rank 2 with vanishing intermediate cohomology modules on the image of the Segre embedding $\mathbb{P}^2$ x $\mathbb{P}^2 \subseteq \mathbb{P}^8$ and its general hyperplane sections.Such a classification extends similar already known results regarding del Pezzo varieties with Picard numbers 1 and 3 and dimension at least 3.

Algebra and Number TheoryDegree (graph theory)Image (category theory)010102 general mathematicsDimension (graph theory)MSC: Primary 14J60 ; secondary 14J45Hyperplane sectionRank (differential topology)01 natural sciencesCohomologySegre embedding[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]CombinatoricsAlgebraMathematics::Algebraic GeometryHyperplane0103 physical sciences010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsMathematics
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