Search results for " Geometry"
showing 10 items of 2294 documents
Geometrically diverse anions in anion–π interactions
2011
The role of different anion geometries in anion–π interactions is discussed. The chemistry described herein is different to the interaction of spherical cations with aromatics. The influence of different geometries makes selective anion recognition more complicated than respective cation sensing. The present structural study reveals attractive interactions between pentafluorophenyl units and geometrically diverse anions (linear, trigonal planar, tetrahedral and octahedral). Due to the electrostatic nature of anion–π interactions, the anion geometry seems to be irrelevant. The size of the anion controls the relative orientation of the anion and the π system (e.g. in compounds 1–3). The dimer…
Quasihyperbolic boundary conditions and capacity: Uniform continuity of quasiconformal mappings
2005
We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.
Modeling of kinetic and static friction between an elastically bent nanowire and a flat surface
2011
Friction forces for a nanowire (NW) elastically bent on flat substrate were investigated both theoretically and experimentally. Models based on elastic beam theory were proposed considering balance of external, frictional, and elastic forces along the NW. The distributed friction force was determined for two cases: (i) the NW was uniformly dragged at its midpoint and bent by kinetic friction forces and (ii) the NW was held in a bent state by static friction forces. The first case considers a uniform distribution of kinetic friction along the NW and enables the measurement of the friction force from the elastically deformed NW profile. The second case exploits the interplay between static fr…
Weak chord-arc curves and double-dome quasisymmetric spheres
2014
Let $\Omega$ be a planar Jordan domain and $\alpha>0$. We consider double-dome-like surfaces $\Sigma(\Omega,t^{\alpha})$ over $\overline{\Omega}$ where the height of the surface over any point $x\in\overline{\Omega}$ equals $\text{dist}(x,\partial\Omega)^{\alpha}$. We identify the necessary and sufficient conditions in terms of $\Omega$ and $\alpha$ so that these surfaces are quasisymmetric to $\mathbb{S}^2$ and we show that $\Sigma(\Omega,t^{\alpha})$ is quasisymmetric to the unit sphere $\mathbb{S}^2$ if and only if it is linearly locally connected and Ahlfors $2$-regular.
Rescaling principle for isolated essential singularities of quasiregular mappings
2012
We establish a rescaling theorem for isolated essential singularities of quasiregular mappings. As a consequence we show that the class of closed manifolds receiving a quasiregular mapping from a punctured unit ball with an essential singularity at the origin is exactly the class of closed quasiregularly elliptic manifolds, that is, closed manifolds receiving a non-constant quasiregular mapping from a Euclidean space.
Spectral rigidity and invariant distributions on Anosov surfaces
2014
This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface $(M,g)$, given a smooth function $f$ on $M$ there is a distribution in the Sobolev space $H^{-1}(SM)$ that is invariant under the geodesic flow and whose projection to $M$ i…
Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere
2013
Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.
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…
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…
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…