Search results for " Geometry"
showing 10 items of 2294 documents
trans-4-Bromo-ONN-azoxybenzene at 100 K.
2004
The crystal structure of the alpha isomer of trans-4-bromoazoxybenzene [systematic name: trans-1-(bromophenyl)-2-phenyldiazene 2-oxide], C(12)H(9)BrN(2)O, has been determined by X-ray diffraction. The geometries of the two molecules in the asymmetric unit are slightly different and are within approximately 0.02 A for bond lengths, approximately 2 degrees for angles and approximately 3 degrees for torsion angles. The azoxy bridges in both molecules have the typical geometry observed for trans-azoxybenzenes. The crystal network contains two types of planar molecules arranged in columns. The torsion angles along the Ar-N bonds are only 7 (2) degrees, on either side of the azoxy group.
Charge density waves in NbSe3: The models and the experimental evidence
2010
a b s t r a c t Charge density wave (CDW) ordering in the prototypical low-dimensional compound NbSe3 is reconsidered. It is shown that the model with two incommensurate modulations, q1 = (0, 0.241, 0) and q2 = (0.5, 0.260, 0.5), localized on type-III and type-I bi-capped trigonal prismatic columns, does not explain details, revealed by various microscopic methods. An alternative explanation, based on the existence of modulated layered nano-domains below both CDW onset temperatures, is suggested. It accounts for the presence of the q2 modulation in the STM images recorded above the T2 CDW transition and for the absence of q2 satellites in the corresponding diffraction patterns. The long per…
Effect of Substituents on the Molecular Shapes of π-Basic Macrotricyclic Receptors
2010
Molecular recognition between receptor and substrate is optimized when these compounds show complementary shapes, sizes, and interacting moieties. A family of C3v-symmetric macrotricycles 1–4 is presented that incorporate resorcinol- and mesitylene-derived “walls” and “cap”, respectively. These compounds feature, in principle, a tetrahedral π-basic cavity. This paper reports the effect of substituents in the “walls” and the “cap” on the shapes of the macrotricycles in solution (1H NMR), the solid state (X-ray diffraction), and gas phase (calculations). Substitution of the lower position of the “walls” by Br (in 3) or MeS (in 4) has the same effect as ethyl substitution of the “cap” (in 2), …
An Enhanced Detector of Blurred and Noisy Edges
2007
Detecting edges in digital images is a tricky operation in image processing since images may contain areas with different degrees of noise, blurring and sharpness. Such operation represents an important step of the whole process of similarity shape analysis and retrieval.
Electrochemical synthesis of 2-arylimino-4,5-di(2-furyl)-1,3-dioxoles and (E)-1,2-di(2-furyl)vinylene bis(N-arylchloroformimidates). HF and B3LYP com…
2009
Abstract Cathodic reductions of 2,2′-furils in the presence of N-arylcarbonimidoyl dichlorides lead to 2-arylimino-4,5-di(2-furyl)-1,3-dioxoles in high yields, along with minor amounts of (E)-1,2-di(2-furyl)vinylene bis(N-arylchloroformimidates). HF and B3LYP density functional theory methods have been applied to the determination of molecular geometries and to study the topomerization mechanism of aryliminodioxoles. The molecular structure of (E)-1,2-di(2-furyl)vinylene bis[N-(2-chloro-4-methylphenyl)chloroformimidate] has been determined by X-ray crystallography and compared with the calculated structure.
Synthesis, X‐ray Structure, Thermal and Magnetic Behavior of [(bipy) 2 Ni 2 (μ‐Cl) 2 Cl 2 (H 2 O) 2 ]: The First Neutral Ferromagnetically Coupled Si…
2007
NiCl2·6H2O and 2,2′-bipyridine (bipy) (1:1) were allowed to react under ambient conditions in dimethyl sulfoxide in the presence of acetylacetone (Hacac). The resulting green solution was concentrated in vacuo, and a green solid was isolated by precipitation with cold acetone. X-ray quality crystals of [(bipy)2Ni2(μ-Cl)2(Cl)2(H2O)2] (1) were grown by subsequent vapor/liquid diffusion of acetonitrile into a methanolic solution for one week. The structure of 1 consists of a dimeric nickel system with each metal atom in an octahedral geometry. Both equatorial bridging and axial chlorine atoms are present in this neutral species. The nickel–nickel distance (3.441 A) is the shortest reported to …
A Weitzenböck formula for the damped Ornstein–Uhlenbeck operator in adapted differential geometry
2001
Abstract On the Riemannian path space we consider the Ornstein–Uhlenbeck operator associated to the Dirichlet form E (f,g)=E〈 ∇ f, ∇ g〉 H , where ∇ is the damped gradient and 〈·,·〉 H the scalar product of the Cameron–Martin space H . We prove a corresponding Weitzenbock formula restricted to adapted vector fileds: the Ricci-tensor is shown to be equal to the identity.
Geometry and analysis of Dirichlet forms (II)
2014
Abstract Given a regular, strongly local Dirichlet form E , under assumption that the lower bound of the Ricci curvature of Bakry–Emery, the local doubling and local Poincare inequalities are satisfied, we obtain that: (i) the intrinsic differential and distance structures of E coincide; (ii) the Cheeger energy functional Ch d E is a quadratic norm. This shows that (ii) is necessary for the Riemannian Ricci curvature defined by Ambrosio–Gigli–Savare to be bounded from below. This together with some recent results of Ambrosio–Gigli–Savare yields that the heat flow gives a gradient flow of Boltzman–Shannon entropy under the above assumptions. We also obtain an improvement on Kuwada's duality …
Evolution Problems Associated to Linear Growth Functionals: The Dirichlet Problem
2003
Let Ω be a bounded set inIR N with Lipschitz continuous boundary ∂Ω. We are interested in the problem
On the Ball-Marsden-Slemrod obstruction for bilinear control systems
2019
International audience; In this paper we present an extension to the case of $L^1$-controls of a famous result by Ball--Marsden--Slemrod on the obstruction to the controllability of bilinear control systems in infinite dimensional spaces.