Search results for " Geometry."

Volumes of certain small geodesic balls and almost-Hermitian geometry

1984

Let D be the characteristic connection of an almost-Hermitian manifold, V D m (r) the volume of a small geodesic ball for the connection D and C C D 1 the first non-trivial term of the Taylor expansion of V D m (r). NK-manifolds are characterized in terms of C C D 1 and a family of Hermitian manifolds for which ∫ M C C D 1 dvol is a spectral invariant is given and one proves that C C D 1 and the spectrum of the complex Laplacian, together, determine the class in which a compact Hermitian manifold lines.

On a-semiaffine planes with invisible lines

1987

Translationsstrukturen, die weder axial noch zentral sind

1979

A topological obstruction to the geodesibility of a foliation of odd dimension

1981

Let M be a compact Riemannian manifold of dimension n, and let ℱ be a smooth foliation on M. A topological obstruction is obtained, similar to results of R. Bott and J. Pasternack, to the existence of a metric on M for which ℱ is totally geodesic. In this case, necessarily that portion of the Pontryagin algebra of the subbundle ℱ must vanish in degree n if ℱ is odd-dimensional. Using the same methods simple proofs of the theorems of Bott and Pasternack are given.

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 …