Modulable and Highly Diastereoselective Carbometalations of Cyclopropenes

The copper‐catalyzed carbomagnesiation reaction of cyclopropenyl esters 1 leads to various substituted cyclopropanes species 3 in good yields with very high diastereoselectivities. The reaction proceeds through a syn‐chelated carbomagnesiation reaction and could be extended to various cyclopropenylmethyl ester derivatives 5 . The potential of this approach was illustrated by the preparation of two consecutive all‐carbon quaternary stereocenters. However, the carbometalation reaction needs to be performed at temperature ranging from ?35 to ?20 °C to avoid subsequent fragmentation reaction into stereodefined β,γ‐nonconjugated unsaturated esters 4 . Alternatively, the carbocupration reaction with organocopper species could also be performed to leads to configurationally stable cyclopropyl copper species 2[Cu] . Additionally, when the Lewis acid character of the copper center is decreased (i.e., RCuCNLi), the reaction proceed with an anti‐selectivity. The diastereodivergent behavior of these organometallic species is of synthetic interest, since both diastereomers syn‐ 3 and anti‐ 3 can be obtained, at will, from the same precursor cyclopropenyl esters 1 .     

Large Amplitude Torsions in Nitrotoluene Isomers Studied by Rotational Spectroscopy and Quantum Chemistry Calculations

Rotational spectra of ortho-nitrotoluene (2-NT) and para-nitrotoluene (4-NT) have been recorded at low and room temperatures using a supersonic jet Fourier Transform microwave (MW) spectrometer and a millimeter-wave frequency multiplier chain, respectively. Supported by quantum chemistry calculations, the spectral analysis of pure rotation lines in the vibrational ground state has allowed to characterise the rotational energy, the hyperfine structure due to the ¹⁴N nucleus and the internal rotation splittings arising from the methyl group. For 2-NT, an anisotropic internal rotation of coupled −CH₃ and −NO₂ torsional motions was identified by quantum chemistry calculations and discussed from the results of the MW analysis. The study of the internal rotation splittings in the spectra of three NT isomers allowed to characterise the internal rotation potentials of the methyl group and to compare them with other mono-substituted toluene derivatives in order to study the isomeric influence on the internal rotation barrier.     

Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating

A novel method for real-time polarization measurement is presented. The method is based on a space-variant wave plate that we realized as a computer-generated space-variant subwavelength dielectric grating. The Stokes parameters of the incident beam are determined by Fourier analysis of the space-variant intensity transmitted through the grating and an analyzer. We discuss the design and realization of such wave plates and demonstrate our technique with polarization measurements of both polarized and partially polarized CO(2)-laser radiation at a wavelength of 10.6 mum.     

Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings

Space-variant Pancharatnam-Berry phase optical elements based on computer-generated subwavelength gratings are presented. By continuously controlling the local orientation and period of the grating we can achieve any desired phase element. We present a theoretical analysis and experimentally demonstrate a Pancharatnam-Berry phase-based diffraction grating for laser radiation at a wavelength of 10.6microm.     

Formation of helical beams by use of Pancharatnam-Berry phase optical elements

Spiral phase elements with topological charges based on space-variant Pancharatnam-Berry phase optical elements are presented. Such elements can be achieved by use of continuous computer-generated space-variant subwavelength dielectric gratings. We present a theoretical analysis and experimentally demonstrate spiral geometrical phases for infrared radiation at a wavelength of 10.6microm .     

Comparison of electron and neutron compton scattering from entangled protons in a solid polymer

We present, for the first time, a direct comparison between electron (ECS) and neutron (NCS) Compton scattering results from protons of a solid polymer. The momentum distributions of hydrogen obtained from ECS and NCS are in excellent agreement. In both experiments, a strong "anomalous" shortfall in the scattering intensity of protons [first detected in liquid water with NCS [Phys. Rev. Lett. 79, 2839 (1997)]]] is found ranging from about 20% up to 50%, depending on the momentum transfer applied. The characteristic times of electron- and neutron-proton collisions lie in the subfemtosecond range. The presented ECS and NCS results provide further direct evidence for this striking effect, which has been ascribed to attosecond quantum entanglement of the protons.     

Magnetic-field dependence of the maximum supercurrent of La2-xCexCuO4-y interferometers: evidence for a predominant dx2-y2 superconducting order parameter

We performed a phase-sensitive test of the symmetry of the superconducting order parameter of the electron doped cuprate La(2-x)Ce(x)CuO(4-y) using a superconducting quantum interferometer with spatially distributed Josephson junctions. The studies were made on a thin film grown on a SrTiO3 tetracrystal substrate. The superconducting transition temperature was about 29 K which indicates that the sample is close to optimal doping. The magnetic field dependence of the critical current gives strong evidence for a predominant dx(2)(-y(2)) order parameter symmetry of the sample measured. It also gives upper limits for the s-wave component in a mixed order parameter of the type s+idx(2)(-y(2)).     

Computation of Almost Split Sequences with Applications to Relatively Projective and Prinjective Modules

Let be an Artin algebra, let mod be the category of finitely generated -modules, and let Amod be a contravariantly finite and extension closed subcategory. For an indecomposable and not Ext-projective module CA, we compute the almost split sequence 0ABC0 in A from the almost split sequence 0DTrCEC0 in mod. Since the computation is particularly simple if the minimal right A-approximation of DTrC is indecomposable for all indecomposable and not Ext-projective CA, we manufacture subcategories A with the desired property using orthogonal subcategories. The method of orthogonal subcategories is applied to compute almost split sequences for relatively projective and prinjective modules.     

Gluing copies of a 3-dimensional polyhedron to obtain a closed nonpositively curved pseudomanifold

Let be a smooth 3-dimensional nonpositively curved Riemannian manifold with corners, whose boundary consists of a finite number of geodesically convex nonpositively curved faces (for example, a Euclidean or hyperbolic polyhedron). We show that it is always possible to glue together finitely many copies of so as to get a nonpositively curved pseudomanifold without boundary.