Nonlinear self-trapping of matter waves in periodic potentials

We report the first experimental observation of nonlinear self-trapping of Bose-condensed 87Rb atoms in a one-dimensional waveguide with a superimposed deep periodic potential . The trapping effect is confirmed directly by imaging the atomic spatial distribution. Increasing the nonlinearity we move the system from the diffusive regime, characterized by an expansion of the condensate, to the nonlinearity dominated self-trapping regime, where the initial expansion stops and the width remains finite. The data are in quantitative agreement with the solutions of the corresponding discrete nonlinear equation. Our results reveal that the effect of nonlinear self-trapping is of local nature, and is closely related to the macroscopic self-trapping phenomenon already predicted for double-well systems.     

Optical imaging in tissue with X-ray excited luminescent sensors

We report a high-spatial resolution imaging technique to measure optical absorption and detect chemical and physical changes on surfaces embedded in thick tissue. Developing sensors to measure chemical concentrations on implanted surfaces through tissue is an important challenge for analytical chemistry and biomedical imaging. Tissue scattering dramatically reduces the resolution of optical imaging. In contrast, X-rays provide high spatial resolution imaging through tissue but do not measure chemical concentrations. We describe a hybrid technique which uses a scanning X-ray beam to irradiate Gd(2)O(2)S scintillators and detect the resulting visible luminescence through the tissue. The amount of light collected is modulated by optical absorption in close proximity to the luminescence source. By scanning the X-ray beam, and measuring total amount of light collected, one can measure the local absorption near scintillators at a resolution limited by the width of luminescence source (i.e. the width of the X-ray excitation beam). For proof of principle, a rectangular 1.7 mm scanning X-ray beam was used to excite a single layer of 8 μm Gd(2)O(2)S particles, and detect the absorption of 5 nm thick silver island film through 10 mm of pork. Lifetime and spectroscopic measurements, as well changing the refractive index of the surroundings indicate that the silver reduces the optical signal through attenuated total internal reflection. The technique was used to image the dissolution of regions of the silver island film which were exposed to 1 mM of H(2)O(2) through 1 cm of pork tissue.     

Catalytic enantioselective oxaziridination

The first catalytic enantioselective synthesis of oxaziridines is presented. The oxidation of aryl and alkyl aldimines with m-CPBA under organocatalytic conditions using cinchona alkaloid-derived catalysts furnished optically active oxaziridines in good yields and high enantioselectivities (up to 94% ee). Mechanistic investigations indicate a stepwise enantioselective oxidation process.     

Harmonic Functions,Conjugate Harmonic Functions and the Hardy Space $$H^1$$ H 1 in the Rational Dunkl Setting

Journal of Fourier Analysis and Applications - In this work we extend the theory of the classical Hardy space $$H^1$$ to the rational Dunkl setting. Specifically, let $$\Delta $$ be the Dunkl...     

Catalytic asymmetric Henry reactions of silyl nitronates with aldehydes

A catalytic enantioselective Henry reaction of silyl nitronates with aldehydes has been developed. Different chiral Lewis acids have been tested for the reaction and it has been found that a variety of chiral copper-ligand complexes can catalyze the Henry reaction. The best yield, diastereo- and enantioselectivity of the nitroalcohols formed are obtained by the application of a copper(II)-diphenyl-bisoxazoline complex as the catalyst in the presence of tetrabutylammonium triphenylsilyldifluorosilicate (TBAT). In order to minimize the epimerization of the nitroaldol products they were converted into the corresponding Mosher esters. The reaction proceeds well for different aromatic aldehydes reacting with alkyl nitronates.     

Enantioselective Formal [4+2] Cycloadditions to 3‐Nitroindoles by Trienamine Catalysis: Synthesis of Chiral Dihydrocarbazoles

The first enantioselective formal [4+2] cycloadditions of 3‐nitroindoles are presented. By using 3‐nitroindoles in combination with an organocatalyst, chiral dihydrocarbazole scaffolds are formed in moderate to good yields (up to 87 %) and enantioselectivities (up to 97 % ee). The reaction was extended to include enantioselective [4+2] cycloadditions of 3‐nitrobenzothiophene. The reaction proceeds through a [4+2] cycloaddition/elimination cascade under mild reaction conditions. Furthermore, a diastereoselective reduction of an enantioenriched cycloadduct is presented. The mechanism of the reaction is discussed based on experimental and computational studies.