Existence of solutions to projected differential equations in Hilbert spaces

We prove existence and uniqueness of integral curves to the (discontinuous) vector field that results when a Lipschitz continuous vector field on a Hilbert space of any dimension is projected on a non-empty, closed and convex subset.

     

An X-ray fluorescence method for gold determination in ore samples

A new method for gold determination in ore is presented. By the method called PREFIX (preconcentration and X-ray fluorescence), it is possible to detect trace concentrations of gold down to the level of 0.2 g/g, without any device.     

A stereoselective and atom-efficient approach to multifunctionalized five- and six-membered rings via a novel michael-initiated intramolecular Diels-Alder furan reaction

[reaction: see text] A variety of key precursors to the intramolecular Diels-Alder reaction of furan diene (IMDAF) have been prepared via a very facile 1,4-addition of O-, S-, N-, and C-centered nucleophiles possessing unsaturated tether to beta-furyl nitroethylene. Subsequent IMDAF reaction of the 1,4-adducts, carried out under thermal conditions, provided five- and six-membered carbocycles and heterocycles fused to an easily cleavable oxabicycloheptene moiety. The structure and stereochemistry of the cycloadducts were determined by 2D-NMR experiments and further confirmed by X-ray crystallography. The salient features of the strategy include high degree of stereoselectivity (>80:20) in the cycloaddition, atom and step economy, and generation of multiple chiral centers and functionalities. The feasibility of the cleavage of the oxa bridge in the cycloadducts to afford novel multifunctional molecules has also been demonstrated.     

α-Hydroxymethylation of conjugated nitroalkenes via the Morita-Baylis-Hillman reaction

The Morita-Baylis-Hillman reaction (MBHR) of conjugated nitroalkenes has been successfully carried out for the first time. A variety of aromatic and heteroaromatic nitroalkenes react with formaldehyde at room temperature in the presence of stoichiometric amounts of imidazole and catalytic amounts of anthranilic acid in THF providing moderate to good yields of the multifunctional adducts in most of the cases.     

Simultaneous Impact of a Two-Link Chain

The study of the planar collisions of a rigid two-link chain with an external surface is presented. There are two points of contact during the impact process with friction, one for each link. For the normal impact, a nonlinear collision force is employed for the elasto-plastic deformation, and the Coulomb’s law models the frictional effects. The impact of the chain is studied numerically, and the results are compared with experiment data obtained from a high-speed camera. Special attention is given to simultaneous impact, slippage, and rebounds at the contact points.     

A possible non-specific carrier for gold analysis in rocks

It is demonstrated that lanthanum can be used as a carrier for trace amounts of gold. The theoretical motivation is discussed.     

GISAXS study of carbon nanotubes grown by CVD

We report a quantitative Grazing Incidence Small Angle X‐ray Scattering (GISAXS) study of a dense film of mutually oriented carbon nanotubes (CNTs) grown by a catalytically‐activated DC HF CCVD process after dispersion of metallic catalytic (Co) islands on SiO₂/Si(100) substrates. The GISAXS pattern analysis is expanded to non‐correlated surface science systems and is based on CNTs density, characteristic lengths, atomic Co dispersion throughout the CNTs and roughnesses of uncorrelated particles. The results are closely compared to SEM and TEM observations. The GISAXS patterns, even dominated by envelope features of disordered objects, provide significant complementary quantitative data about CNTs films. The results underline that cobalt continuously fills the nanotube in the course of the growth and that the CNTs experience a large tendency toward mutual alignment. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aligned carbon nanotubes catalytically grown on iron-based nanoparticles obtained by laser-induced CVD

Iron-based nanoparticles are prepared by a laser-induced chemical vapor deposition (CVD) process. They are characterized as body-centered Fe and Fe₂O₃ (maghemite/magnetite) particles with sizes ≤5 and 10 nm, respectively. The Fe particles are embedded in a protective carbon matrix. Both kind of particles are dispersed by spin-coating on SiO₂/Si(1 0 0) flat substrates. They are used as catalyst to grow carbon nanotubes by a plasma- and filaments-assisted catalytic CVD process (PE-HF-CCVD). Vertically oriented and thin carbon nanotubes (CNTs) were grown with few differences between the two samples, except the diameter in relation to the initial size of the iron particles, and the density. The electron field emission of these samples exhibit quite interesting behavior with a low turn-on voltage at around 1 V/μm.     

A formal [3+2] cycloaddition for the synthesis of bicyclo[3.2.1]octanes

A new and a direct synthetic method for the construction of the bicyclo[3.2.1]octane system is envisioned by assembling cyclic allylsilanes with electron-deficient double bonds in a single step via a formal diastereoselective Lewis acid-promoted [3+2] cycloaddition.     

FIR spectroscopy of ethyl bromide and trioxane: New laser transitions and assignments

Eight new optically pumped far infrared laser transitions from ethyl bromide and 22 from trioxane are presented. For each new line we give the wavelength, the polarization relative to that of the pump laser and the absorption offset relative to the CO₂ center frequency. The assignment of the rotovibrational states for the pump and the emission transitions of ethyl bromide are calculated. We also partly assigned the rotational levels of trioxane.