Function spaces between BMO and critical Sobolev spaces

The function spaces Dk(Rn) are introduced and studied. The definition of these spaces is based on a regularity property for the critical Sobolev spaces Ws,p(Rn), where sp=n, obtained by J. Bourgain, H. Brezis, New estimates for the Laplacian, the div-curl, and related Hodge systems, C. R. Math. Acad. Sci. Paris 338 (7) (2004) 539-543 (see also J. Van Schaftingen, Estimates for L¹-vector fields, C. R. Math. Acad. Sci. Paris 339 (3) (2004) 181-186). The spaces Dk(Rn) contain all the critical Sobolev spaces. They are embedded in BMO(Rn), but not in VMO(Rn). Moreover, they have some extension and trace properties that BMO(Rn) does not have.     

“Surprising kinetics” or the major role of trace quantities in radical chain mechanisms

Although hydrogen abstraction from 1,1,1,2-tetrachloroethane should produce only one kind of radical, CCl₃CHCl, the presence of small amounts of trichloroethene, as impurity as well as product of reaction, induces the formation of the a priori unexpected CHCl₂CCl₂ radicals. The importance of this radical in the reaction pathways of the chlorination and the chlorine induced dehydrochlorination of CCl₃CH₂Cl, under different experimental conditions, is computed and discussed. For example, at 380 K, and for small partial pressures of chlorine (2 torr), the CHCl₂CCl₂ radicals account for more than 70% of the formation of the reaction products after only 2% reaction. The major role of trace quantities in long chain radical reactions is emphasized. © 1993 John Wiley & Sons, Inc.     

Synthesis and some chemical transformations of 3-ferrocenyl-3-phenylcyclopropene

Crystalline 3-ferrocenyl-3-phenylcyclopropene was obtained by dehydrobromination of 2-bromo-l-ferrocenyl-l-phenylcyclopropane with potassiumtert-butoxide in dimethyl sulfoxide. The compound synthesized undergoes catalytic hydrogenation to l-ferrocenyl-I-phenylcyclopropane, reacts with 1,3-diphenylisobenzofuran to give the expected product of stereospecific [4+2[-cycloaddition and 3-ferrocenylindene, and also undegoes opening of the small ring on treatment with superacids to give 3-ferrocenylindene as the major product. The data of single crystal X-ray diffraction analysis of 1-ferrocenyl-l-phenylcyclopropane and the diene adduct of 3-ferrocenyl-3-phenylcyclopropene with 1,3-diphenylisobenzofuran are given.     

The Millimeter-Wave Spectrum of 2,3-Dihydrofuran

The millimeter-wave spectrum of 2,3-dihydrofuran in the ground and five ring-puckering excited states has been measured in the frequency range 100–250 GHz. The ground and first ring-puckering excited states have been fitted to a two-state Hamiltonian including Coriolis coupling interaction. The determined energy difference of 18.684(7) cm⁻¹between these states and theaandbtype coupling parameters are consistent with the ring-puckering potential function and the previously observed dependence of the centrifugal distortion constants Δ_JK, Δ_K, and δ_K. A small ring-puckering dependence of the quartic centrifugal distortion constants Δ_Jand δ_Jhas been also observed. This dependence is well accounted for in terms of the ring-puckering potential function and the vibrational dependence of the rotational constants.     

Positive Solutions to Boundary Value Problems for Second Order Ordinary Differential Equations with Singular Nonlinearities

This paper deals with the existence of solutions to the periodic and the Sturm-Liouville boundary value problems for second order ordinary differential equations with singular nonlinearity. The results are obtained by use of some continuation theorems in the absence of a priori bounds of Capietto-Mawhin-Zanolin.     

Kinetic energy oscillations in annular regions of ultracold neutral plasmas

A study of ion equilibration in annular regions of ultracold strontium plasmas is reported. Plasmas are formed by photoionizing laser-cooled atoms with a pulsed dye laser. The experimental probe is spatially-resolved absorption spectroscopy using the ²S_1/2-²P_1/2 transition of the Sr⁺ ion. The kinetic energy of the ions is calculated from the Doppler broadening of the spectrum, and it displays clear oscillations during the first microsecond after plasma formation. The oscillations, which are a characteristic of strong coulomb coupling, are fit with a simple phenomenological model incorporating damping and density variation in the plasma.