On the structures of alpha-lithiated sulfoxide,sulfone and sulfonium systems. Implications for the stereochemistry of functionalization of carbon atoms adjacent to sulfur

The fully optimized geometries of C-S torsional isomers of LiCH₂SHO, LiCH₂SHO₂, and LiCH₂SH₂⁺ have been computed at the 3–21G^* level. The global minima of the sulfoxide and sulfone contain intramolecular LiO bonds. In the presence of Li⁺, intermolecular LiO bonding alters the structure of the alpha-lithiated sulfoxide, and the CLi bond is antiperiplanar to oxygen. The alpha-lithiated sulfonium cation exhibits no unusual conformational features, and a low barrier to CS torsion. The implications of these results upon the stereochemistry of functionalization of a carbon atom adjacent to sulfur by a lithiation-quenching sequence are discussed.     

How do clarinet players adjust the resonances of their vocal tracts for different playing effects?

In a simple model, the reed of the clarinet is mechanically loaded by the series combination of the acoustical impedances of the instrument itself and of the player's airway. Here we measure the complex impedance spectrum of players' airways using an impedance head adapted to fit inside a clarinet mouthpiece. A direct current shunt with high acoustical resistance allows players to blow normally, so the players can simulate the tract condition under playing conditions. The reproducibility of the results suggest that the players' "muscle memory" is reliable for this task. Most players use a single, highly stable vocal tract configuration over most of the playing range, except for the altissimo register. However, this "normal" configuration varies substantially among musicians. All musicians change the configuration, often drastically for "special effects" such as glissandi and slurs: the tongue is lowered and the impedance magnitude reduced when the player intends to lower the pitch or to slur downwards, and vice versa.     

Phase diagrams of lyotropic cholesteric fluids

Experimental investigations of lyotropic cholesterics fluids are presented which show that changes in the shape anisotropy and chirality of the micellar population determine the topology of the temperature-concentration phase diagrams. For given amounts of the substances which induce the chirality and modify the shape anisotropy of the micelles, two distinct biaxial cholesteric phases are disclosed in the phase diagrams. This is interpreted in the framework of the catastrophe theory of phase transitions.     

Observation of Scholte-like waves on the liquid-loaded surfaces of periodic structures

The observation of Scholte-like ultrasonic waves travelling along the water-loaded surfaces of solids with periodically varying properties is reported. Results are presented for two 2D superlattices that intersect the surface normally: a laminated solid of alternating 0.5 mm thick layers of aluminium and a polymer, and a hexagonal array of polymer rods of lattice spacing 1 mm in an aluminium matrix. The surface waves are generated and detected by line-focus acoustic lenses aligned parallel to each other, and separated by varying distances. For homogeneous solids, phase matching constraints do not allow the Scholte wave to be coupled into with an experimental configuration of this type, and this is demonstrated with results on a uni-directional carbon-fibre/epoxy composite. These constraints are relaxed for a periodic solid, where coupling takes place through Umklapp processes. In our experiments, the source pulse is fairly broadband, extending up to about 6 MHz, whereas the spectrum of the observed Scholte arrival is peaked at around 4 MHz. We attribute this to a resonance in the surface response of the solid associated with the superlattice structure. On rotating the solid about its surface normal, the Scholte wave displays a characteristic variation in phase arrival time and, to a lesser extent, also group arrival time. This variation is well accounted for with a model that incorporates Umklapp processes in the solid's surface response.     

Continuity properties of decomposable probability measures on euclidean spaces

It is shown that every full e^A decomposable probability measure on R^k, where A is a linear operator all of whose eigenvalues have negative real part, is either absolutely continuous with respect to Lebesgue measure or continuous singular with respect to Lebesgue measure. This result is used to characterize the continuity properties of random variables that are limits of solutions of certain stochastic difference equations.     

Optimal iterative processes for root-finding

Letf ₀(x) be a function of one variable with a simple zero atr ₀. An iteration scheme is said to be locally convergent if, for some initial approximationsx ₁, ...,x _s nearr ₀ and all functionsf which are sufficiently close (in a certain sense) tof ₀, the scheme generates a sequence {x _k} which lies nearr ₀ and converges to a zeror off. The order of convergence of the scheme is the infimum of the order of convergence of {x _k} for all such functionsf. We study iteration schemes which are locally convergent and use only evaluations off,f, ...,f ^[d] atx ₁, ...,x _k–1 to determinex _k, and we show that no such scheme has order greater thand+2. This bound is the best possible, for it is attained by certain schemes based on polynomial interpolation.This work was supported (in part) by the Office of Naval Research under contract numbers N0014-69-C-0023 and N0014-71-C-0112.     

Measurement of the nuclear spin diffusion barrier around Eu2+ ions in CaF2

The NMR spectrum of discrete ¹⁹F nuclear spins surrounding paramagnetic Eu²⁺ impurities in CaF₂ is observed at 1.6 K by high-sensitivity NMR. All but the very nearest nuclei are found to have an appreciable thermal contact with the bulk nuclei. A microscopic analysis of the electron-nuclear and nuclear-nuclear spin coupling mechanisms gives results in accord with this observation.