Generation and fate of free radicals of Δ2-oxazolin-5-ones

The reaction of Δ² -oxazolin-5-ones 1a and 1b with nickel peroxide in benzene produces the corresponding 4,4-dehydrodimers 5a and 5b as the main products in yields over 75%. Under the same conditions, the 2-aryl -4-methyl - Δ²-oxazolin-5-ones 1c, 1d and 1e yield five products. In the case of 1c, the constituents of the product mixture were separated and identified as two 4,4-dehydrodimers ( meso and d] pair isomers) 5c and 5c', (40.7%), 2,4-dehydrodimer 6c (34.9%), acetylanisoylimide 8c (8.5%) and anisamide (15.9%). Adequate mechanistic schemes are discussed to account for the products formed.     

Observations of vacuum spark dynamics from its X-ray emission

The behavior of a medium energy (~1 kJ) pulse-power-driven vacuum spark is shown to depend on the electrode material and form of the anode in otherwise similar conditions of operation. The dynamical evolution of the discharge is followed from its soft X-ray emission. The electrode materials compared are titanium and aluminum with a form of anode that is tubular or conical. The use of a tubular anode favors a more uniform sheath and a better formation of a dense Z-pinch and the ensuing hot spots are found to be at least twice as bright. The position of the brightest spots differs according to the material and the electrode shape, and is found to coincide with the shape of the sheath. The energy output is measured and the density of the plasma in the hot spots may be calculated     

A spectrophotometric kinetic assay for acid phosphatases with aromatic phosphates

Acid phosphatases are measured by monitoring the rate of decomposition of various phenolic phosphates and/or production of the phenol at pH 4.8 (acetate buffer). All the substrates tested obey pseudo-first order kinetics; calibration plots are linear over wide ranges.     

Observations of plasma dynamics in a gas-embedded compressionalZ-pinch

A series of experiments carried out in a gas embedded compressional Z-pinch are presented. A dc micro discharge of 150 μA between two conical sharp edged electrodes is established to produce a hollow cylindrical discharge. A few nanoseconds before the application of the main voltage, a pulsed laser is focused through the anode onto the cathode. With this preionization scheme an initial coaxial current structure is established. H₂ and D₂ at a pressure of 1/3 atm were used as a working gas. The experiments have been carried out using a pulse power generator capable of delivering current of up to I~200 kA with a dI/dt>10¹² A/s. The use of H₂ and D₂ allows the study of discharges with the same electrical properties, but with different dynamics. At early times this preionization scheme produces a coaxial double column pinch, which as current rises, coalesces into a single column becoming a gas embedded compressional Z-pinch. Diagnostics used are current and voltage monitors, single frame holographic interferometry and shadowgraphy, visible streak camera, and single frame image converter camera. Electron density, line density, pinch radius, and plasma motion are obtained from the optical diagnostics. It was found that the maximum electron density achieved on axis is greater than twice the expected value according with the filling pressure used in the discharges, which contrasts with a traditional gas embedded pinch in which the density is lower than the expected value from filling pressure. The expansion rate of the plasma column is reduced to a third of the observed value for the single channel laser initiated gas embedded pinch. These measurements agree with the existence of a central current channel in this new configuration of gas embedded pinch. The experimental results clearly show that compression is achieved with the composite preionization scheme     

Quasiconformal extensions to space of Weierstrass-Enneper lifts

The Ahlfors-Weill extension of a conformal mapping of the disk is generalized to the Weierstrass-Enneper lift of a harmonic mapping of the disk to a minimal surface, producing homeomorphic and quasiconformal extensions to space. The extension is defined through the family of best Möbius approximations to the lift applied to a bundle of euclidean circles orthogonal to the disk. Extension of the planar harmonic map is also obtained subject to additional assumptions on the dilatation. The hypotheses involve bounds on a generalized Schwarzian derivative for harmonic mappings in terms of the hyperbolic metric of the disk and the Gaussian curvature of the minimal surface. Hyperbolic convexity plays a crucial role.     

An extension of a theorem of Gehring and Pommerenke

Gehring and Pommerenke have shown that if the Schwarzian derivativeSf of an analytic functionf in the unit diskD satisfies |Sf(z)|≤, 2(1 - |z|²)^–2 thenf(D) is a Jordan domain except whenf(D) is the image under a Möbius transformation of an infinite parallel strip. The condition |Sf(z)|≤ 2(1 - |z|²)^–2 is the classical sufficient condition for univalence of Nehari. In this paper we show that the same type of phenomenon established by Gehring and Pommerenke holds for a wider class of univalence criteria of the form|Sf(z)|≤p(|z|) also introduced by Nehari. These include|Sf((z)|≤π ²/2 and|Sf((z)|≤4(1-|z| ²)^–1. We also obtain results on Hölder continuity and quasiconformal extensions.     

Nehari-type families of harmonic mappings

We introduce affine and linearly invariant families of locally injective harmonic mappings of the unit disk $\mathbb{D}$. We derive sharp distortion theorems for the Jacobian that are used to establish a uniform modulus of continuity for the quasiconformal mappings in each class. Finally, we find a converse of a recent theorem of Chen and Ponnusamy characterizing when the image $f(\mathbb{D})$ under a quasiconformal harmonic univalent mapping is a John domain.