Unique continuation theorems for the\bar \partial - Operator and applications

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz ₀ of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away fromz ₀ cannot vanish to infinite order atz ₀ unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection and kernel in planar domains. Research supported by NSF Grant DMS-8922810.     

The effects of temperature and pressure on the lifetime of benzophenone emission

The variation in the lifetime of flash-excited gaseous benzophenone with pressure and temperature indicates that (1) self-quenching is a relatively inefficient process for the long-lived emission, k_sq = 9 × 10⁵ M^?1 s^?1 (estimated from solution data) at 25°C and 1.2 × 10⁷ M^?1 s^?1 at 170°C and (2) the lifetime decreases with increasing temperature as a result of photochemical and photophysical decay pathways which have significant activation energies. The importance of diffusion to the walls on lifetime measurements is discussed.     

In situ UV-visible spectroscopic measurements of kinetic parameters and active sites for catalytic oxidation of alkanes on vanadium oxides

In situ diffuse reflectance UV-visible spectroscopy was used to measure the dynamics of catalyst reduction and oxidation during propane oxidative dehydrogenation (ODH) on VOx/gamma-Al2O3. Transients in UV-visible intensity in the near-edge region were analyzed using a mechanistic model of ODH reactions. Rate constants per site for the kinetically relevant reduction step (C-H bond activation) measured using this analysis are slightly larger than those obtained from steady-state ODH rates normalized by surface V. The ratio of these values provides a measure of the fraction of the V surface sites that are active for ODH (0.6-0.7, for V surface densities of 2.3-34 V nm(-2)). This suggests that some of the V atoms are either inaccessible or inactive. Reoxidation rate constants, which cannot be obtained from steady-state analysis, are 10(3)-10(5) times larger than those for the C-H bond activation reduction step.