Uniqueness of analytic continuation: Necessary and sufficient conditions

Necessary and sufficient conditions for uniqueness of analytic continuation are investigated for a system of m ? 1 first-order linear homogeneous partial differential equations in one unknown, with complex-valued $\text{b}$^∞ coefficients, in some connected open subset of $\text{R}$^k, k ? 2. The type of system considered is one for which there exists a real k-dimensional, $\text{b}$^∞, connected C-R submanifold M^k of $\text{C}$ⁿ, for k, n ? 2, such that the system may be identified with the induced Cauchy-Riemann operators on M^k. The question of uniqueness of analytic continuation for a system of partial differential equations is thus transformed to the question of uniqueness of analytic continuation for C-R functions on the manifold M^k ? Cⁿ. Under the assumption that the Levi algebra of M^k has constant dimension, it is shown that if the excess dimension of this algebra is maximal at every point, then M^k has the property of uniqueness of analytic continuation for its C-R functions. Conversely, under certain mild conditions, it is shown that if M^k has the property of uniqueness of analytic continuation for all $\text{b}$^∞ C-R functions, and if the Levi algebra has constant dimension on all of M^k, then the excess dimension must be maximal at every point of M^k.     

Infrared radiative transfer in planetary atmospheres—I. Effects of computational and spectroscopic economies on thermal heating/cooling rates

The availability of accurate spectroscopic data and improved knowledge of continuum absorption characteristics has required a further detailed study of i.r. radiative transfer. A sophisticated radiative transfer scheme based upon the Mayer-Goody random band model is developed and the derived transmissivities for H₂O, CO₂ and O₃ are calibrated against laboratory measurements. This calibrated scheme is used to assess the effects on calculated heating/cooling rate profiles of introducing computational and spectroscopic economies.     

A journey through quality control

The Euroanalysis VII conference in Vienna included a two-day session: Quality Assurance in Analytical Chemistry. The contributions comprised 15 lectures devoted to: intra-laboratory quality measures, inter-laboratory control, formal aspects and accreditation and implementation. The paper presents an overview of the main items developed by the contributors.A survey on the session on Quality Assurance in Analytical Chemistry of Euroanalysis VIIThe authors thank the organizers of EUROANALYSIS VII and in particular Dr. B. Griepink and Dr. E. Maier of the Community Bureau of Reference (BCR) of the CEC for their support and considerable contributions.     

Line assignments and intensities of the ν2 + ν3 − ν2 band of 12CH4

As part of a comprehensive effort to compile line parameters of methane from 2400 to 3200 cm^?1, the P and R branches of the ν₂ + ν₃ ? ν₂ band of CH₄ at 3010 cm^?1 were assigned through upper state J = 9. The process utilized the analysis of ν₂ + ν₃ at 4544 cm^?1 by J. C. Hilico, J. Degni, J. P. Champion, and G. Guelachvili (J. Mol. Spectrosc.81, 277–302 (1980)) and the ν₂ levels derived from the infrared spectrum by Margolis (in preparation) to predict the positions of the hot band. Experimentally determined lower-state energies were used to confirm assignments, and line intensities of the 300 transitions assigned are observed on the order of 10^?3 cm^?2 atm^?1 or less.     

Line intensities of Co2 in the 2.0 micron region

The line intensities of the three δ-δ bands of CO₂ and their associated Π-Π hot bands in the 2.0 υ region have been measured using a combination of long optical paths and low sample pressures with high resolution (0.035 cm^-1). These intensities yield total band strengths of 0.200, 0.969, 0.288, 0.0017, 0.062 and 0.028 cm^-2 atm^-1 at 296 K for the 04⁰1-00⁰0, 12⁰1-00⁰0, 20⁰1-00⁰, 05¹1-01¹0, 13¹1-01¹0 and 21¹1-01 ¹0 bands, respectively. The rotationless dipole moment matrix element and the German-Wallis coefficients are also determined for each band.     

Ultrafast dynamics in the dispersed phase of oil-in-water microemulsions: monosubstituted benzenes incorporated into dodecyltrimethylammonium bromide (DTAB) aqueous micelles

Time-resolved optical Kerr effect spectroscopy has been used to probe the molecular environment afforded by the hydrophobic core of oil-in-water microemulsions. This was achieved by measuring the ultrafast dynamics of a series of benzene derivatives (benzonitrile, nitrobenzene, fluorobenzene, styrene, and toluene) incorporated as the oil phase within oil-in-water microemulsions and comparing them to the dynamics in neat liquid and the liquid diluted in nonpolar solvent. Polar and strongly interacting liquids (benzonitrile and nitrobenzene) showed dynamics in the microemulsion that are similar to those in the solution phase, while weakly interacting and mildly polar liquids (fluorobenzene, styrene and toluene) reveal dynamics more similar to those of the neat liquid. This suggests stabilization of the polar dispersed phase in polar regions of the micelle.     

Delicious not siliceous: expanded carbohydrates as renewable separation media for column chromatography

Expansion of native corn starch produces a high surface area mesoporous material capable of acting as a novel stationary phase for separating various mixtures of compounds.