Collisional parameters of H2O lines: effects of vibration

A complex semiclassical model for the calculation of line widths and shifts of H₂O broadened by N₂, derived from the Robert and Bonamy approach, is tested by comparisons with measurements for selected transitions in various vibrational bands. The lines retained, which involve rotational states with Kc=J or J−1 have been chosen for two reasons. The first is that they show large variations of the widths with J and thus enable a severe test of the model. The second is that, as explained in this paper, they are well-suited for the study of the effects of vibration on the collisional parameters. The measured values have been extracted from an updated version of a database built years ago (JQSRT 52 (1994) 481) that contains all available measurements. Comparisons between experimental and calculated widths and shifts at room temperature illustrate the quality of the model and clearly demonstrate, for the first time, that there is a vibrational dependence of the broadening. Values of collisional parameters are first studied in fundamental bands. This shows that the theoretical approach accounts for most of the dependence of broadening and shifting on rotational quantum numbers: the variations of γ, which reach a factor of nearly 20 from low to high J values, are correctly accounted for by the model as are some specific features of the shifts δ. Analysis confirms that the bending and stretching vibrations have significantly different effects on δ, due to the vibrational dependence of the intermolecular potential. On the other hand, differences on the widths are rather small with slightly smaller broadening for lines of the bending band. Calculations show that there is a spectroscopic effect, due to the larger rotational constant A in the v₂=1 state. Calculations made for overtone bands involving numerous quanta of the stretching vibration are then presented. They predict that a significant dependence of the width should be observed for high J lines due to the effect of vibration on the interaction potential. This is confirmed by comparisons with measurements for lines involving a change of three and four quanta of stretching vibration.     

Synthesis of optically active 6-substituted 2-(aminomethyl)chromans

Three novel, optically active, 6-substituted 2-(aminomethyl)chromans were synthesized from readily available chroman 2-carboxylic acid precursors. These chroman-containing primary amines are useful building blocks for the synthesis of chroman-derived pharmaceutical agents.     

Hollow latex particles as submicrometer reactors for polymerization in confined geometries

A method was developed for free‐radical polymerization in the confines of a hollow latex particle. Hollow particles were prepared via the dynamic swelling method from polystyrene seed and divinylbenzene and had hollows of 500–1000 nm. So that these hollow poly(divinylbenzene) particles could function as submicrometer reactors, the particles were filled with a monomer (N‐isopropylacrylamide) via the dispersion of the dried particles in the molten monomer. The monomer that was not contained in the hollows was removed by washing and gentle abrasion. Free‐radical polymerization was then initiated by γ radiolysis in the solid state. Transmission electron microscopy showed that poly(N‐isopropylacrylamide) formed in the hollow interior of the particles, which functioned as submicrometer reactors. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5706–5713, 2004     

PSL2(59) is a Subgroup of the Monster

A computer construction of the Monster is used to prove thatPSL(2, 59) is a subgroup of the Monster.     

Metric Embeddings—Beyond One-Dimensional Distortion

The extensive study of metric spaces and their embeddings has so far focused on embeddings that preserve pairwise distances. A very intriguing concept introduced by Feige allows us to quantify the extent to which larger structures are preserved by a given embedding. We investigate this concept, focusing on several major graph families such as paths, trees, cubes, and expanders. We find some similarities to the regular (pairwise) distortion, as well as some striking differences.     

Space time-index plots for probing dynamical nonstationarity

We propose a simple method to efficiently probe dynamical nonstationarity in observed time series. In a space time-index plot, the density distributions as a function of normalized time-index are V-shaped due to nonstationarity. We show that this method is workable for short data sets and typical examples are illustrated.     

The Jacobian and the Ginzburg-Landau energy

We study the Ginzburg-Landau functional for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional. Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001     

Directed metalation/ligand coupling approach to the enantioselective synthesis of 1,1′-binaphthyls

Introduction of a 2-isopropoxycarbonyl or 2-NN-dimethylcarbamoyl group into homochiral 1-p-tolyl- or 1-t-butyl-sulfinylnaphthalenes, via directed metalation reaction, followed by ligand coupling reaction with 1-naphthylmagnesium bromide, furnished atropisomeric 1,1′-binaphthyls in 82–95% enantiomeric excess (e.e.).