Are there more than five linearly-independent collision invariants for the Boltzmann equation?

The problem of finding the summational collision invariants for the Boltzmann equation is tackled with the aim of proving that the most general solution of the problem is not different from the standard one even when the equation defining a collision invariant is only satisfied almost everywhere inR ³×R ³×S ². The collision invariant is assumed to be in the Hilbert spaceH of the functions which are square integrable with respect to a Maxwellian weight.     

Oscillatory Perturbations of Linear Problems at Resonance

This paper is concerned with a study of bounded perturbations of resonant linear problems. It follows from our results that for certain types of bounded domains Ω ? Rⁿ, n ≥ 2, the Dirichlet problem $\matrix{\Delta u+\lambda_{1}u+g(u)=h(x),\ \ \ x\in\Omega\cr \quad\quad\quad\quad\quad\quad u=0,\ \ \ x\in\partial\Omega,}$ has infinitely many positive solutions, in case λ₁ is the principal eigenvalue of ?Δ subject to trivial Dirichlet boundary conditions, g is a nontrivial periodic nonlinearity of zero mean and ∫_03A9h(x)?(x)dx = 0, where ? is an eigenfunction corresponding to λ₁.     

Gas chromatographic/mass spectrometric determination of vinyl acetate levels in air

The determination of vinyl acetate at parts per 10⁹ by volume (ppbv) levels in air by gas chromatography/mass spectrometry (GC/MS) was achieved by optimizing the GC conditions and choosing specific extraction solvents that are sufficiently pure. The ideal solvent should not give rise to fragment ions at m/z 43, in order to rule out any possible interference during the monitoring of the same vinyl acetate ion. Traces of acetone and butan-2-one in solvents suitable for this GC/MS determination may also mislead the detection of vinyl acetate. A 440 μl volume of a mixture of tetrachloroethylene containing 9% acetonitrile allowed the recovery of more than 90% of the ester with a detection limit of 1.5 ppbv in air together with a good linearity of response.     

Simulation of aerated lagoon using artificial neural networks and multivariate regression techniques

The aim of this study was to develop an empirical model that provides accurate predictions of the biochemical oxygen demand of the output stream from the aerated lagoon at International Paper of Brazil, one of the major pulp and paper plants in Brazil. Predictive models were calculated from functional link neural networks (FLNNs), multiple linear regression, principal components regression, and partial least-squares regression (PLSR). Improvement in FLNN modeling capability was observed when the data were preprocessed using the PLSR technique. PLSR also proved to be a powerful linear regression technique for this problem, which presents operational data limitations.     

Banana-shaped molecules peculiarly oriented in a magnetic field: (2)H NMR spectroscopy and quantum mechanical calculations.

The orientational properties of the banana-shaped liquid crystal 4-chloro-1,3-phenylenebis{4-[4'-(10-undecenyloxy)]benzoyloxy} benzoate (ClPbis11BB) are reported in the nematic phase under the effect of an external magnetic field. A new hypothesis, which states that the central ring of the aromatic core is oriented perpendicularly to the external magnetic field, is proposed. In support of this hypothesis, a series of studies based on (2)H NMR spectroscopy, both in the bulk and in solution, are discussed. (2)H NMR measurements on three selectively deuterium-labelled isotopomers are presented, together with DFT results from B3LYP/cc-pvDz calculations performed on the aromatic core. The rather flat shape of the investigated intramolecular energy surface allows for several different conformations to be populated, the computed magnetic susceptibilities of which are consistent with the proposed hypothesis of peculiar orientation of banana-shaped molecules. Moreover, the orientation of the magnetic susceptibility tensor is shown to be strongly dependent on the internal conformation of the banana-shaped molecules.     

Complexation of the Non-steroidal Anti-inflammatory Drug Nabumetone with Modified and Unmodified Cyclodextrins

The inclusion of the anti-inflammatory drug, Nabumetone, in -, - and hydroxypropyl--cyclodextrin (CDs) is studied using UV-VIS absorption and steady-state fluorescence emission. Binding constants and thermodynamic parameters of complex formation are determined by spectrofluorimetry. The inclusion phenomena of Nabumetone with the three cyclodextrins is compared with that of the well known similar anti-inflammatory drug Naproxen. In the case of Nabumetone pronounced differences are observed in the complexation process with each cyclodextrin whereas the respective Naproxen complexes are nearly identical. ¹H-NMR experiments show that the inclusion process in Nabumetone can occur either through the substituents in the -2 (butanone) or -6 (methoxy) positions in the naphthalene ring.