Quantitative analysis by comprehensive two-dimensional gas chromatography using interval Multi-way Partial Least Squares calibration

A new approach for target quantitative analysis for comprehensive two-dimensional gas chromatography (GC × GC), interval Multi-way Partial Least Square (iNPLS) is presented and evaluated in this paper. In iNPLS, the two-dimensional chromatogram is split in small sections; each of these pieces is treated as an independent new chromatogram. Separated conventional NPLS calibration models for the concentration of the target analyte are built for each of the pieces of the whole chromatogram, and the best model is selected for quantitative analysis. An algorithm for iNPLS running on MatLab platform was written, preliminarily evaluated with using solutions of model compounds with different chemical properties and subsequently applied to quantify some allergens in perfume samples. The results were found to be adequate, and good precision and accuracy was obtained even for poorly resolved peaks.     

The IVP for the Benjamin-Ono equation in weighted Sobolev spaces

We study the initial value problem associated to the Benjamin-Ono equation. The aim is to establish persistence properties of the solution flow in the weighted Sobolev spaces , s∈R, s?1 and s?r. We also prove some unique continuation properties of the solution flow in these spaces. In particular, these continuation principles demonstrate that our persistence properties are sharp.     

On the inertia sets of some symmetric sign patterns

A matrix whose entries consist of elements from the set {+, −, 0} is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices.     

Synthesis of single- and multi-wall carbon nanotubes over supported catalysts

The quantities of deposited carbon were measured and the quality of the nanotubes was characterized by means of transmission electron microscopy and scanning tunneling microscopy. The inner and outer diameters of the nanotubes were also measured and the diameter distribution histograms were established. The multi-wall straight and coiled nanotubes were found to be quite regular with an average inner (outer) diameter of 4–7 nm (15–25 nm) and with lengths up to 50 μm. The walls contain concentric cylindrical graphene sheets separated by the graphitic interlayer distance. The single-wall nanotubes were found as bundles of hundreds of aligned straight 1-nm-diameter nanotubes with lengths up to 1-μm. The influence of various parameters such as the method of catalyst preparation, the nature and the pore size of the support, the nature of the metal, the quantity of catalyst active particles, and the reaction conditions on the nanotubes formation were studied. The numbers and dimensions of the catalyst active particles dispersed on the support were found to be of importance in regulating the shape of the produced nanotubes. Following these results, a model of growth mechanism was suggested for the nanotubes obtained by this method. Received: 5 January 1998     

A Global Method for Relaxation

A new method for the identification of the integral representation of a class of functionals defined on (where represents the family of open subsets of Ω) is presented. Applications are derived, such as the integral representation of the relaxed energy in corresponding to a functional defined in with a discontinuous integrand with linear growth; relaxation and homogenization results in are recovered in the case where bulk and surface energies are present. (Accepted April 20, 1998)     

A study of hadronic decays of the ϒ′

We present a detailed study of the decays ?′ → π⁺π^?? and ?′ → π⁰π⁰?, where the ? decays subsequently to e⁺e^? or μ⁺μ^?. The results are obtained from a sample of 146 000 ?′ decays observed with the CUSB detector at the Cornell Electron Storage Ring. We derive branching fractions of (18.9 ± 2.6)% for ?′ → π′π^?? and (10.3 ± 2.3)% for ?′ → π⁰π⁰?, and determined partial widths for these decays. Invariant mass and angular distributions of both the π⁺π^? and π⁰π⁰ systems are presented. We also set a limit on the branching fraction for ?′ → η? of less than 0.2% at the 90% confidence level.     

A three-body scattering problem in the molecular mass limit

A three-body problem is studied that involves the scattering of a heavy particle from a bound state of a heavy and a light particle. For fairly large mass ratios we find many partial waves involved in the scattering with both elastic and inelastic resonances present. It is also found that virtually all of the breakup inelasticity is in the odd partial waves, if the heavy particles are identical bosons. The same problem is solved in the Born-Oppenheimer approximation and it is found that the effective potential between the heavy particles develops an imaginary part in the odd partial waves and thus gives a quantitative account of the three-body results including the inelasticity. The linear combination of nuclear orbitais method is applied to the same problem and is found to be inadequate.