Multivariate design

In multivariate data analysis such as principal components analysis (PCA) and projections to latent structures (PLS), it is essential that the training set systems (objects) are selected to provide data with substantial information for model parametrization, and to represent properly any future situations where the multilvariate model is used for predictions. In the framework of multivariate projections (PCA, SIMCA and PLS), elementary concepts of statistical design (fractional factorials and composite designs) can be used with the latent variables (PC or PLS scores) as design variables. The plan of action thus becomes: (1) problem formulation (specify aim and model, make a conceptual division of the investigated system into subsystems); (2) collection of multivariate data for each type of subsystems; (3) estimation of the practical dimensionality of the data for each type of subsystems by PC or PLS analysis; (4) use of the PC or PLS scores (t) as design variables in the combination of subsystems to systems in the training set; (5) measurement of responses (Y); (6) analysis of data by PCA or PLS; (7) interpretation of results with possible feedback to steps 1, 2 or 3. The procedures are illustrated by two problems: a structure/activity relationship for a family of peptides, and optimization of an organic synthesis with respect to system variables (solvent, substrate, co-reactant_) and process variables (temperature, reactant concentrations).     

Pd-catalyzed intramolecular direct arylations at high temperature

Pd-catalyzed cyclodehydrohalogenation involving oxidative addition of aromatic C-Br or activated azaheteroaromatic C-Cl bonds and C(sp²)-H activation have been investigated at high reaction temperatures (180-200 °C). This allowed the fast (10-30 min) synthesis of a variety of azaheteroaromatic ring systems (dibenzo[f,h]phthalazine, dibenzo[f,h]cinnoline, benzofuro[2,3-d]pyridazine, 5H-pyridazino[4,5-b]indole, 7H-indolo[2,3-c]quinoline and 5H-δ-carboline) in moderate to good yields.     

Unexpected reactions associated with the xanthate‐mediated polymerization of N‐vinylpyrrolidone

The monomer N‐vinylpyrrolidone (NVP) undergoes side reactions in the presence of R group functional xanthates and impurities. The fate of the monomer NVP and a selection of six O‐ethyl xanthates during xanthate‐mediated polymerization were studied via NMR spectroscopy. A high number of by‐products were identified. Significant side reactions affecting NVP include the formation of an unsaturated dimer and hydration products in bulk or in solution in C₆D₆. In addition, the xanthate adjacent to a NVP unit was found to undergo elimination at moderate temperature (60–70 °C), resulting in unsaturated species and the formation of new xanthate species. The presence of the chlorinated compound α‐chlorophenyl acetic acid, ethyl ester, a precursor in the synthesis of the xanthate S‐(2‐ethyl phenylacetate) O‐ethyl xanthate, resulted in a dramatic increase in the rate of side reactions such as unsaturated dimer formation and a high ratio of unsaturated chain ends. The conditions for the occurrence of such side reactions are discussed in this article, with relevance to increasing the control over the polymerization kinetics, endgroup functionality, and control over the molar mass distribution. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6575–6593, 2008     

Localization of intracular and intraorbital foreign bodies by means of A-scan ultrasonography.

This paper discusses the use of ultrasonography in ophthalmology for foreign body localization and detection. The problems and advantages of using A-scann methods to verify and improve upon x-ray diagnosis are considered.     

Asymptotic regularity of solutions to Hartree–Fock equations with Coulomb potential

We study the asymptotic regularity of solutions to Hartree–Fock (HF) equations for Coulomb systems. To deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo‐differential operators on conical manifolds. First, the non‐self‐consistent‐field case is considered, which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator, which guarantee ellipticity for the local part of the Fock operator on the open stretched cone ?₊ × S². This proves the existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed‐point approach based on Cancès and Le Bris analysis of the level‐shifting algorithm, we show via another bootstrap argument that the corresponding self‐consistent‐field solutions to the HF equation have the same type of asymptotic regularity. Copyright © 2008 John Wiley & Sons, Ltd.