An asymptotic finite element method for improvement of solutions of boundary layer problems

Summary A scheme that uses singular perturbation theory to improve the performance of existing finite element methods is presented. The proposed scheme improves the error bounds of the standard Galerkin finite element scheme by a factor of O(ⁿ⁺¹) (where is the small parameter andn is the order of the asymptotic approximation). Numerical results for linear second order O.D.E.'s are given and are compared with several other schemes.     

Retention of Cr(III) by high-performance chelation ion chromatography interfaced to inductively-coupled plasma mass spectrometric detection with collision cell

High-performance chelation ion chromatography (HPCIC) was employed to retain cationic Cr(III) on an anion-exchange column and hence allow the separation of the two most prevalent forms of chromium, Cr(II) and Cr(VI). A mobile phase of nitric acid was utilized at pH = 1.5; additionally, 2,6-pyridinedicarboxylic acid was used at a concentration of 6 mM. Additives with different structural characteristics were used in an effort to elucidate retention mechanisms. Inductively-coupled plasma mass spectrometry was used for chromium detection. A collision cell was utilized to reduce chloride-based polyatomic ions that may interfere with the detection of Cr(III), and a detection limit study yielded levels in the low part-per-billion range. The newly developed method was applied to the chromatographic analysis of samples of an incubation medium containing Cr(VI) incubated with cell nuclei.     

A convenient and inexpensive conversion of an aziridine to an oxazolidinone

The conversion of an aziridine to the corresponding oxazolidinone using only carbon dioxide and a catalytic amount of lithium iodide is discussed. In all cases, either no reaction occurred or a high yield of product was obtained. HMPA has been added to the reaction mixture, as needed, to drastically improve the regioselectivity. Net retention of stereochemistry between the starting aziridine and the product oxazolidinone was observed.     

Direct HPLC resolution of beta-aminoalcohol (tazifylline,ranolazine, sotalol) enantiomers

Summary A routine chiral analysis has been developed to control the optical purity of chiral drugs and to monitor their asymmetric synthesis. The recent advent of new chiral stationary phases for HPLC enabled us to achieve the direct resolution of chiral drugs without any derivatization. The factors affecting chiral resolution on a new alpha₁-acid glycoprotein column (EnantioPac, LKB) were assessed with three beta-aminoalcohols.     

Polarization-mixing optical parametric oscillator

We report the experimental realization of a new type of optical parametric oscillator in which oscillation is achieved by polarization rotation in a linear retarder, followed by nonlinear polarization mixing. The mixing is performed by a type II degenerate parametric downconversion in a periodically poled KTP crystal pumped by a 1064 nm pulsed Nd:YAG pump. A single, linearly polarized beam, precisely at the degenerate wavelength is generated. The output spectrum has a narrow linewidth (below the instrumentation bandwidth of 1 nm) and is highly stable with respect to variations in the crystal temperature.     

Reactions in water: alkyl nitrile coupling reactions using Fenton's reagent

The coupling reaction of water-soluble alkyl nitriles using Fenton's reagent (Fe(II) and H2O2) is described. The best metal for the reaction is iron(II), and the greatest yields are obtained when the concentration of the metal is kept low. Hydrogen-atom abstraction is selective, preferentially producing the radical alpha to the nitrile. In order to increase the production of dinitrile, in situ reduction of iron(III) to iron(II), using a variety of reducing agents, was investigated.     

The reactivity of a nucleophilic nickel acylate complex

The reactivity of a nucleophilic nickel acylate complex with a tungsten carbene complex, Fe(CO)₅, Cr(CO)₆, PPh₃, and CO was investigated. With the tungsten carbene complex, a methyl transfer occurred. With the metal carbonyl complexes, the acylate group on the nickel and a carbonyl on the iron or chromium traded places. With the PPh₃ and CO, the acylate anion was replaced by the phosphine or CO ligand.     

The effect of water on the physicochemical and mechanical properties of gelatin

Strips of gelatin have been prepared by extrusion at different water contents varying from 20 to 50% H₂O (dry weight basis, d.w.b.). The processes of subsequent hydration or dehydration of these strips were followed by dynamic mechanical thermal analysis (DMTA), wide-angle X-ray diffraction and NMR relaxation measurements. A comparison of the calculated dependence of theT _g of gelatin (T _g anhydrous, 200?C) on water content (using the Ten Brinke and Karasz equation) with experimental results derived from DMTA showed that freshly extruded material followed the theoretical plot below 25% H₂O (d.w.b.), but at higher water contents, the7 _g deviated positively, probably due in part to the effect of delayed re-equilibration of water content after thawing of separated ice crystals. The experimental results determined after storage for one week fell on a different line, with aT _g of 145?C for anhydrous gelatin Possibly, theT _g is elevated by crystallization — a view supported by the WAXS spectra. The NMR relaxation results also showed a profound mobilization of the gelatin protons at water contents greater than 25% d.w.b.     

Intermediate subfactors with no extra structure

If are type II factors with and we show that restrictions on the standard invariants of the elementary inclusions , , and imply drastic restrictions on the indices and angles between the subfactors. In particular we show that if these standard invariants are trivial and the conditional expectations onto and do not commute, then is or . In the former case is the fixed point algebra for an outer action of on and the angle is , and in the latter case the angle is and an example may be found in the GHJ subfactor family. The techniques of proof rely heavily on planar algebras.