Combined analysis by GC (RI), GC-MS and 13C NMR of the supercritical fluid extract of Abies alba twigs

Two samples (leaves and twigs) of Abies alba Miller from Corsica were extracted using supercritical CO2 and their chemical compositions were compared with those of the essential oils obtained from the same batch of plant material. In total 45 components were identified using combined analysis by GC (RI), GC-MS and 13C NMR. It was observed that the contents of monoterpenes (mainly represented by limonene, alpha-pinene and camphene) were significantly lower in the supercritical fluid extract (SFE) than in the essential oil (EO). Conversely, the proportions of sesquiterpenes were much higher in CO2 extracts than in essential oils (around 30% vs 4%). Cis-abienol, a diterpene alcohol, was identified only in SFE, and the proportions of this constituent (7.5% and 17.3%) were determined using quantitative 13C NMR since it was under estimated using the standard conditions of GC.     

Microbial transformation of marine halogenated sesquiterpenes

The sesquiterpene pacifenol is one of the main constituents of the red alga Laurencia claviformis. Earlier work on the semisynthetic derivatives of pacifenol afforded a series of halogenated sesquiterpenes. The aim of the present work was to obtain new hydroxylated derivatives of halogenated sesquiterpenes by means of microbial transformation using Aspergillus niger, Gibberella fujikuroi and Mucor plumbeus. The best results were obtained with M. plumbeus. The microbiological transformation by M. plumbeus of pacifenol, and two semisynthetic derivatives, is described. The structures of the new compounds obtained were determined by spectroscopic means.     

Novel and highly sensitive mixed-polymeric electrokinetic chromatography system for determination of contaminants and impurities of heparin samples

A mixed‐polymeric electrokinetic chromatography system has been developed for the simultaneous determination of a contaminant like oversulfated condroitin sulfate (OSCS) and impurities expressed as dermatan (Der) in heparin (Hep) samples. The EKC system consisted of 0.5% w/v polymeric β‐CD, 0.4% w/v tetronic^® 1107 and 400 mM tris‐phosphate buffer at pH 3.5. The optimized electrophoretic conditions included the use of an uncoated‐silica capillary of 50 cm of total length and 75 μm id, an applied voltage of ?7 kV, a temperature of 30°C and 200 nm UV‐detection. The highly sensitive method developed showed low values of LOD, 0.07% w/w (0.07 μg/mL) (OSCS) and 0.1% w/w (0.1 μg/mL) (Der), and values of LOQ 0.2% w/w (0.2 μg/mL) (OSCS) and 0.3% w/w (0.3 μg/mL) (Der) with a concentration level of Hep sample as low as 0.1 mg/mL. Additional parameters of validation such as specificity, linearity, accuracy, and robustness were evaluated according to international guidelines. Owing to its simplicity, high sensitivity, and reliability, the proposed method can be an advantageous alternative to the traditional methodologies for the analysis of Hep in raw material and specially in finished products because of the low amounts of Hep sample required.     

Inverse subspace problems with applications

Given a square matrix A, the inverse subspace problem is concerned with determining a closest matrix to A with a prescribed invariant subspace. When A is Hermitian, the closest matrix may be required to be Hermitian. We measure distance in the Frobenius norm and discuss applications to Krylov subspace methods for the solution of large‐scale linear systems of equations and eigenvalue problems as well as to the construction of blurring matrices. Extensions that allow the matrix A to be rectangular and applications to Lanczos bidiagonalization, as well as to the recently proposed subspace‐restricted SVD method for the solution of linear discrete ill‐posed problems, also are considered.Copyright © 2013 John Wiley & Sons, Ltd.     

An alternating extragradient method with non euclidean projections for saddle point problems

In this work we analyze a first order method especially tailored for smooth saddle point problems, based on an alternating extragradient scheme. The proposed method is based on three successive projection steps, which can be computed also with respect to non Euclidean metrics. The stepsize parameter can be adaptively computed, so that the method can be considered as a black-box algorithm for general smooth saddle point problems. We develop the global convergence analysis in the framework of non Euclidean proximal distance functions, under mild local Lipschitz conditions, proving also the \(\mathcal {O}(\frac{1}{k})\) rate of convergence on the primal–dual gap. Finally, we analyze the practical behavior of the method and its effectiveness on some applications arising from different fields.     

Support functions and integral formulas in the Lorentzian plane

In the Lorentzian plane, the support function of a closed convex curve is not a periodic one. We redefine this concept and the envelope of a families of lines. Using these, we prove integral formulas in the Crofton's style for convex sets in the Lorentzian plane. Received 10 February 2000.