Aubry sets vs. Mather sets in two degrees of freedom

Let L be an autonomous Tonelli Lagrangian on a closed manifold of dimension two. We prove that for a large set of cohomology classes, the Aubry set consists of periodic orbits.     

Mañé's conjectures in codimension 1

We prove Mañé's conjectures [ 9 ] in the context of codimension 1 Aubry‐Mather theory. © 2011 Wiley Periodicals, Inc.     

Specific molecular and cellular events induced by irradiated X‐ray photoactivatable drugs raise the problem of co‐toxicities: particular consequences for anti‐cancer synchrotron therapy

Synchrotrons are capable of producing intense low‐energy X‐rays that enable the photoactivation of high‐Z elements. Photoactivation therapy (PAT) consists of loading tumors with photoactivatable drugs and thereafter irradiating them at an energy, generally close to the K‐edge of the element, that enhances the photoelectric effect. To date, three major photoactivatable elements are used in PAT: platinum (cisplatin and carboplatin), iodine (iodinated contrast agents and iododeoxyuridine) and gadolinium (motexafin gadolinium). However, the molecular and cellular events specific to PAT and the radiobiological properties of these photoactivatable drugs are still misknown. Here, it is examined how standard and synchrotron X‐rays combined with photoactivatable drugs impact on the cellular response of human endothelial cells. These findings suggest that the radiolysis products of the photoactivatable drugs may participate in the synergetic effects of PAT by increasing the severity of radiation‐induced DNA double‐strand breaks. Interestingly, subpopulation of highly damaged cells was found to be a cellular pattern specific to PAT. The data show that the efficiency of emerging anti‐cancer modalities involving synchrotron photoactivation strongly depends on the choice of photoactivatable drugs, and important series of experiments are required to secure their clinical transfer before applying to humans.     

Application of several modified peak purity assays to real complex multicomponent mixtures by high-performance liquid chromatography with diode-array detection.

Simple to use interactive self-modelling mixture analysis (SIMPLISMA), orthogonal projection (OPA) and Needle Search (NS) approaches have been applied to the determination of a number of compounds present in a complex multicomponent system. None of these three approaches succeeded completely when they were tested using the whole data matrix. When OPA and NS were applied to three simpler submatrices, obtained by dividing the total data matrix, and where a smaller number of compounds were present, better performance was achieved.     

Selection of reversed-phase liquid chromatographic columns with diverse selectivity towards the potential separation of impurities in drugs

To select appropriate stationary phases from the continuously expanding supply of potentially suitable HPLC columns, the properties of 28 frequently applied stationary phases were determined by measuring several chromatographic parameters. From these results, based on chromatographic expertise, eight stationary phases with different properties and selectivities were selected. The aim of this study is to apply chemometric tools to evaluate the initially selected set of columns, i.e. a more systematic approach for making such a selection is examined. Starting from the information obtained on the 28 stationary phases, the re-evaluation was performed independently based on the chemometric techniques Pareto-optimality, principal component analysis (PCA), and Derringer's desirability functions. The aim was to select a set of efficient columns exhibiting large selectivity differences. The chemometrically selected stationary phases were divided in groups based on hydrophobicity, a critical retention-determining property in reversed-phase chromatography. This allowed to further reducing the selection to three columns. It is demonstrated that the selection by the chemometric approaches in general is fairly comparable with the initial selection.     

Separation strategy for acidic chiral pharmaceuticals with capillary electrochromatography on polysaccharide stationary phases

The effect of five factors on the capillary electrochromatographic enantioseparation of acidic compounds was studied using an experimental design. The studied factors were pH, acetonitrile content in the mobile phase, temperature, buffer concentration, and applied voltage. These experiments allowed defining a generic separation strategy applicable on acidic compounds with chemical and structural diversity. The starting screening conditions consist of a 45 mM ammonium formate electrolyte at pH 2.9 mixed with 65% acetonitrile, an applied voltage of 15 kV, and a temperature of 25 degrees C. The screening phase occasionally can be followed by an optimization procedure. Evaluation of the proposed strategy pointed out that it allows achieving baseline resolution within a relatively short time when a beginning of separation is obtained at the starting conditions. This strategy revealed enantioselectivity for 11 compounds out of 15, of which 10 could be baseline-separated after the proposed optimization steps.     

The application of multivariate techniques to data from spanish glass-making objects from the Roman Era

Three multivariate techniques (principal components analysis, correspondence factor analysis and spectral map analsis) are applied to x-ray fluorescence data from glass-making objects from the 5th century AD found in Tarragona (Tarraco in the Roman Empire). The information obtained by displaying th eobjects and variables in each reduced factor space is compared. The presence of redundant information is shown. The visualization of groups of objects and of the relationship between objects and variables allows the formulation of hypotheses concerning the origin of the samples and the presence of local glassworks.     

Extraction of organic acids by ion-pair formation with tri-n-octylamine : Part. 1. Extraction Rate and Influence of pH and Ionic Strength

The extraction scheme for dyes, developed previously, is applied to benzoic acid and its hydroxylated derivatives. Extractions are done with tri-n-octylamine at pH 5.5 and an ionic strength of 0.1 into chloroform. Equilibrium is attained in 20 min or less. The influences of pH and ionic strength of the extraction medium on the recoveries are described. The scheme developed for dyes is applicable for benzoic acid and salicyclic acid; for more polar acids the pH and ionic strength must be changed in order to maximize the recovery.