Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.     

A comparative study of several HPLC methods for determining free amino acid profiles in honey

A study of the viability of three derivatizing reagents for obtaining amino acid profiles in honey through high performance liquid chromatography (HPLC) is presented. A method using diode array detection based on a reaction with diethyl ethoxymethylene malonate (DEMM) and two other methods using fluorescence detection based on derivatization with fluorenylmethyl chloroformate (FMOC-Cl) and 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC) have been developed. The three methods yield detection limits close to the ppb level, but vary in relation to other analytical characteristics. The use of methyl chloroformate derivatives allows the profile to be obtained with the greatest sensitivity within a short time frame. On applying such methods to honey samples of diverse botanical origin, we observe that the proline values obtained are always lower than those found using the official spectrophotometric method, thereby underlining the advisability of using HPLC methods to reduce uncertainty in these results.     

Analysis of citrates and benzoates used in poly(vinyl chloride) by supercritical fluid extraction and gas chromatography

Supercritical fluid extraction (SFE) has been demonstrated to be a useful tool in the determination of additives in polymeric materials. This paper describes the determination of some citrates and benzoates in poly(vinyl chloride) blended with 33–34% of plasticizer using off-line SFE followed by gas chromatography. Experimental factors affecting SFE have been studied by gravimetric analysis, followed by analysis of the extracts using a gas chromatograph equipped with a flame ionization detector. The extraction process is governed by the solubility of the plasticizers in the supercritical fluid or by their diffusion through the polymer matrix, which depend on the pressure and temperature used. Maximum extraction (>99%) is obtained at pressures and temperatures higher than 40 MPa and 80 °C, respectively. Due to purge losses, the collection efficiency of plasticizers into a liquid solvent ranges from 85 to 90%. The applicability of the SFE method is demonstrated using real samples and comparing the results with those obtained by conventional Soxhlet extraction.     

Validation of the thermodynamic model of inorganic arsenic in non polluted river waters of the Basque country (Spain)

The thermodynamic model of inorganic arsenic was validated by comparing the predicted As(III) concentration with the experimentally determined one in several river waters samples of the Basque Country (Spain) collected in two sampling campaigns: spring and autumn 2000. This model takes into account the acid-base equilibria of As(III) and As(V) together with the redox equilibria between the H₃AsO₃ and H₃AsO₄ species. A correct prediction of As(III) concentration requires the knowledge of the total concentration of arsenic, pH, redox potential (referred to hydrogen electrode), and ionic strength values of the solution. The estimation of the activity coefficients of the arsenic species was performed by means of the Modified Bromley’s Methodology (MBM).In order to perform the experimental As(III) determination, an analytical method was implemented by using an ion exchange separation of As(III)/As(V) on a continuous FIA-IE-HG-AAS system. The total arsenic concentration was determined together with total concentration of the main alkaline or alkaline-earth metals and anions in the natural waters. Temperature compensated measurements of the pH and redox potentials were made in-situ at the sampling sites.For both seasonal campaigns, the agreement between predicted and experimental As(III) is really high for those samples belonging to non polluted river waters.     

Asymmetric hetero Diels-Alder as an access to carbacephams.

A short and efficient asymmetric synthesis of the (6R,7S)-7-tert-butoxycarbonylamino-2-ketocarbacepham is described. The key step involves the hetero Diels-Alder reaction of the benzylimine derived from the enantiomer of Garner's aldehyde with Danishefsky's diene.     

Correct structures of Diels-Alder adducts from the natural cyclolignan thuriferic acid and its 8-epimer

A detailed analysis of one- and two-dimensional ¹H and ¹³C NMR data for the endo and the exo adducts, obtained by Diels-Alder reaction of thuriferic and epithuriferic acids with cyclopentadiene is described. The unequivocal spectral data assignment of the endo and exo structures was complemented with molecular modelling studies and confirmed through X-ray diffraction studies.     

Arsenic Speciation Analysis in Solutions Treated with Zeolites

Experiments have been carried out to study the behaviour of organoarsenicals treated with zeolites by means of speciation analysis. IC-ICP-MS was applied to identify and quantify arsenite, arsenate and the following organoarsenicals: monomethylarsonic acid (MMA), dimethylarsinic acid (DMA), trimethylarsine oxide (TMAO), tetramethylarsonium bromide (TMA⁺), arsenobetaine (AsB) and arsenocholine (AsC). Zeolites loaded with ferrous ions did not significantly increase the retention of inorganic arsenic species compared to the native zeolites, while there was a ten-fold removal of arsenate relating to arsenite. The formation of As(V) and DMA in the leachates containing clinoptilolites and mordenites was confirmed in the presence of natural and synthetic zeolites. Arsenobetaine and arsenocholine yielded higher levels of arsenate than the methylated species.     

Evaluation of a purge-and-trap injection system for capillary gas chromatography-microwave induced plasma-atomic emission spectrometry for the determination of volatile selenium compounds in water

A method is presented for the selective determination of the volatile selenium species dimethylselenide and dimethyldiselenide, using a commercially available purge-and-trap injection system coupled to capillary gas chromatography-microwave induced plasma-atomic emission spectrometry. The efficiency of the purging step was evaluated and the parameters affecting the purge and trap processes were optimized. The method was applied to the determination of volatile selenium compounds in lake water. Relative detection limits of 2ng/l for dimethylselenide and dimethyldiselenide, corresponding to an absolute detection limit of 10 pg, were achieved.     

Micellar solutions of sulfobetaine surfactants in water-ethylene glycol mixtures: surface tension, fluorescence, spectroscopic, conductometric, and kinetic studies

Micellization in water-ethylene glycol (EG) N-dodecyl, N-tetradecyl, and N-hexadecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (SB3-12, SB3-14, and SB3-16, respectively) micellar solutions, with the weight percent of EG changing within the range 0-40, was studied by means of surface tension measurements. Information about the influence of the added EG on the aggregation number of the sulfobetaine micelles and on the polarity of the interfacial region of micelles was obtained through fluorescence and spectroscopic measurements. Surface tension measurements also provide information about the dependence of the surface excess concentration, the minimum area per surfactant molecule, the surface pressure at the cmc, and the standard Gibbs energy of adsorption on the added weight percent of the organic solvent. The Gordon parameter of the water-EG mixtures was also estimated by means of surface tension measurements. The thermodynamic and structural changes originated by the presence of EG control the micellar kinetic effects observed in the reaction methyl 4-nitrobenzenesulfonate + Br(-) occurring in the water-EG sulfobetaine micellar solutions. Information about the distribution of bromide ions between the bulk and micellar pseudophases was obtained through conductivity measurements. The kinetic micellar effects were quantitatively explained by using the pseudophase kinetic model.     

Vascular endothelial and smooth muscle cell culture on NaOH-treated poly(epsilon-caprolactone) films: a preliminary study for vascular graft development

Tissue engineering offers the potential of providing vessels that can be used to replace diseased and damaged native blood vessels. The endothelization of a synthetic vascular graft minimizes the failures associated with blood clotting and platelet activation. The aim of this study was to culture vascular-derived endothelial and smooth muscle cells on both untreated and NaOH-treated poly(epsilon-caprolactone) (PCL) films, a biocompatible and bio-resorbable polymer, and to evaluate the behavior of both cell types as a preliminary study for vascular graft development. PCL films were prepared by hot pressing; characterized by DSC, IR, SEM, and scanning force microscopy; and treated with NaOH to increase the surface hydrophilicity before cell culture. Endothelial and smooth muscle cells, isolated from pig cava vein, were characterized by immunofluorescence and confocal microscopy studies of endothelial nitric oxide synthase and alpha-smooth muscle actin. Good adhesion, growth, viability and morphology of both the endothelial and smooth muscle cells on PCL films were obtained, but a light stimulation of mitochondrial activity was observed during short culture times. NaOH treatment improved the adhesion and enhanced the proliferation in both cell types. This verified the possible use of this modified polymer as a support in the preparation of a synthetic vascular graft. [Diagram: see text] SEM micrograph of smooth muscle cells cultured on NaOH-treated PCL film. (Original magnification: 1000x).