Direct and iterative solution of the generalized Dirichlet–Neumann map for elliptic PDEs on square domains

In this work we derive the structural properties of the Collocation coefficient matrix associated with the Dirichlet–Neumann map for Laplace’s equation on a square domain. The analysis is independent of the choice of basis functions and includes the case involving the same type of boundary conditions on all sides, as well as the case where different boundary conditions are used on each side of the square domain. Taking advantage of said properties, we present efficient implementations of direct factorization and iterative methods, including classical SOR-type and Krylov subspace (Bi-CGSTAB and GMRES) methods appropriately preconditioned, for both Sine and Chebyshev basis functions. Numerical experimentation, to verify our results, is also included.     

Study of fossil bones by synchrotron radiation micro‐spectroscopic techniques and scanning electron microscopy

Earlymost Villafranchian fossil bones of an artiodactyl and a perissodactyl from the Milia excavation site in Grevena, Greece, were studied in order to evaluate diagenetic effects. Optical microscopy revealed the different bone types (fibro‐lamellar and Haversian, respectively) of the two fragments and their good preservation state. The spatial distribution of bone apatite and soil‐originating elements was studied using micro‐X‐ray fluorescence (µ‐XRF) mapping and scanning electron microscopy. The approximate value of the Ca/P ratio was 2.2, as determined from scanning electron microscopy measurements. Bacterial boring was detected close to the periosteal region and Fe bearing oxides were found to fill bone cavities, e.g. Haversian canals and osteocyte lacunae. In the perissodactyl bone considerable amounts of Mn were detected close to cracks (the Mn/Fe weight ratio takes values up to 3.5). Goethite and pyrite were detected in both samples by means of metallographic microscopy. The local Ca/P ratio determined with µ‐XRF varied significantly in metal‐poor spots indicating spatial inhomogeneities in the ionic substitutions. XRF line scans that span the bone cross sections revealed that Fe and Mn contaminate the bones from both the periosteum and medullar cavity and aggregate around local maxima. The formation of goethite, irrespective of the local Fe concentration, was verified by the Fe K‐edge X‐ray absorption fine structure (XAFS) spectra. Finally, Sr K‐edge extended XAFS (EXAFS) revealed that Sr substitutes for Ca in bone apatite without obvious preference to the Ca₁ or Ca₂ unit‐cell site occupation.     

On integral representation and the Choquet boundary for convolution algebras of measures

We show that the Choquet boundary of a convolution algebra of measures is contained in the set of generalized characters of idempotent modulus. We then give a number of sufficient conditions for Choquet boundary points and determine the Choquet boundary for some examples, including the examples of Hewitt-Kakutani and Simon. Finally we state and prove a theorem of Bochner's type forL-algebras generated by a single measure.     

Organic residue analysis of Neolithic pottery from North Greece

Organic residues associated with Neolithic pottery from two Late Neolithic sites, Paliambela and Makriyalos (Northern Greece), were analyzed by gas chromatography-mass spectrometry. The study aimed at identifying the origin of the tar used for waterproofing and gluing broken pots. Reference tars were prepared in laboratory conditions by pyrolysis of the bark from three tree species, namely from Betula pendula (silver birch), Ostrya carpinifolia (hop hornbeam) and Carpinus orientalis (Eastern hornbeam). The results suggest that mostly birch bark tar was used as glue for fixing broken pieces of the pots as well as for waterproofing close-shaped vessels. None of the archaeological tars derived from the two hornbeams. The analysis shows certain variability in the composition of birch bark tar, which is related to the production technique and to the re-use of tar. Of particular interest is the presence of characteristic diterpenoid biomarkers in several samples, which indicates that pine pitch was used for gluing and pine resin for waterproofing vessels for liquids. Correspondence: Sophia Mitkidou, Department of Science, School of Technological Applications, Technological Institute of Kavala, Greece     

Circulatory bubble dynamics: From physical to biological aspects

Bubbles can form in the body during or after decompression from pressure exposures such as those undergone by scuba divers, astronauts, caisson and tunnel workers. Bubble growth and detachment physics then becomes significant in predicting and controlling the probability of these bubbles causing mechanical problems by blocking vessels, displacing tissues, or inducing an inflammatory cascade if they persist for too long in the body before being dissolved. By contrast to decompression induced bubbles whose site of initial formation and exact composition are debated, there are other instances of bubbles in the bloodstream which are well-defined. Gas emboli unwillingly introduced during surgical procedures and ultrasound microbubbles injected for use as contrast or drug delivery agents are therefore also discussed. After presenting the different ways that bubbles can end up in the human bloodstream, the general mathematical formalism related to the physics of bubble growth and detachment from decompression is reviewed. Bubble behavior in the bloodstream is then discussed, including bubble dissolution in blood, bubble rheology and biological interactions for the different cases of bubble and blood composition considered.     

Microwave-assisted versus conventional decomposition procedures applied to a ceramic potsherd standard reference material by inductively coupled plasma atomic emission spectrometry

Inductively coupled plasma atomic emission spectrometry (ICP-AES) is a powerful, sensitive analytical technique with numerous applications in chemical characterization including that of ancient pottery, mainly due to its multi-element character, and the relatively short time required for the analysis. A critical step in characterization studies of ancient pottery is the selection of a suitable decomposition procedure for the ceramic matrix. The current work presents the results of a comparative study of six decomposition procedures applied on a standard ceramic potsherd reference material, SARM 69. The investigated decomposition procedures included three microwave-assisted decomposition procedures, one wet decomposition (WD) procedure by conventional heating, one combined microwave-assisted and conventional heating WD procedure, and one fusion procedure. Chemical analysis was carried out by ICP-AES. Five major (Si, Al, Fe, Ca, Mg), three minor (Mn, Ba, Ti) and two trace (Cu, Co) elements were determined and compared with their certified values. Quantitation was performed at two different spectral lines for each element and multi-element matrix-matched calibration standards were used. The recovery values for the six decomposition procedures ranged between 75 and 110% with a few notable exceptions. Data were processed statistically in order to evaluate the investigated decomposition procedures in terms of recovery, accuracy and precision, and eventually select the most appropriate one for ancient pottery analysis.     

Fast screening of perfluorooctane sulfonate in water using vortex-assisted liquid-liquid microextraction coupled to liquid chromatography-mass spectrometry

Fast screening of trace amounts of the perfluorooctane sulfonate anion (PFOS) in water samples was performed following a simple, fast and efficient sample preparation procedure based on vortex-assisted liquid-liquid microextraction (VALLME) prior to liquid chromatography-mass spectrometry. VALLME initially uses vortex agitation, a mild emulsification procedure to disperse microvolumes of octanol, a low density extractant solvent, in the aqueous sample. Microextraction under equilibrium conditions is thus achieved within few minutes. Subsequently, centrifugation separates the two phases and restores the initial microdrop shape of the octanol acceptor phase, which can be collected and used for liquid chromatography-single quadrupole mass spectrometry analysis. Several experimental parameters were controlled and the optimum conditions found were: 50 μL of octanol as the extractant phase; 20 mL aqueous donor samples (pH=2); a 2 min vortex extraction time with the vortex agitator set at a 2500 rpm rotational speed; no ionic strength adjustment. Centrifugation for 2 min at 3500 rpm yielded separation of the two phases throughout this study. Enhanced extraction efficiencies were observed at low pH which was likely due to enhanced electrostatic interaction between the negatively PFOS molecules and the positively charged octanol/water interface. The effect of pH was reduced in the presence of sodium chloride, likely due to electrical double layer compression. The linear response range for PFOS was from 5 to 500 ng L(-1) (coefficient of determination, r(2), 0.997) and the relative standard deviation for aqueous solutions containing 10 and 500 ng L(-1) PFOS were 7.4% and 6.5%, respectively. The limit of detection was 1.6 ng L(-1) with an enrichment factor of approximately 250. Analysis of spiked tap, river and well water samples revealed that matrix did not affect extraction.     

Fast Biosynthesis of GFP Molecules: A Single‐Molecule Fluorescence Study

It's not easy being green : Real‐time visualization of labeled ribosomes and de novo synthesized green fluorescent protein molecules using single‐molecule‐sensitive fluorescence microscopy demonstrates that the mutant GFPem is produced with a characteristic time of five minutes. Fluorescence of the fastest GFP molecules appears within one minute (see picture).

     

Strahlensysteme Mit Speziellen Eigenschaften

In this paper a formula which is derived in [4, p.273] for a rectilinear congruence Σ is expressed in terms of well-known Σ and its middle envelope. Further motivated by this formula we study some specific congruences.