Error estimates on anisotropic elements for functions in weighted Sobolev spaces

In this paper we prove error estimates for a piecewise average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions.

Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses.

Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems.

Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements.

As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained.

     

Dreikörperkräfte und die Stabilität einfacher Kristallgitter

Observed stability of crystal structures for rare-gas atoms, alkali halides and for those II–VI and III–V compounds whose ions are isoelectronic with rare-gas atoms is correlated with atomic and ionic interactions in dense media. On the basis of central forces essential discrepancies between theory and experiment occur. Further analysis indicates that strong, simultaneous interactions of exchange type between three atoms or three ions play an important role in determining the stable crystal structure. An evaluation of such three-body interactions is carried out in first and second orders of perturbation theory, using effective-electron wave functions of Gaussian form. It is shown that the theory accounts for all observed stability relations on a quantitative basis. The stability of the face-centered cubic configuration for solids of heavy rare gases is explained. Also, the occurrence of the cesium chloride structure for some of the heavy alkali halides and the magnitude of observed transition pressures are reproduced by the theory. In addition, it is shown that three-ion interactions are responsable for the occurrence of the sphalerite (zincblende) and wurtzite configurations with II–VI and III–V compounds, without covalent bonding between the ions being involved. General laws are given which govern the relative stability of the sodium chloride, cesium chloride, sphalerite and wurtzite configurations for these types of compounds.     

The surface enhanced Raman spectrum of 2,6-lutidine

The surface enhanced Raman spectrum of 2,6-lutidine adsorbed on a polycrystalline Ag surface is reported along with a discussion of the effect on the methyl vibrations of adsorption on the electrode. The observation of an AgN stretch and small shifts of the methyl vibrations on the surface lead to a model of the molecule-surface interaction. If the molecule is adsorbed on a (100) or (110) face, surface roughness on an atomic scale is required to explain the observations. If the molecule is adsorbed on a (111) face, no surface roughness need be invoked. In either case a metalnitrogen bond somewhere between the van der Waals (physisorbed) and covalent (chemisorbed) limits is indicated.     

Evidence for a Ag adatom-molecule complex in surface enhanced raman scattering

The SERS spectrum of molecules adsorbed on Ag sols show, lines, in the 200–300 cm^?1 region in the absence of Cl^? ions These lines are attributed to a Ag-N complex and frequency calculations show that they correspond to the vibrations of the molecule bound to a single silver atom.     

First track-structure measurements of 20 MeV protons with the STARTRACK apparatus

The STARTRACK experimental set-up, mounted on the +50° beam line of the Tandem-Alpi particle accelerator of Legnaro National Laboratories, has been conceived to give an experimental basis to nanodosimetric calculations. STARTRACK is based on a detection system able to measure ionization cluster distributions in a 20 nm propane site with a resolution of one ionization. The experimental layout has been designed to minimize pile-up distortions. The background noise is filtered by off-line dedicated software. Electron cluster distribution of 20 MeV protons has been measured. Monte Carlo data and experimental data are pretty well consistent.     

Kinetic and equilibrium studies on the polyazamacrocycle neotetren: metal-complex formation and DNA interaction

The macrocyclic polyamine 2,5,8,11,14-pentaaza[15]-[15](2,9)[1,10]phenanthrolinophane (neotetren) is studied in its ability to coordinate Cu(ii) even at very low pH values and to interact, as a metal complex, with DNA. The kinetics and equilibria for 1 : 1 and 2 : 1 metal-ligand complexes formation are studied by the stopped-flow method and UV spectrophotometry. Differently protonated complexes are formed, with rate constants much lower than that of water exchange at copper(II) and other Cu(II)/amine systems, this behaviour being ascribed to ring effects and intra-molecular hydrogen bonds. Concerning the DNA/copper(II)-neotetren complexes interaction, analysis of data suggests an intercalative mode of binding. The kinetic results for both DNA/CuL and DNA/Cu(2)L systems agree with the sequence D + S <-->D,S <-->DS where the metal complexes (D) react with the DNA sites (S) leading to fast formation of an externally bound form (D,S) which is converted into an intercalated complex (DS). A very slow process is also detected and ascribed to a conformational change in the polynucleotide secondary structure where the metal centre plays a crucial role. Chromatographic experiments demonstrate that both the investigated Cu(II)/L complexes are able to cleave DNA, but only in the presence of hydrogen peroxide.     

Hidden constructions in abstract algebra (6): The theorem of Maroscia and Brewer & Costa

We give a constructive deciphering for a generalization of the Quillen-Suslin theorem due to Maroscia and Brewer & Costa stating that finitely generated projective modules over , where is a Prüfer domain with Krull dimension ≤1, are extended from .     

Effect of Pt particle size and distribution on photoelectrochemical hydrogen evolution by p-Si photocathodes

In this work, we investigate the effect of the average size and density of Pt clusters on silicon on the photoelectrochemical production of hydrogen. The metallization of Si is performed via electroless deposition from aqueous HF solutions and from water-in-oil microemulsions. The first method enables control of the average diameter and density of Pt clusters by properly changing the deposition parameters like HF concentration and immersion times. However, on one hand, size dispersion is relatively wide and particles agglomeration may occur with this deposition technique. On the other hand, Pt islands with smaller dimensions at the nanoscale as well as with a narrower size distribution are deposited from reversed micellar solutions. Photoelectrochemical experiments show that the effect of Pt morphology on photoconversion efficiency strongly depends on light intensity. At low power of illumination (10 mW/cm2), Pt islands with a mean diameter of 100 nm and a density of 15 particles/microm2, which can be obtained via electroless deposition from a HF-based solution, provide the best photoelectrochemical performance. Nevertheless, this configuration of Pt clusters yields an abrupt collapse of photoconversion efficiency from 31% to 11.8% when the light power is increased up to 100 mW/cm2. At this light intensity, Pt islands with a mean size and density of approximately 40 nm and 75 particles/microm2, respectively, obtained via the microemulsion method, allow photoconversion efficiency as high as 20% to be achieved.