Approximation on the sphere using radial basis functions plus polynomials

In this paper we analyse a hybrid approximation of functions on the sphere by radial basis functions combined with polynomials, with the radial basis functions assumed to be generated by a (strictly) positive definite kernel. The approximation is determined by interpolation at scattered data points, supplemented by side conditions on the coefficients to ensure a square linear system. The analysis is first carried out in the native space associated with the kernel (with no explicit polynomial component, and no side conditions). A more refined error estimate is obtained for functions in a still smaller space. Numerical calculations support the utility of this hybrid approximation.      

Modification of Amorphous Mesoporous Zirconia Nanoparticles with Bisphosphonic Acids: A Straightforward Approach for Tailoring the Surface Properties of the Nanoparticles

The use of readily prepared bisphosphonic acids obtained in few steps through a thio-Michael addition of commercially available thiols on tetraethyl vinylidenebisphosphonate enables the straightforward surface modification of amorphous mesoporous zirconia nanoparticles. Simple stirring of the zirconia nanoparticles in a buffered aqueous solution of the proper bisphosphonic acid leads to the surface functionalization of the nanoparticles with different kinds of functional groups, charge and hydrophobic properties. Formation of both chemisorbed and physisorbed layers of the bisphosphonic acid take place, observing after extensive washing a grafting density of 1.1 molecules/nm² with negligible release in neutral or acidic pH conditions, demonstrating stronger loading compared to monophosphonate derivatives. The modified nanoparticles were characterized by IR, XPS, ζ-potential analysis to investigate the loading of the bisphosphonic acid, FE-SEM to investigate the size and morphologies of the nanoparticles and ³¹P and ¹H MAS NMR to investigate the coordination motif of the phosphonate units on the surface. All these analytical techniques demonstrated the strong affinity of the bisphosphonic moiety for the Zr(IV) metal centers. The functionalization with bisphosphonic acids represents a straightforward covalent approach for tailoring the superficial properties of zirconia nanoparticles, much straightforward compared the classic use of trisalkoxysilane or trichlorosilane reagents typically employed for the functionalization of silica and metal oxide nanoparticles. Extension of the use of bisphosphonates to other metal oxide nanoparticles is advisable.     

Kinetic parameter estimation of solvent‐free reactions monitored by 13C NMR spectroscopy,a case study: Mono‐ and di‐(hydroxy)ethylation of aniline with ethylene carbonate

The kinetics of solvent‐free reactions can be followed in situ by ¹³C nuclear magnetic resonance (NMR) spectroscopy, provided that the reaction mixture can be maintained liquid at the monitoring temperature. The pros and cons of the technique and the correct translation of the signal intensities into concentrations are discussed. A good model for this investigation is the reaction of ethylene carbonate ( 1 ) with aniline ( 2 ) at 140°C, two alkylation products of N‐mono‐ and N, N‐bis‐(2‐hydroxy)ethylation of aniline form (compounds 3 and 4 , respectively). The overall reaction occurs with heavy volume shrinking, so that the physical as well as the chemical features evolve during the course of the process. The chemical evolution is described by the kinetic constants k₁ and k₂ of the two N‐alkylation steps, the physical evolution by the time‐dependent activity coefficients α(t). Two complementary procedures are utilized for the determination of these parameters. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 154–160, 2011     

Tin amalgam mirrors: investigation by XRF, SEM-EDS, XRD and EPMA-WDS mapping

Ancient mirrors were constituted by a tin-mercury amalgam layer superimposed to a glass sheet. This was the only one method used until the nineteenth century, when the wet silvering process was invented. The tin amalgam is a binary alloy of tin and mercury constituted by two different phases: a mercury-rich liquid phase and a tin-rich solid phase. The amalgam alteration produces mercury loss and a general growth of the solid crystalline phase. In addition, tin dioxide and monoxide are formed with a consequent decrease of the amalgam adhesion to the glass. These degradation phenomena led to reduction or disappearance of the mirror reflective power. The aim of this study was the characterization of the amalgam layers of eight mirror samples dating during the seventeenth and nineteenth centuries. The samples were analyzed by X-ray diffraction and by a Scanning Electron Microscope with an Energy Dispersive Spectrometer (SEM-EDS), and for the first time on this type of alloy by X-ray Fluorescence and EPMA-WDS (Electron Probe Micro Analysis with Wavelength Dispersive Spectrometry) elemental mapping. The contents of tin, mercury, and some trace elements in the amalgam layers have been determined. The investigation of the superficial patterns of the amalgam by SEM, EPMA-WDS mapping, and SEM-EDS allowed a first understanding of some morphologies and processes of the degradation of the amalgam layer.     

Selective mono-C-methylations of arylacetonitriles and arylacetates with dimethylcarbonate: a mechanistic investigation

The very high mono-C-methylation selectivity (>99%) of arylacetic acid derivatives (ArCH2X; X = CN, CO2Me) with dimethyl carbonate (DMC) is due to a mechanism that involves consecutive methoxycarbonylation, methylation, and demethoxycarbonylation steps. Important aspects of this mechanism are clarified herein by a kinetic investigation. In the case of arylacetonitriles, at 140 degrees C, the comparison of the rate constants of model reactions involving 2-phenyl propionitrile, phenylacetonitrile, 2-methoxycarbonylphenylacetonitrile, and 2-methyl-2-methoxy carbonylphenyl acetonitrile (compounds 1a-4a, respectively) with DMC indicates that the methylation process is the fastest and the irreversible step, which drives the overall reaction to completion. The situation is reversed for arylacetic esters, where the methylation is more difficult than the demethoxycarbonylation reaction; therefore, a higher reaction temperature is required.     

Polynomial interpolation and cubature over polygons

We have implemented a Matlab code to compute Discrete Extremal Sets (of Fekete and Leja type) on convex or concave polygons, together with the corresponding interpolatory cubature formulas. The method works by QR and LU factorizations of rectangular Vandermonde matrices on Weakly Admissible Meshes (WAMs) of polygons, constructed by polygon quadrangulation.