The Problem of the Pointwise Fourier Inversion for Piecewise Smooth Functions of Several Variables

We study the pointwise convergence problem for the inverse Fourier transform of piecewise smooth functions, i.e., whether S_rD f (\bx) ? f (\bx)S_{\rho D} f (\bx) \to f (\bx) as r? ￥\rho \to \infty . r? ￥\rho \to \infty . Here for \bx,\bxi ? \Rn\bx,\bxi \in \Rn S_rDf(\bmx)=\dsf1(2p)^n/2\intli_rD [^(f)](\bxi) e^{\dst iá\bmx,\bxi?} d\bxi . S_{\rho D}f(\bm{x})=\dsf1{(2\pi)^{n/2}}\intli_{\rho D} \widehat{f}(\bxi) e^{\dst i\langle\bm{x},\bxi\rangle} d\bxi~. is the partial sum operator using a convex and open set DD containing the origin, and rD={ r\bxi:\bxi ? D }\rho D=\left\{ \rho \bxi:\bxi\in D \right\}.     

Sub-bundles of the complexified tangent bundle

We study embeddings of complex vector bundles, especially line bundles, in the complexification of the tangent bundle of a manifold. The aim is to understand implications of properties of interest in partial differential equations.

     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.     

Complete caps in projective spaces PG (n, q)

A computer search in the finite projective spaces PG(n, q) for the spectrum of possible sizes k of complete k-caps is done. Randomized greedy algorithms are applied. New upper bounds on the smallest size of a complete cap are given for many values of n and q. Many new sizes of complete caps are obtained.     

Potentiometric studies on the complexation of copper(II) by phenolic acids as discrete ligand models of humic substances

Studies on the complexation of copper(II) by phenolic acids, as ligand models of humic substances were done by potentiometry. The acids under study were: 3,4-dihydroxyhydrocinnamic acid or hydrocaffeic acid (1), 3,4-dihydroxyphenylacetic acid (2) and 3,4-dihydroxybenzoic acid or protocatechuic acid (3). Acidity constants of the ligands and the formation constants of metal-ligand complexes were evaluated by computer programs. The carboxylic group of the phenolic acids has different pK_a1 values, being the dissociation constants intrinsically related with the distance between the function and the aromatic nucleus. The results obtained allow concluding that acidity constants of the catechol moiety of the compounds are similar with pK_a2 and pK_a3 values between 9.47-9.41 and 11.55-11.70. The complexation properties of the three ligands towards copper(II) ion are quite similar, being the species found not different either in nature or stability. Although the model ligands have some structural differences no significant differences were found in their complexation properties towards copper(II). So, it can be postulated that complexation process is intrinsically related with the presence of a catechol group.     

Coupling Cloud Point Extraction to Instrumental Detection Systems for Metal Analysis

The purpose of this article is to review and evaluate cloud point extraction of metals and its coupling to different contemporary instrumental methods of analysis. This review covers a selection of the literature published on this topic over the period mainly between 1997 and September 2005 (consisting of 50 publications). The current state of the art for CPE concerning metals and metal chelates is presented with special emphasis on the hyphenation of this interesting extraction/preconcentration approach mediated by surfactants to spectrophotometry, atomic spectroscopy and separation techniques. We present contemporary CPE developments concerning metal speciation and determination and their application to different environmental, clinical, geological and food samples. Strategies for method development as well as future perspectives are also covered.