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%.     

Thermal and dilute-solution properties of zwitterionic copolymers

We report the synthesis, characterization, thermal and dilute-solution properties of zwitterionic copolymers of the sulfobetaine type, where the proportion of ionic groups is varied over a wide range. Two different structures are considered: poly (2-vinyl pyridine sulfopropyl betaine) and poly (4-vinyl pyridine sulfopropyl betaine). Synthesis is carried out to obtain random copolymers which are further characterized and their ionic content determined. At low proportions of ionic groups, the behavior is similar to that observed in ionomers, with substantial differences between the two structures, Increased interaction among the zwitterionic groups at higher charge densities is evidenced, which leads to the formation of clusters and agglomerates. An increase in the intrinsic viscosity with salt content in aqueous solutions is also observed. This behavior is analogous to that of homopolymers with 100% ionic content, but with particular features of interest.     

Determination of oxidized and reduced glutathione, by capillary zone electrophoresis, in Brassica juncea plants treated with copper and cadmium

A rapid method of capillary zone electrophoresis is described to determine the oxidized (GSSG) and reduced (GSH) form of glutathione in plant tissue. In order to separate both analytes in a fused-silica capillary, the pH and composition of the electrolyte solution were optimized. The electrolyte composition was 100 mmol/L, borate 25 mmol/L Tris, and 0.2% w/v metaphosphoric acid (MPA), pH 8.2. Some instrumental conditions used to run the samples were hydrostatic injection for 30 s, 30 kV applied voltage, and UV detection (185 nm) at 25 degrees C. Linearity and useful range obtained for the calibration curves were optimum, with correlation coefficients about 0.999 in the 0-120 micromol/L range. The migration time was highly reproducible, less than 5 min being afforded to run a sample. Electrolyte buffer and samples required a careful pH control for optimal separation of both analytes. This aspect constitutes a critical analytical step when acids are used in the procedure for sample preparation. Simultaneous analysis of GSH and GSSG may provide a useful tool for comparative studies of plants in order to select those species with a potential capacity for detoxification from toxic elements or those appearing promising from phytoremediation for these elements.     

Determination of organic acids of low molecular weight and phosphate in soil by capillary electrophoresis

Capillary zone electrophoresis with indirect UV detection at 254 nm was found to be suitable for the determination of organic acids and phosphate in aqueous extracts of soil. The best support electrolyte solution was found to be 10 mM p-hydroxybenzoic acid with 0.5 mM tetradecyltrimethylammonium bromide to reverse electroosmotic flow. This methodology was tested with 9 analytes found in soils: acetate, citrate, formate, phosphate, lactate, oxalate, pyruvate, succinate, and tartrate. The results obtained show that the methodology is adequate for most of the analytes. The sensitivity to oxalate and citrate was low, and the high concentrations of major inorganic anions interfered with the detection of the former. The methodology was applied to the analysis of aqueous extracts of soil samples. Formate, phosphate, lactate, and acetate anions were detected in most of the samples.     

Electrical resistivity, optical and magnetic properties of the layered oxyselenide SmCuOSe

The electrical and magnetic properties of the tetragonal phase SmCuOSe are reported as a function of the temperature. The optical properties were studied by means of diffuse reflectance spectrum in the UV-Vis range. The electrical resistivity measurements as well as diffuse reflectance spectrum show that SmCuOSe is a semiconductor with an optical band gap (E_g) of 2.6 eV. In this phase, Cu is at its monovalent oxidation state and, as such, it does not contribute to the total magnetic moment, whereas Sm is in its 3+ oxidation state, with a large VanVleck contribution due to the admixture of the fundamental state with higher energy levels.