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%.     

Protection against photoaging in the hairless mouse by the isoflavone equol

Topical application of the isoflavone equol immediately following solar-simulated UV (SSUV) radiation exposure has previously been demonstrated to have significant photoprotective effects. Equol reduced both the inflammatory edema and the systemic suppression of the contact hypersensitivity reaction in hairless mice. Furthermore, daily topical equol application immediately following irradiation during a 10-week chronic SSUV exposure regime also reduced photocarcinogenesis severity in the mouse. This study examines the potential for topical equol to prevent photoaging in response to chronic SSUV irradiation for up to 30 weeks. We did not find consistent expression of the characteristic markers of photoaging until 30 weeks, although moderate epidermal hyperplasia and a transient increase in dermal mast cell numbers were evident after 1 week. Daily application of 10 muM equol lotion significantly reduced these early changes. However after 30 weeks of SSUV exposure, photoaging was well developed, as shown histologically by markedly increased epidermal hyperplasia, increased dermal mast cell number, pronounced focal elastotic deposits, degraded dermal collagen and deposition of glycosaminoglycans in the lower dermis. Topical equol treatment protected significantly from each of these impairments, as demonstrated histologically and quantitatively. Additionally, equol was found to have strong antioxidant action against acute UVA (320-400 nm)-induced lipid peroxidation of mouse skin, this property accounting for its antiphotoaging mechanism. The evidence for equol's antiphotoaging activity, taken together with its anti-inflammatory, immunoprotective and anticarcinogenic efficacy against SSUV irradiation in the mouse, suggests that equol could be developed as a helpful topical photoprotective agent for daily use by humans.     

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.