On Solutions of Linear Ordinary Difference Equations in their Coefficient Field

We extend the notion of monomial extensions of differential fields, i.e. simple transcendental extensions in which the polynomials are closed under differentiation, to difference fields. The structure of such extensions provides an algebraic framework for solving generalized linear difference equations with coefficients in such fields. We then describe algorithms for finding the denominator of any solution of those equations in an important subclass of monomial extensions that includes transcendental indefinite sums and products. This reduces the general problem of finding the solutions of such equations in their coefficient fields to bounding their degrees. In the base case, this yields in particular a new algorithm for computing the rational solutions of q -difference equations with polynomial coefficients.     

Soft purification of N-doped and undoped multi-wall carbon nanotubes

A soft method for purifying multi-wall carbon nanotubes (N-doped and undoped) is presented. The technique includes a hydrothermal/ultrasonic treatment of the material in conjunction with other subsequent treatments, including the extraction of polyaromatic compounds, dissolution of metal particles, bundle exfoliation, and uniform dispersion. This method avoids harsh oxidation protocols that burn (via thermal treatments) or functionalize (by introducing chemical groups) the nanotubes. We show a careful analysis of each purification step and demonstrate that the technique is extremely efficient when characterizing the materials using scanning electron microscopy (SEM), energy dispersive x-ray analysis (EDAX), scanning tuneling electron microscopy (STEM), x-ray powder diffraction (XRD), diffuse reflectance Fourier transform infrared (DRFTIR) spectroscopy and thermogravimetric analysis (TGA).     

Chlorination of organophosphorus pesticides in natural waters

Unknown second-order rate constants for the reactions of three organophosphorus pesticides (chlorpyrifos, chlorfenvinfos and diazinon) with chlorine were determined in the present study, and the influence of pH and temperature was established. It was found that an increase in the pH provides a negative effect on the pesticides degradation rates. Apparent second-order rate constants at 20 degrees C and pH 7 were determined to be 110.9, 0.004 and 191.6 M(-1) s(-1) for chlorpyrifos, chlorfenvinfos and diazinon, respectively. A higher reactivity of chlorine with the phosphorothioate group (chlorpyrifos and diazinon) than with the phosphate moiety (chlorfenvinfos) could explain these results. Intrinsic rate constant for the elementary reactions of chlorine species with chlorpyrifos and diazinon were also calculated, leading to the conclusion that the reaction between hypochlorous acid and the pesticide is predominant at neutral pH. The elimination of these pesticides in surface waters was also investigated. A chlorine dose of 2.5 mg L(-1) was enough to oxidize chlorpyrifos and diazinon almost completely, with a formation of trihalomethanes below the EU standard for drinking water. However, the removal of chlorfenvinfos was not appreciable. Therefore, chlorination is a feasible option for the removal of organophosphorus pesticides with phosphorothioate group during oxidation and disinfection processes, but not for the elimination of pesticides with phosphate moiety.     

Comment on "Tunable three-dimensional intensity distribution by a pure phase-shifting apodizer"

In the past few years, many radially symmetric pupil masks have been designed for the control of the light intensity distribution near the geometrical focus of optical systems. A recent paper by Gao et al. [Appl. Opt. 44, 4870 (2005)] analyzed the performance of binary 0-pi phase-only masks for an incident beam with Gaussian amplitude. Some inaccuracies of the analysis concerning the evolution of the Strehl ratio with the mask parameters are corrected.     

Principal components analysis of the photoresponse nonuniformity of a matrix detector

The principal component analysis is used to identify and quantify spatial distributions of relative photoresponse as a function of the exposure time for a visible CCD array. The analysis shows a simple way to define an invariant photoresponse nonuniformity and compare it with the definition of this invariant pattern as the one obtained for long exposure times. Experimental data of radiant exposure from levels of irradiance obtained in a stable and well-controlled environment are used.     

Coupling solar photo-Fenton and biotreatment at industrial scale: main results of a demonstration plant

This paper reports on the combined solar photo-Fenton/biological treatment of an industrial effluent (initial total organic carbon, TOC, around 500mgL(-1)) containing a non-biodegradable organic substance (alpha-methylphenylglycine at 500mgL(-1)), focusing on pilot plant tests performed for design of an industrial plant, the design itself and the plant layout. Pilot plant tests have demonstrated that biodegradability enhancement is closely related to disappearance of the parent compound, for which a certain illumination time and hydrogen peroxide consumption are required, working at pH 2.8 and adding Fe(2+)=20mgL(-1). Based on pilot plant results, an industrial plant with 100m(2) of CPC collectors for a 250L/h treatment capacity has been designed. The solar system discharges the wastewater (WW) pre-treated by photo-Fenton into a biotreatment based on an immobilized biomass reactor. First, results of the industrial plant are also presented, demonstrating that it is able to treat up to 500Lh(-1) at an average solar ultraviolet radiation of 22.9Wm(-2), under the same conditions (pH, hydrogen peroxide consumption) tested in the pilot plant.     

Transverse load and orientation measurement with multicore fiber Bragg gratings

We demonstrate the sensitivity of Bragg gratings in a multicore fiber to transverse load. The Bragg peaks are split because of stress-induced birefringence, the magnitude of which depends upon the load and grating position relative to the load axis. Experiments show that a set of gratings in a four-core fiber can measure a load axis angle to +/- 5 degrees and a load magnitude to +/- 15 N m(-1) up to 2500 N m(-1). We consider alternative designs of multicore fiber for optimal load sensing and compare experimental and modeled data.     

Effect of ionizing radiation on the properties of arc-induced long-period fiber gratings

We experimentally study the effect of ionizing radiation on the properties of long-period gratings fabricated in two pure-silica-core fibers with the arc-discharge technique. It is observed that the spectra of the gratings remain almost unchanged after being subjected to doses in excess of 0.5 MGy. The results also show that the gratings' temperature and strain sensitivities are not affected by gamma radiation.     

Polynomial Kernel Discriminant Analysis for 2D visualization of classification problems

Neural Computing and Applications - In multivariate classification problems, 2D visualization methods can be very useful to understand the data properties whenever they transform the n-dimensional...