Fractional Newton-Raphson Method Accelerated with Aitken's Method

The Newton-Raphson (N-R) method is characterized by the fact that generating a divergent sequence can lead to the creation of a fractal, on the other hand the order of the fractional derivatives seems to be closely related to the fractal dimension, based on the above, a method was developed that makes use of the N-R method and the fractional derivative of Riemann-Liouville (R-L) that has been named as the Fractional Newton-Raphson (F N-R) method. In the following work we present a way to obtain the convergence of the F N-R method, which seems to be at least linearly convergent for the case where the order $\alpha$ of the derivative is different from one, a simplified way to construct the fractional derivative and fractional integral operators of R-L is presented, an introduction to the Aitken's method is made and it is explained why it has the capacity to accelerate the convergence of iterative methods to finally present the results that were obtained when implementing the Aitken's method in F N-R method.Comment: Newton-Raphson Method, Fractional Calculus, Fractional Derivative of Riemann-Liouville, Method of Aitken. arXiv admin note: substantial text overlap with arXiv:1710.0763

Tunneling Splittings in Mn12-Acetate Single Crystals

A Landau-Zener multi-crossing method has been used to investigate the tunnel splittings in high quality Mn$_{12}$-acetate single crystals in the pure quantum relaxation regime and for fields applied parallel to the magnetic easy axis. With this method several individual tunneling resonances have been studied over a broad range of time scales. The relaxation is found to be non-exponential and a distribution of tunnel splittings is inferred from the data. The distributions suggest that the inhomogeneity in the tunneling rates is due to disorder that produces a non-zero mean value of the average transverse anisotropy, such as in a solvent disorder model. Further, the effect of intermolecular dipolar interaction on the magnetic relaxation has been studied.Comment: Europhysics Letters (in press). 7 pages, including 3 figure

X-Ray Fluorescence Analysis of Ground Coffee

Coffee is becoming one of the most popular beverages in Mexico. In the present work, X-ray Fluorescence (XRF) was used to determine the contents of several elements (with atomic numbers between 11 and 38) in 11 samples of commercial ground coffee, comparing with another one of soluble coffee and two of used ground coffee. Samples were dried at room temperature and pelletized. XRF analyses were carried out using a spectrometer based on an Rh X-ray tube, registering the characteristic x-rays with a Silicon Drift Detector. The system detection calibration and accuracy check was performed through the analysis of NIST certified reference materials 1547 (peach leaves), 1570a (spinach leaves), 1573a (tomato leaves), and 1571 (orchid leaves). As a general rule, the elemental concentrations measured are similar in all samples of coffee, in values not exceeding toxic levels. However, the differences among the elemental concentrations are shown

Use of CdS from Teaching-Laboratory Wastes as a Photocatalyst for the Degradation of Fluoroquinolone Antibiotics in Water

Laboratory wastes containing Cd2+ and water polluted by pharmaceuticals represent an environmental concern. In this work, a proof concept, consisting of the use of teaching-laboratory wastes to synthesize CdS and its subsequent use as a photocatalyst to degrade fluoroquinolone antibiotics, was developed. The CdS was prepared by extraction with thioacetamide and calcination (at 450 °C) and characterized using several techniques. The photocatalytic activity of the CdS, to degrade levofloxacin and norfloxacin, was tested, and the routes involved in the process and the primary transformations of the fluoroquinolones were established. Moreover, the ability of CdS-photocatalysis to eliminate levofloxacin in simulated matrices of fresh urine and hospital wastewater was evaluated. The characterization analyses indicated that the CdS semiconductor was synthesized successfully. Effectively, the CdS acted as a photocatalyst toward degradation of levofloxacin, involving the action of superoxide anion radical, holes, and singlet oxygen mainly. The process induced transformations on the methyl-piperazyl moiety, plus hydroxylation of the fluoroquinolone nucleus on levofloxacin. Additionally, CdS-photocatalysis was highly selective for the elimination of the target pollutant in both tested matrices. Our research indicated the good potentiality of recycling teaching-laboratory wastes to generate photocatalysts to degrade organic pollutants. This work was presented at 4° Congreso Colombiano de Procesos Avanzados de Oxidación (4CCPAOx)