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

Meta-analysis of a very low proportion through adjusted wald confidence intervals

In this paper we will discuss the meta-analysis of one low proportion. It is well known, that there are several methods to perform the meta-analysis of one proportion, based on a linear combination of proportions or transformed proportions. However, in the context of a linear combination of binomial proportions has been proposed some approximate estimators with some improvements on low proportion estimation. In this paper we will show, with a simple adaptation, the possible contribution of several approximate adjusted Wald confidence intervals (CIs) for the meta-analysis of proportions. In the context of low proportions, a simulation study scenario is carried out to compare these CIs amongst themselves and with other available methods with respect to bias and coverage probabilities, using the fixed effect or the random-effects model. Pointing our interest in rare events (analogous for the abundant events) and taking into account the prevalence estimation of the Methicillin-resistant Staphylococcus aureus with mecc gene, we discuss the choice of the meta-analysis methods on this low proportion. The default meta-analysis methods of meta-analysis software programs are not always the best choice, in particular to the meta-analysis of one low proportion, where the methods including the adjusted Wald can outperform.publishe

New method for non-standard invisible particle searches in tau lepton decays

Motivated by models proposed to explain the Standard Model anomalies, and the unprecedented $\tau^{+}\tau^{-}$ data to be collected by the Belle~II experiment during the next years, we study the kinematics of tau pair decays and propose a new method to search for lepton flavor violating processes in tau lepton decays to invisible beyond Standard Model particles, such as $\tau \to \ell \alpha$, where $\ell$ is either an electron or a muon, and $\alpha$ is a massive particle that escapes undetected. The new method improves by one order of magnitude the expected upper limit on the $\tau \to \ell \alpha$ production in 3x1 prong tau decays and establishes the possibility of performing this search in 1x1 prong tau decays which has not been previously considered.Comment: 6 pages, 7 figure

Performance Modelling and Analysis of Mobile Wireless Networks

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Production of Aspergillus niger GH1 tannase using solid-state fermentation

The production of tannase by Aspergillus niger GH1 in solid-state fermentation (SSF) was evaluated. Several concentrations of tannic acid (12.5, 25, 50 and 100 g/L) were tested in a model culture system. Column reactors were packed with polyurethane foam impregnated with liquid medium and inoculated with fungal spores. Tannase production was kinetically monitored by 48 h. Tannic acid uptake was spectrophotometrically measured and extracellular and intracellular tannase activities were assayed by HPLC-chromatography. Tannase activity increased with increasing concentration of tannic acid. Maximum extracellular and intracellular tannase activities (11.35 and 6.95 U/mL respectively) were recorded with 100 g/L of tannic acid. The substrate uptake was 100% at concentrations of 12.5, 25 and 50 g/L, while 74.4% was consumed in the presence of 100 g/L of tannic acid after 48 h of culture. These results suggest that high concentrations of tannins can be removed by SSF and tannase production can be reached in high levels.The present work was performed as part of a cooperative agreement between the Universidad Autonoma de Coahuila (UAdeC, Mexico) and the Universidade do Minho (UM, Portugal) within a specific international exchange program (VALNATURA project, alfa network from European Union) undertaken at the Biological Engineering Department (UM, Portugal) M A Cruz-Hernandez thanks to Concejo nacional de Ciencia y Tecnologia (CONACYT) the fellowship to study the doctoral program at the Department of Biotechnology (UAdeC