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

Sets of Fractional Operators and Some of Their Applications

This chapter presents one way to define Abelian groups of fractional operators isomorphic to the group of integers under addition through a family of sets of fractional operators and a modified Hadamard product, as well as one way to define finite Abelian groups of fractional operators through sets of positive residual classes less than a prime number. Furthermore, it is presented one way to define sets of fractional operators which allow generalizing the Taylor series expansion of a vector-valued function in multi-index notation, as well as one way to define a family of fractional fixed-point methods and determine their order of convergence analytically through sets

Testing balanced counseling to improve provider-client interaction in Guatemala\u27s MOH clinics

The job aids–assisted Balanced Counseling Strategy adopted by Guatemala’s Ministry of Health required specific instructions for use by nonprofessional providers and an intervention that assured provider compliance with the behavioral requirements of the new paradigm. Results show that the trained providers outperformed the controls in quality of care at each level of session length, but used nine extra minutes per session on average. Nonprofessional providers can take advantage of the job aids–assisted Balanced Counseling Algorithm and substantially improve their quality of care. Extra time invested in counseling new family planning clients will be easily absorbed insofar as they continue to represent a small portion of the total demand for services at the clinics

Effects of IGSS\u27 job aids-assisted Balanced Counseling Algorithms on quality of care and client outcomes

This study identified a need to improve the quality of care at the main maternity hospital of the Social Security Institute (IGSS) in Guatemala. Problems included very short counseling sessions, counseling not focused on clients’ needs, redundancy in the role of physicians and social workers as providers, skewed method mix, and low client return rate for method resupply. The intervention, using Balanced Counseling Algorithms, changed the counseling behavior of physicians and social workers and enhanced the quality of family planning care. The report includes recommendations for continuing these improvements: monitoring provider implementation of the job aids–assisted Balanced Counseling Algorithms, monitoring provider output, adjusting institutional policy and goals to the reality of client preferences, testing reformulated post-choice strategy, and paying particular attention to clients who choose oral contraceptives or condoms

Sobre el problema inverso de difusión

Infiltration is physically described in order to model it as a diffusion stochasticprocess. Theorem M-B 1 is enunciated; whose main objective is the inverse diffusionproblem. The theorem is demonstrated in the specific context of solution injectability,and it is applied to solve the inverse diffusion problem in the presence of Boltzmann’sgroup. The inverse problem of the similarity exponent is solved following group analysismethods. The dispersion of a water drop in a three-dimensional porous medium isapplied; a result which in turn is applicable to drop irrigation.Keywords: inverse problems, group analysis of differential equations, similarity, fractals,diffusion, porous medium.Se describe f´?sicamente la infiltracci´on para modelarla como un proceso estoc´asticode difusi´on. Se enuncia el teorema M-B 1, cuyo objeto principal es el problema inversode difusi´on. Se demuestra dicho teorema, en el contexto particular de la inyectividadde la soluci´on y se aplica para resolver el problema inverso de difusi´on en presencia delgrupo de Boltzmann. Se resuelve el problema inverso del exponente de similaridad porlos m´etodos del an´alisis de grupo. Se aplica a la dispersi´on de una gota en un medioporoso tridimensional, resultado a su vez aplicable en el caso del riego por goteo.Palabras clave: Problemas inversos, an´alisis de grupo de ecuaciones diferenciales, similaridad,fractales, difusi´on, medios porosos

Structural characterisation of porous copper sheets fabricated by lost carbonate sintering applied to tape casting

In this article, we describe experimental investigations of the structural characterisations of double-layered porous copper tapes of thickness down to 0.74 mm. The porous sheets were produced by a process combing tape casting and lost carbonate sintering (LCS) to control both the porosity and pores distribution of the sheets. By varying the values of processing parameters, double-layer (porous and dense) structured tapes with open cell structure and porosities ranging from 50.0 to 81.5% are produced. Scanning electron microscopy and actual size image analysis were employed to measure the pore size and surface porosity of the porous sample. The pore size distribution was characterised using Micro-CT scanner running Skyscan NRecon software and CTAn software. A helium pycnometer was employed to obtain the bulk porosity of the porous copper samples. Statistical analysis of these measurements was used to assess the efficiency and consistency of the space holder technique used to generate porosity, as well as to draw information about the influence that different processing routes have on the resulting mesostructure of the porous copper metal, and on its properties

Aproximación fractal para semivariogramas freáticos

Hausdorff’s measure is integrated upon, and H¨older’s exponent is obtained as thecodimension DT ? D of the fractal in the Euclidian space in which it is immersed.This has resulted from the application of Daniell’s integral conception, which makesit possible to integrate Lipschitz’s and H¨older’s functions into Baire’s measures andto define fractal space with Hutchinson’s metric.The power for the potentiated model of the semivariograms of stationary processesis obtained. It is applied to the levels of the phreatic strata of Valle del Carrizo,Sinaloa, Mexico, and the experimental semivariograms, and those of the adjustmentwith a potential model are created, with the finding that its power is = 1,5. It isalso found that the fractal dimension of these strata is 2,25.Keywords: fractals, H¨older, codimension, similarity, semivariogram, groundwater.Se integra sobre la medida de Hausdorff y se obtiene el exponente H¨older como lacodimensi´on DT ?D del fractal, en el espacio Euclidiano en que se encuentra inmerso.´Esto ha resultado de la aplicaci´on de la concepci´on de integral de Daniell, que posibilitaintegrar funciones de Lipschitz y de H¨older sobre las medidas de Baire y tambi´en, dedefinir el espacio de fractales con la m´etrica de Hutchinson.Se obtiene la potencia para el modelo [potenciado]* de los semivariogramas de procesosestacionarios. Se aplica a los niveles de los mantos fre´aticos del Valle del Carrizo,Sinaloa, M´exico, y se crean los semivariogramas experimentales y el de ajuste con unmodelo potencial, encontr´andose que su potencia es = 1,5. Se obtiene tambi´en, quela dimensi´on fractal de estos mantos es de 2,25.Palabras clave: Fractales, H¨older, codimensi´on, similaridad, semivariograma, fre´atico

Enhancing quality for clients: The balanced counseling strategy

A central focus of high-quality family-planning care is the interaction between clients and the providers who serve them. In the ideal client-provider interaction, the provider treats all clients respectfully, responds to their reproductive needs and intentions, helps in the selection of the most appropriate family planning method, and offers sufficient information to use the method safely and effectively. To improve the quality of the client-provider interaction, Population Council staff developed a “Balanced Counseling Strategy,” a type of algorithm or decision tree, to be used in combination with several job aids, or visual memory aids. The Balanced Counseling Strategy structures the client-provider interaction to focus on the client’s needs and support the client’s choice of an appropriate method, and leads to improvements in the client-provider interaction when providers use the strategy along with job aids. This brief describes the Balanced Counseling Strategy as an ongoing approach to improving quality of care. It outlines the origin and rationale for developing the strategy and details its subsequent adaptation for use in other contexts

Effects of Mesterolone in the physiology, welfare and masculinization of the neotropical tambaqui Colossoma macropomum.

For Brazilian aquaculture, tambaqui Colossoma macropomum is the main native species. In farming conditions, females can grow up to 50% more than the males, most likely for entering puberty later than males. As tambaqui sex-determination system is XX/XY, there is the possibility to generate monosex population of females by crossing out normal females with neo-males (genetic females -XX displaying male phenotype). The goal of this study was to invert the sex phenotype of female tambaqui using mesterolone, which is a synthetic androgen derivative of dihydrotestosterone. Since in fish the hematological parameters may alter as a result of pollutants or drugs used in aquaculture, we evaluated the welfare of treated fish through biomarkers of liver function, i. e. biochemical parameters and histopathological analysis of the liver

Effect of Chronic Administration of Resveratrol on Cognitive Performance during Aging Process in Rats

The increase in the elderly population has generated concern to meet health demands. The research efforts to elucidate the mechanisms of damage associated with aging have also been significantly increased, especially in order to avoid the reduction of the cognitive abilities in geriatric patients, resulting from the damage generated mainly at the level of the hippocampus during old age. At present, many studies describe resveratrol as an antiaging component. There are reports that it can activate the Sirt1 gene related to antiaging, emulating the effects obtained by caloric restriction in rodents. The aim of the study was to evaluate the effect of chronic administration of resveratrol (10 mg/kg) on cognitive performance in behavioral tests after 8 months of treatment and on the preservation of cerebral integrity in the cytoarchitecture of regions CA1 and CA2. Results showed that the cytoarchitecture of the CA1 and CA2 regions in the hippocampus retained their integrity over time in rats treated with resveratrol, and the behavioral test performed revealed that chronic resveratrol administration for 8 months showed improvements in cognitive performance. The results indicate that resveratrol may exhibit therapeutic potential for age-related conditions