A multiscale collocation method for fractional differential problems

We introduce a multiscale collocation method to numerically solve differential problems involving both ordinary and fractional derivatives of high order. The proposed method uses multiresolution analyses (MRA) as approximating spaces and takes advantage of a finite difference formula that allows us to express both ordinary and fractional derivatives of the approximating function in a closed form. Thus, the method is easy to implement, accurate and efficient. The convergence and the stability of the multiscale collocation method are proved and some numerical results are shown.We introduce a multiscale collocation method to numerically solve differential problems involving both ordinary and fractional derivatives of high order. The proposed method uses multiresolution analyses (MRA) as approximating spaces and takes advantage of a finite difference formula that allows us to express both ordinary and fractional derivatives of the approximating function in a closed form. Thus, the method is easy to implement, accurate and efficient. The convergence and the stability of the multiscale collocation method are proved and some numerical results are shown

A fractional spline collocation method for the fractional order logistic equation

We construct a collocation method based on the fractional B-splines to solve a nonlinear differential problem that involves fractional derivative, i.e. the fractional order logistic equation. The use of the fractional B-splines allows us to express the fractional derivative of the approximating function in an analytic form. Thus, the fractional collocation method is easy to implement, accurate and efficient. Several numerical tests illustrate the efficiency of the proposed collocation method.We construct a collocation method based on the fractional B-splines to solve a nonlinear differential problem that involves fractional derivative, i.e. the fractional order logistic equation. The use of the fractional B-splines allows us to express the fractional derivative of the approximating function in an analytic form. Thus, the fractional collocation method is easy to implement, accurate and efficient. Several numerical tests illustrate the efficiency of the proposed collocation method

Some results on a new refinable class suitable for fractional differential problems

In recent years, we found that some multiscale methods applied to fractional differential problems, are easy and efficient to implement, when we use some fractional refinable functions introduced in the literature. In fact, these functions not only generate a multiresolution on R, but also have fractional (non-integer) derivative satisfying a very convenient recursive relation. For this reason, in this paper, we describe this class of refinable functions and focus our attention on their approximating properties

A collocation method based on discrete spline quasi-interpolatory operators for the solution of time fractional differential equations

In many applications, real phenomena are modeled by differential problems having a time fractional derivative that depends on the history of the unknown function. For the numerical solution of time fractional differential equations, we propose a new method that combines spline quasi-interpolatory operators and collocation methods. We show that the method is convergent and reproduces polynomials of suitable degree. The numerical tests demonstrate the validity and applicability of the proposed method when used to solve linear time fractional differential equations

Spot-test identification and rapid quantitative sequential analysis of dipyrone

A qualitative spot-test and tandem quantitative analysis of dipyrone in the bulk drug and in pharmaceutical preparations is proposed. The formation of a reddish-violet color indicates a positive result. In sequence a quantitative procedure can be performed in the same flask. The quantitative results obtained were statistically compared with those obtained with the method indicated by the Brazilian Pharmacopoeia, using the Student's t and the F tests. Considering the concentration in a 100 µL aliquot, the qualitative visual limit of detection is about 5×10-6 g; instrumental LOD ≅ 1.4×10-4 mol L-1 ; LOQ ≅ 4.5×10-4 mol L-1.Um método spot-test qualitativo e seqüencialmente quantitativo é proposto para análise de dipirona em fármaco puro e em preparações farmacêuticas. A formação de coloração vermelho-violeta indica um resultado qualitativo positivo. Na seqüência, um procedimento quantitativo pode ser realizado no mesmo frasco. Os resultados quantitativos obtidos foram comparados estatisticamente com os resultados obtidos pelo método indicado pela Farmacopéia Brasileira, utilizando o teste t de Student e o teste F. Considerando a concentração em uma alíquota de 100 µL, o limite qualitativo visual de detecção foi de cerca 5×10-6 g; instrumentalmente o limite de detecção foi de LOD ≅ 1.4×10-4 mol L-1 e o limite de quantificação de LOQ ≅ 4.5×10-4 mol L-1.4146Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

A simplified reflectometric method for the rapid determination of dipyrone in pharmaceutical formulations

This paper describes a simple, portable and environmentally friendly method for the rapid determination of dipyrone in pharmaceuticals by using diffuse reflectance spectroscopy. The proposed method is based on the reflectance measurements of the orange compound produced from the spot test reaction between dipyrone and p-dimethylaminocinnamaldehyde (p-DAC), in acid medium, using a filter paper as solid support. Experimental design methodologies were used to optimize the measurement conditions. All reflectance measurements were carried out at 510 nm and the linear range was from 1.42 × 10-4-2.85 × 10-3 mol L-1, with a correlation coefficient of 0.999. The limit of detection (LOD) and the limit of quantification (LOQ) were 1.20 × 10-5 mol L-1 and 4.00 × 10-5 mol L-1, respectively. The intraday precision and interday precision were studied for 10 replicate analyses of 7.90 × 10-4 mol L-1 dipyrone solution. The coefficients of variation were 1.1 and 0.9%, respectively. The proposed method was applied successfully to the determination of dipyrone in commercial brands of pharmaceuticals. No interferences were observed from the common excipients in formulations. The results obtained by the proposed method were favorably compared with those given by the Brazilian Pharmacopoeia procedure at 95% confidence level. ©2007 Sociedade Brasileira de Química

Spectrophotometric determination of paracetamol in pharmaceuticals using microwave-assisted hydrolysis and a micellar medium

A new spectrophotometric method employing a micellar medium is proposed for the determination of paracetamol in pharmaceuticals. The method is based on the acid hydrolysis of paracetamol to p-aminophenol (PAP), which under acidic conditions reacts with p-dimethylaminocinnamaldehyde (pDAC), producing a red compound (λmax = 530 nm). This reaction can be enhanced five-fold in the presence of sodium dodecyl sulfate (SDS). The effects of all the parameters involved in both the hydrolysis step and the derivatization reaction were investigated using experimental design methodologies. The method presented a linear range of 0.2 to 3.9 μg mL–1 and an excellent correlation coefficient (r = 0.9996). The limit of detection was estimated to be 30.0 μg/L. The technique was successfully applied for the determination of paracetamol in commercial brands of pharmaceuticals. No interferences from the excipients commonly used in commercial formulations were observed, and the results obtained compared favorably with measurements made using the United States Pharmacopeia procedure, at a 95 % confidence level.Colegio de Farmacéuticos de la Provincia de Buenos Aire

Development of a potentiometric flufenamate ISE and its application to pharmaceutical and clinical analyses

The characteristics, performance, and application of an electrode, namely, Pt vertical bar Hg vertical bar Hg-2(FF)(2)vertical bar Graphite, where FF stands for flufenamate ion, are described. This electrode responds to FF with sensitivity of (-58.6 +/- 1.2) mV decade(-1) over the range 1.0 x 10(-6) - 1.0 x 10(-2) mol L-1 at pH 6.0-9.0 and a detection limit of 7.1 x 10(-7) mol L-1. The electrode is easily constructed at a relatively low cost with fast response time (within 10-25 s) and can be used for a period of 5 months without any considerable change in its performance characteristics. The proposed electrode displayed good selectivity for flufenamate in the presence of several substances as well as in the presence of some carboxylate and inorganic anions. The electrode was successfully applied to the determination of flufenamic acid in pharmaceuticals and human serum samples

A simple and green analytical method for the determination of formaldehyde

A green spectrophotometric analytical method for determination of formaldehyde in commercial samples was designed and investigated. Replacement of hazardous reagents was explored to attain the clean chemistry standards. The method is based on formaldehyde reaction with chromotropic acid in the presence of magnesium sulphate producing a stable complex Mg(2+)/cyclotetrachromotropylene (lambda(max) = 535 nm). To the best of our knowledge, there are no reports on the use of the above mentioned reaction for this determination. The experimental conditions were optimized by the response surface methodologies. Beer's Law is obeyed in a concentration range of 3 to 11 mg L(-1) of formaldehyde with a correlation coefficient of 0.999. The proposed method was applied for the determination of formaldehyde in commercial disinfectants and deffrizing hair products. The results were favorably compared with those of the official method, with good accuracy and precision

Traditional landscape and rural development: comparative study in three terraced areas in northern, central and southern Italy to evaluate the efficacy of GAEC standard 4.4 of cross compliance

The recent National Strategic Plan 2007-2013 has introduced landscape as a strategic objective of the rural sector. This represents a minor revolution in the way of visualizing the role of the landscape, together with that of agriculture and the rural territory as a whole, and demonstrates the importance of treating the landscape with a systematic point of view. As part of the Efficond project, three sample areas have been identified, each of about 800-1000 hectares, in zones with important historical - cultural landscapes that are included in the National Catalogue of Historical Rural Landscapes. For each sample area a methodology has been applied, defined Historical Cultural Evaluation Approach, developed as part of a project for the monitoring of the Tuscan landscape that we have simplified and adapted. This methodology is based on the consideration that the landscape is the result of the centuries-old interaction between man and the environment, and so to define an element of the landscape as characteristic it is necessary to evaluate the land use dynamics and landscape changes that took place in the past, identifying those that have persisted for a long time, are slowly evolving or stabilized. The study of the historical landscape, which in the proposed methodology refers to the 50’s, has been done through the interpretation and analysis of aerial photographs taken on the GAI flight in 1954, and has allowed the characteristic, traditional and historical elements of that landscape to be identified and an insight to be gained into the cultural identity of the area. Through the creation of specific indices of density and intensity of the terracing obtained by photo-interpretation, field surveys and GIS elaborations, it was possible to classify the sample areas for this specific and important landscape element, compare the results in two periods and evaluate their frequency in the territory. Multi-temporal comparative analysis is being used increasingly often, especially for the study of territories of value, and in our case has been accompanied both by mapping of the landscape dynamics, which identifies the areas subject to transformations in the considered period, and by tables and figures that allow the evolution of a unit of land use to be followed, observing how this has evolved over time. The evaluation of these evolutionary dynamics has then been integrated with a set of indices, in part borrowed from landscape ecology, and in part specifically developed for areas historically shaped by man, which demonstrate that the landscape has become less fragmented and that the layout of fields has been adapted to a different agricultural model that has profoundly changed the structure of the traditional landscape. The efficacy of the laws protecting the characteristic elements of the landscape is strictly linked to the maintenance of its diversity and typicality and conservation of the complexity of the landscape mosaic. Its evaluation necessitates a historical analysis of the evolutionary dynamics conducted at a purely local level