Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Using fractional derivatives for the joint ontrol of hexapod robots

This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

Fractional central differences and derivatives

Journal of Vibration and Control, 14(9–10): 1255–1266, 2008

SPE-LC-FD Determination of Polycyclic Aromatic Hydrocarbon Monohydroxy Derivatives in Cephalopods

A new analytical methodology, based on liquid chromatography with fluorescence detection (LC-FD), after extraction, enzymatic hydrolysis, and solid-phase extraction (SPE) through Oasis HLB cartridges, was developed and validated for the simultaneous determination of three monohydroxy derivatives of polycyclic aromatic hydrocarbons (PAHs). The optimized analytical method is sensitive, accurate, and precise, with recoveries between 62 and 110% and limits of detection of 227, 9, and 45 ng/g for 1-hydroxynaphthalene, 2-hydroxyfluorene, and 1-hydroxypyrene, respectively. Their levels were estimated in different cephalopod matrices (edible tissues and hemolymph). The methodology was applied to samples of the major cephalopod species consumed worldwide. Of the 18 samples analyzed, 39% were contaminated with 1-hydroxynaphthalene, which was the only PAH metabolite detected. Its concentration ranged from 786 to 1145 ng/g. This highly sensitive and specific method allows the identification and quantitation of PAH metabolites in forthcoming food safety and environmental monitoring programs.

The key role of coligands in novel ruthenium(II)-cyclopentadienyl bipyridine derivatives: Ranging from non-cytotoxic to highly cytotoxic compounds

A new family of eight ruthenium(II)-cyclopentadienyl bipyridine derivatives, bearing nitrogen, sulfur, phosphorous and carbonyl sigma bonded coligands, has been synthesized. Compounds bearing nitrogen bonded coligands were found to be unstable in aqueous solution, while the others presented appropriate stabilities for the biologic assays and pursued for determination of IC50 values in ovarian (A2780) and breast (MCF7 and MDAMB231) human cancer cell lines. These studies were also carried out for the [5: HSA] and [6: HSA] adducts (HSA = human serum albumin) and a better performance was found for the first case. Spectroscopic, electrochemical studies by cyclic voltammetry and density functional theory calculations allowed us to get some understanding on the electronic flow directions within the molecules and to find a possible clue concerning the structural features of coligands that can activate bipyridyl ligands toward an increased cytotoxic effect. X-ray structure analysis of compound [Ru(eta(5)-C5H5)(bipy)(PPh3)][PF6] (7; bipy = bipyridine) showed crystallization on C2/c space group with two enantiomers of the [Ru(eta(5)-C5H5)(bipy)(PPh3)](+) cation complex in the racemic crystal packing. (C) 2015 Elsevier Inc All rights reserved.

Microencapsulation of herbicide MCPA with native beta-cyclodextrin and its methyl and hydroxypropyl derivatives: An experimental and theoretical investigation

When a pesticide is released into the environment, most of it is lost before it reaches its target. An effective way to reduce environmental losses of pesticides is by using controlled release technology. Microencapsulation becomes a promising technique for the production of controlled release agricultural formulations. In this work, the microencapsulation of chlorophenoxy herbicide MCPA with native b-cyclodextrin and its methyl and hydroxypropyl derivatives was investigated. The phase solubility study showed that both native and b-CD derivatives increased the water solubility of the herbicide and inclusion complexes are formed in a stoichiometric ratio of 1:1. The stability constants describing the extent of formation of the complexes have been determined by phase solubility studies. 1H NMR experiments were also accomplished for the prepared solid systems and the data gathered confirm the formation of the inclusion complexes. 1H NMR data obtained for the MCPA/CDs complexes disclosed noticeable proton shift displacements for OCH2 group and H6 aromatic proton of MCPA provided clear evidence of inclusion complexation process, suggesting that the phenyl moiety of the herbicide was included in the hydrophobic cavity of CDs. Free energy molecular mechanics calculations confirm all these findings. The gathered results can be regarded as an essential step to the development of controlled release agricultural formulations containing herbicide MCPA.

Quinoxaline, its derivatives and applications: A state of the art review.

Quinoxaline derivatives are an important class of heterocycle compounds, where N replaces some carbon atoms in the ring of naphthalene. Its molecular formula is C8H6N2, formed by the fusion of two aromatic rings, benzene and pyrazine. It is rare in natural state, but their synthesis is easy to perform. In this review the State of the Art will be presented, which includes a summary of the progress made over the past years in the knowledge of the structure and mechanism of the quinoxaline and quinoxaline derivatives, associated medical and biomedical value as well as industrial value. Modifying quinoxaline structure it is possible to obtain a wide variety of biomedical applications, namely antimicrobial activities and chronic and metabolic diseases treatment.

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

The key role of coligands in novel ruthenium(II)-cyclopentadienyl bipyridine derivatives: ranging from non-cytotoxic to highly cytotoxic compounds

A new family of eight ruthenium(II)-cyclopentadienyl bipyridine derivatives, bearing nitrogen, sulfur, phosphorous and carbonyl sigma bonded coligands, has been synthesized. Compounds bearing nitrogen bonded coligands were found to be unstable in aqueous solution, while the others presented appropriate stabilities for the biologic assays and pursued for determination of IC50 values in ovarian (A2780) and breast (MCF7 and MDAMB231) human cancer cell lines. These studies were also carried out for the [5: HSA] and [6: HSA] adducts (HSA=human serum albumin) and a better performance was found for the first case. Spectroscopic, electrochemical studies by cyclic voltammetry and density functional theory calculations allowed us to get some understanding on the electronic flow directions within the molecules and to find a possible clue concerning the structural features of coligands that can activate bipyridyl ligands toward an increased cytotoxic effect. X-ray structure analysis of compound [Ru(η(5)-C5H5)(bipy)(PPh3)][PF6] (7; bipy=bipyridine) showed crystallization on C2/c space group with two enantiomers of the [Ru(η(5)-C5H5)(bipy)(PPh3)](+) cation complex in the racemic crystal packing.

A Review of Definitions for Fractional Derivatives and Integral

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

Modulação do estado redox em bactérias por quinoxalinas

As quinoxalinas são compostos heterocíclicos que têm, entre outras, capacidades antimicrobianas, inclusivamente contra bactérias resistentes aos antimicrobianos convencionais. Os mecanismos pelos quais estes compostos exercem a sua atividade ainda não está completamente esclarecido. O objetivo do presente estudo é avaliar o efeito redox em sinergismo/antagonismo com as quinoxalinas em modelos de bactérias com e sem resistências a antimicrobianos. No que se refere aos compostos foram utilizados a quinoxalina 1,4-dióxido (QNX), 2-metil-3-benzilquinoxalina-1,4-dióxido (2M3BQNX), 2-metilquinoxalina-1,4-dióxido (2MQNX) e a 2-amino-3-cianoquinoxalina-1,4-dióxido (2A3CQNX). Quanto aos modelos procariotas, foram utilizados a Salmonella enterica, Klebsiella pneumoniae, Enterococcus faecalis, Staphylococcus saprophyticus, Enterobacter aerogenes, Enterobacter cloacae, Staphylococcus aureus ATCC 25923, Methicillin-resistant Staphylococcus aureus ATCC 43300, Escherichia coli TEM 201 e Escherichia coli TEM 180. Nos compostos químicos em que se verificou a Concentração Mínima Inibitória (CMI), realizou-se o estudo do comportamento do crescimento bacteriano. Relativamente ao estado redox, foi avaliado para cada estirpe sensível, através do rácio GSH/GSSG, nas doses inibitórias e não inibitórias de cada composto. Os resultados apresentam que todos os compostos testados, à exceção do 2M3BQNX, têm atividade antimicrobiana na maioria das estirpes, excetuando a E. faecalis e a S. saprophyticus. Os rácios GSH/GSSG apontam para o efeito oxidante em K. pneumoniae e S. enterica e antioxidante na E. aerogenes. A conclusão do estudo sugere que os compostos apresentam elevada capacidade antibacteriana e influência no equilíbrio redox das bactérias, podendo contribuir para o esclarecimento do mecanismo de ação dos derivados das quinoxalinas 1-4 dióxido, nas bactérias.