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.

Glucose-6-phosphate dehydrogenase and glutathione reductase activity in methemoglobin reduction by methylene blue and cyst amine: study on glucose-6-phosphate dehydrogenase-deficient individuals, on normal subjects and on riboflavin-treated subjects

The authors have standardized methods for evaluation of the activity of the glucose-6-phosphate dehydrogenase and of glutathione reductase. The general principle of the first method was based on methemoglobin formation by sodium nitrite followed by stimulation of the glucose-6-phosphate dehydrogenase with methylene blue. Forty six adults (23 males and 23 females) were studied. Subjects were not G6PD deficient and were aged 20 to 30 years. The results showed that methemoglobin reduction by methylene blue was 154.40 and 139.90 mg/min (p<0.05) for males and females, respectively, in whole blood, and 221.10 and 207.85 mg/min (n.s.), respectively, in washed red cells. These data showed that using washed red cells and 0.7g% sodium nitrite concentration produced no differences between sexes and also shortened reading time for the residual amount of methemoglobin to 90 minutes. Glutathione reductase activity was evaluated on the basis of the fact that cystamine (a thiol agent) binds to the SH groups of hemoglobin, forming complexes. These complexes are reversed by the action of glutathione reductase, with methemoglobin reduction occurring simultaneously with this reaction. Thirty two adults (16 males and 16 females) were studied. Subjects were not G6PD deficient and were aged 20 to 30 years. Methemoglobin reduction by cystamine was 81.27 and 91.13 mg/min (p<0.01) for males and females, respectively. These data showed that using washed red cells and 0.1 M cystamine concentration permits a reading of the residual amount of methemoglobin at 180 minutes of incubation. Glutathione reductase activity was evaluated by methemoglobin reduction by cystamine in 14 females before and after treatment with 10 mg riboflavin per day for 8 days. The results were 73.69 and 94.26 jug/min (p<0.01) before and after treatment, showing that riboflavin treatment increase glutathione reductase activity even in normal individuals. Three Black G6PD-deficient individuals (2 males and 1 female) were also studied. The G6PD and glutathione reductase were partially activated, the change being more intense in males. On the basis of race and of the laboratory characteristics observed, it is possible to suggest that the G6PD deficiency of these individuals is of the African type and that the female is heterozygous for this deficiency. Analysis of the results as a whole permitted us to conclude that the methods proposed here were efficient for evaluating the activity of the glucose-6-phosphate dehydrogenase and of glutathione reductase. The latter is dependent on the pentose pathway, which generates NADPH, and on riboflavin, a FAD precursor vitamin.

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.

Biological activity of well defined hydantoin derivatives on efflux pump systems of bacteria and cancer cells

A multi-resistência a antibióticos e medicamentos usados em quimioterapia é um dos grandes problemas com os quais as instituições de saúde se debatem hoje em dia. A acção provocada por bombas de efluxo é uma das suas causas. Estas bombas têm uma importância fundamental, uma vez que, ao expelirem todo o tipo de tóxicos para o exterior das células, também expelem medicamentos, fazendo com que estes não tenham o efeito desejado dentro delas. As bombas de efluxo são transportadores que se encontram nas membranas de todo o tipo de células. Existem dois grandes tipos de bombas de efluxo: as primárias e as secundárias. As primeiras conferem multi-resistência principalmente em células eucariotas, como as células do cancro em humanos, tendo como função a mediação da repulsa de substâncias tóxicas por intermédio da hidrólise de ATP. A primeira a ser descoberta e mais estudada destas bombas foi a ABCB1 que é o gene que codifica a glicoproteína-P (P de permeabilidade). Enquanto as secundárias, que são a maior fonte de multi-resistência em bactérias, promovem a extrusão de substâncias tóxicas através da força motriz de protões. Neste tipo de bombas são conhecidas quatro famílias principais, das quais uma das mais importantes é a superfamília RND, uma vez que inclui a bomba AcrAB-TolC, que é muito importante no metabolismo xenobiótico de bactérias Gramnegativas, nomeadamente a E.coli. Com o objectivo de reverter a multi-resistência, tanto em células eucariotas como procariotas, têm-se desenvolvido estratégias de combate que envolvem a descoberta de substâncias que inibam as bombas de efluxo. Assim sendo, ao longo dos tempos têm sido descobertas variadas substâncias que cumprem este objectivo. É o caso, por exemplo, dos derivados de fluoroquinolonas usados como inibidores de bombas de efluxo em bactérias ou do Tamoxifen, utilizado na terapia de pacientes com cancro da mama. Um dos grupos de substâncias estudados para o desenvolvimento de possíveis compostos que actuem como reversores de multi-resistência são os compostos derivados de hidantoínas. Estes, são conhecidos por possuírem uma grande variedade de propriedades bioquímicas e farmacológicas, sendo portanto usados para tratarem algumas doenças em humanos, como a epilepsia. Nestes, estão englobados compostos com actividade anti-convulsão que constitui a sua grande mais-valia e, dependente da substituição no anel que os constitui, uma grande variedade de outras propriedades farmacológicas como a anti-fungica, a anti-arritmica, a anti-viral, a anti-diabética ou por exemplo a antagonização de determinados receptores, como os da serotonina. Apesar de pouco usados em estudos experimentais para desenvolver substâncias anti-carcinogénicas, existem alguns estudos com este efeito. Objectivos: O presente projecto envolve o estudo de bombas de efluxo primárias e secundárias, em células eucariotas e procariotas, respectivamente. Em bactérias, foram usados quatro modelos experimentais: Staphylococcus aureus ATCC 25923, Enterococcus faecalis ATCC 29212, E. coli AG 100 e Salmonella Enteritidis NCTC 13349. Em células de cancro foram usadas, células T de linfoma de rato parentais e células T de linfoma de rato transfectadas com o gene humano MDR-1. O principal objectivo deste estudo foi a pesquisa de novos moduladores de bombas de efluxo presentes em bactérias e células do cancro, tentando assim contribuir para o desenvolvimento de novos agentes farmacológicos que consigam reverter a multi-resistência a medicamentos. Assim sendo foram testados trinta compostos derivados de hidantoínas: SZ-2, SZ-7, LL-9, BS-1, JH-63, MN-3, TD-7k, GG-5k, P3, P7, P10, P11, RW-15b, AD-26, RW-13, AD-29, KF-2, PDPH-3, Mor-1, KK-XV, Thioam-1, JHF-1, JHC-2, JHP-1, Fur-2, GL-1, GL-7, GL-14, GL-16, GL-18. Como forma de atingir estes objectivos, a actividade biológica dos trinta compostos derivados de hidantoínas foi avaliada nas quatro estirpes de bactérias da seguinte forma: foram determinadas as concentrações mínimas inibitórias dos trinta compostos como forma de definir as concentrações em que os compostos seriam utilizados. Os compostos foram posteriormente testadas com um método fluorométrico de acumulação de brometo de etídeo, que é um substrato comum em bombas de efluxo bacterianas, desenvolvido por Viveiros et al. A actividade biológica dos compostos derivados de hidantoínas nas células de cancro foi demonstrada por diferentes métodos. O efeito anti-proliferativo e citotóxico dos trinta compostos foi avaliado nas células T de linfoma de rato transfectadas com o gene humano MDR-1 pelo método de thiazolyl de tetrazólio (MTT). Como o brometo de etídeo também é expelido pelos transportadores ABC, estes compostos foram posteriormente testados com um método fluorométrico de acumulação de brometo de etídeo desenvolvido por Spengler et al nos dois diferentes tipos de células eucariotas. Resultados: A maioria dos compostos derivados de hidantoínas foi eficaz na modulação de bombas de efluxo, nas duas estirpes de bactérias Gram-negativas e nos dois diferentes tipos de células T de linfoma. Em contraste com estes resultados, nas duas estirpes de células Gram-positivas, a maioria dos compostos tiveram pouco efeito na inibição de bombas de efluxo ou até nenhum, em muitos dos casos. De uma maneira geral os melhores compostos nas diferentes estirpes de bactérias foram: Thioam-1, SZ-2, P3, Rw-15b, AD-26, AD-29, GL-18, GL-7, KF-2, SZ-7, MN-3, GL-16 e GL- 14. Foram portanto estes os compostos que provocaram maior acumulação de brometo de etídeo, inibindo assim com maior eficácia as bombas de efluxo. No presente estudo, a maioria dos compostos conseguiu inibir a resistência provocada pela bomba de efluxo ABCB1, tanto nas células parentais bem como nas células que sobre-expressam esta bomba, causando a acumulação de brometo de etídeo dentro das células. As células que sobreexpressam a bomba ABCB1 foram posteriormente testadas com citometria de fluxo que é a técnica padrão para pesquisa de inibidores de bombas de efluxo. Os compostos que foram mais efectivos na inibição da bomba ABCB1, causando assim maior acumulação de brometo de etídeo nas células que sobre-expressam esta bomba foram: PDPH-3, GL-7, KK-XV, AD-29, Thioam-1, SZ-7, KF-2, MN-3, RW-13, LL-9, P3, AD-26, JH-63 e RW- 15b. Este facto não corroborou totalmente os resultados da citometria de fluxo uma vez que os moduladores que provocaram maior inibição da bomba ABCB1 foram o MN-3, JH-63 e o BS-1, sendo que o último não foi seleccionado como um bom composto usando o método fluorométrico de acumulação de brometo de etídeo. Conclusão: Os compostos derivados de hidantoínas testados tiveram maior efeito nas estirpes de bactérias Gram-negativas do que nas Gram-positivas. Relativamente às células eucariotas, as estruturas mais activas apresentam substituintes aromáticos bem como alguns fragmentos aminicos terciários.

Development of new biomaterials based on liquid crystalline phases of cellulose derivatives

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do Grau de Mestre em Engenharia Biomédica

Numerical calculation of the left and right fractional derivatives

The calculation of fractional derivatives is an important topic in scientific research. While formal definitions are clear from the mathematical point of view, they pose limitations in applied sciences that have not been yet tackled. This paper addresses the problem of obtaining left and right side derivatives when adopting numerical approximations. The results reveal the relationship between the resulting distinct values for different fractional orders and types of signals.