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.

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.

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution.

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.

Bioatividade da quinoxalina 1,4-dióxido e seus derivados

O objetivo deste estudo consiste em avaliar a atividade antimicrobiana da quinoxalina 1,4-dióxido e alguns dos seus derivados em estirpes bacterianas e leveduras. Os compostos estudados foram a quinoxalina 1,4-dióxido (QNX), 2-metilquinoxalina-1,4-dióxido (2MQNX), 2-metil-3-Benzoilquinoxalina-1,4-dióxido (2M3BenzoilQNX), 2-metil-3-benzilquinoxalina-1,4-dióxido (2M3BQNX), 2-amino-3-cianoquinoxalina-1,4-dióxido (2A3CQNX), 3-metil-2-quinoxalinacarboxamida-1,4-dióxido (3M2QNXC), 2-hidroxifenazina–N-dióxido (2HF) e 3-metil-N-(2-metilphenil)quinoxalinacarboxamida-1,4-dioxido (3MN(2MF)QNXC). Os modelos procariotas selecionados para este estudo foram o Staphylococcus aureus ATCC 6538, Staphylococcus aureus ATCC 6538P, Staphylococcus aureus ATCC 29213, Escherichia coli ATCC 25922, Escherichia coli S3R9, Escherichia coli S3R22, Escherichia coli TEM CTX-M9, Escherichia coli TEM-1, Escherichia coli AmpC MOX-2, Escherichia coli CTX-M2 e Escherichia coli CTX-M9. A Candida albicans ATCC 10231 e a Saccharomyces cerevisiae PYCC 4072 constituíram os modelos eucariotas deste estudo. Para os compostos químicos que apresentem atividade pelo método de difusão em disco, será determinada a Concentração Mínima Inibitória (CMI), bem como a viabilidade e o crescimento (na presença e na ausência dos compostos químicos). Os resultados deste estudo mostram atividade antimicrobiana para a maioria dos compostos estudados em todos os modelos procariotas Gram negativos, à exceção da E.coli CTX-M2 e CTX-M9 e nenhuma atividade nos modelos eucariotas. O estudo da viabilidade/curvas de morte em bactérias e num modelo eucariota (S.cerevisiae) sugerem que alguns destes compostos constituem potenciais drogas para a quimioterapia antibacteriana.

Macrociclos tetrapirrólicos e produtos de contraste iodados: uma nova abordagem

O trabalho descrito no presente documento reporta a preparação de derivados tetrapirrólicos iodados de tipo porfirina tornando-os potenciais veículos a meio de contraste iodado, usado em radiodiagnóstico. Com os resultados deste trabalho irá ser realizado um pedido de patente das moléculas e portanto, o acesso a este trabalho será restrito nos termos do Código da Propriedade Industrial, aprovado pelo Decreto de Lei nº 36/2003 de 5 de Março. Na primeira fase do trabalho, foi sintetizado o derivado porfirínico simétrico, meso-substituído, contendo um total de 8 iodos. Este foi preparado por condensação do pirrol e do aldeído iodado em meio ácido e na presença de nitrobenzeno. Foram ainda preparados as respetivas metaloporfirinas contendo os iões metálicos de manganês e gadolínio. Posteriormente foi avaliada a capacidade destes derivados atenuarem o feixe de raio-X, através da mediação das Unidades de Hounsfield, após serem adquiridas imagens por Tomografia Computorizada. Na segunda fase do trabalho procedeu-se ao estudo da influência destes compostos na diferenciação celular, usando como modelo as células de pré-adipócitos 3T3-L1. Foi avaliada a diferenciação celular, através da quantificação de lípidos das células maduras, marcados com Red Oil O, por espectrofotometria de Visível 3 e 10 dias após a administração dos derivados em estudo.

A long-term risk management tool for electricity markets using swarm intelligence

This paper addresses the optimal involvement in derivatives electricity markets of a power producer to hedge against the pool price volatility. To achieve this aim, a swarm intelligence meta-heuristic optimization technique for long-term risk management tool is proposed. This tool investigates the long-term opportunities for risk hedging available for electric power producers through the use of contracts with physical (spot and forward contracts) and financial (options contracts) settlement. The producer risk preference is formulated as a utility function (U) expressing the trade-off between the expectation and the variance of the return. Variance of return and the expectation are based on a forecasted scenario interval determined by a long-term price range forecasting model. This model also makes use of particle swarm optimization (PSO) to find the best parameters allow to achieve better forecasting results. On the other hand, the price estimation depends on load forecasting. This work also presents a regressive long-term load forecast model that make use of PSO to find the best parameters as well as in price estimation. The PSO technique performance has been evaluated by comparison with a Genetic Algorithm (GA) based approach. A case study is presented and the results are discussed taking into account the real price and load historical data from mainland Spanish electricity market demonstrating the effectiveness of the methodology handling this type of problems. Finally, conclusions are dully drawn.

Antimicrobial activity of pyrazine and quinoxaline N,N’-dioxide heterocyclic compounds

The nitrogen heterocyclic organic compounds 1,4 dioxide pyrazine and quinoxaline derivatives have been widely studied due to their potential use as synthetic drugs. The thermochemical study of three N,N´-dioxides: 2,3,5-trimethylpyrazine-1,4-dioxide, tetramethylpyrazine-1,4-dioxide and 6-chloro-2,3-dimethilquinoxaline 1,4-dioxide has been recently developed in order to establish relationships among the energetical, structural and reactivity properties [4,5]. Several studies have reported their pharmacological activity, particularly as antimicrobial agents [1,2,3]. It has also been established a relation between energetical and structural properties and biological activity, once these compounds present N – oxide bonds, increasing their oxidative capacity. The present work reports the study of antimicrobial activity for those compounds against the bacteria Geobacillus stearothermophylus, Staphylococcus aureus, Streptococcus agalactiae, Escherichia coli and also against the yeasts Saccharomyces cerevisiae PYCC 4072, Candida albicans PYCC3436T, Candida tropicalis PYCC, Issatchenka Orientalis PYCC. The determination of the minimal inhibitory concentration (MIC), points to an antimicrobial activity and the preliminary results indicate that these compounds may be potential candidates as antimicrobial drugs with clinical, agriculture or food industries applications.

Anti-pneumoscystis carinni activitiy of primaquine imidazolidin-4-ones

Pneumocystis pneumonia (PCP) is one of the most frequent causes of mortality among HIV-infected patients. Primaquine (PQ) is an antimalarial 8-aminoquinoline effective against PCP when given in combination with clindamycin. This has drawn the attention of Medicinal Chemists towards the anti-PCP activity of 8-aminoquinolines, not only confined to those exhibiting antimalarial activity [1]. It is thought that anti-PCP 8-aminoquinolines exert their anti-PCP activity by acting on the electronic transport and redox system of the P. carinii pathogen [1]. Recently, our research group has been developing imidazolidin-4-one derivatives of PQ (Scheme 1), targeting novel compounds with improved therapeutic action, namely, higher resistance to metabolic inactivation, lower toxicity and equal or higher antimalarial activity than that of the parent drug [2,3]. These imidazolidin-4-ones were seen to block the transmission of rodent malaria, caused by Plasmodium berghei on BalbC mice, to the mosquito vector Anopheles stephensi [3]. The anti-PCP activity of our PQ derivatives is now under study and preliminary in vitro assays [4] show that some of the compounds exhibit slight to moderate activity after a 72 h incubation period against P. carinii. In one case, the IC50 was comparable to that of parent PQ. Both these studies and forthcoming results from ongoing biological assays will be presented and discussed.

Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Derivative-free nonlinear optimization filter simplex

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.