979 resultados para Riemann-Liouville derivatives and integrals of fractional order


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Chemical analysis carried out in leaves of 18 specimens of Piper aduncum L. (Piperaceae) occurring at Ripasa Reserve, Araraquara, SP, Brazil indicated two distinct populations when investigated over a period of 14 months (January 2000 to February 2001) and then submitted to cluster analysis. The two groups were characterized by accumulation of prenylated benzoic acids, chromenes and dihydrochalcone, respectively. A total of seven compounds were identified by HPLC analysis and compared with standards including two prenylated benzoic acid [aduncumene (1) and 3-(3'-7'-dimethyl-2'-6'-octadienyl)-4-methoxy-benzoic acid (5)], four chromenes [methyl 2,2-dimethyl-8-(3'-methyl-2'-butenyl)-2H-1-chromene-6-carboxylate (4), methyl 2,2-dimethyl-2H-1-chromene-6-carboxylate (2b), methyl 8-hydroxy-2,2-dimethyl-2H-1-chromene-6-carboxylate (3) and 2,2-dimethyl-2H-1-chromene-6-carboxylic acid (2a)] and one dihydrochalcone [2',6'-dihydroxy-4'-methoxy-dihydrochalcone (6)].

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The natural chlorophyll degradation results in noncolored chlorophyll catabolites (NCCs), but there are controversies if these are the final products. The formation and degradation of NCCs during soybean seed (Glycine max L. Merrill) maturation and two drying temperatures were investigated. Soybean was harvested at six maturation stages. The effect of postharvest drying at 40 and 60 degrees C on the NCC formation was analyzed by high-performance liquid chromatography (HPLC), and results were expressed as areas under the curve. All samples contained fractions with an absorption maximum at 320 nm, typical for NCC. The amounts of NCC increased until 114 days after planting and were significantly lower in advanced maturation stages. These results indicate that the NCC in soybeans might not be the final products of chlorophyll degradation. Their reduction in advanced maturation stages may be due to further metabolization. Heating soybeans at 40 and 60 degrees C promoted unnatural chlorophyll degradation and impaired the formation of NCC.

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The goal of this study is to produce oleanolic acid derivatives by biotransformation process using Mucor rouxii and evaluate their antimicrobial activity against oral pathogens. The microbial transformation was carried out in shake flasks at 30A degrees C for 216 h with shaking at 120 rpm. Three new derivatives, 7 beta-hydroxy-3-oxo-olean-12-en-28-oic acid, 7 beta,21 beta-dihydroxy-3-oxo-olean-12-en-28-oic acid, and 3 beta,7 beta,21 beta-trihydroxyolean-12-en-28-oic acid, and one know compound, 21 beta-hydroxy-3-oxo-olean-12-en-28-oic acid, were isolated, and the structures were elucidated on the basis of spectroscopic analyses. The antimicrobial activity of the substrate and its transformed products was evaluated against five oral pathogens. Among these compounds, the derivative 21 beta-hydroxy-3-oxo-olean-12-en-28-oic acid displayed the strongest activity against Porphyromonas gingivalis, which is a primary etiological agent of periodontal disease. In an attempt to improve the antimicrobial activity of the derivative 21 beta-hydroxy-3-oxo-olean-12-en-28-oic acid, its sodium salt was prepared, and the minimum inhibitory concentration against P. gingivalis was reduced by one-half. The biotransformation process using M. rouxii has potential to be applied to the production of oleanolic acid derivatives. Research and antimicrobial activity evaluation of new oleanolic acid derivatives may provide an important contribution to the discovery of new adjunct agents for treatment of dental diseases such as dental caries, gingivitis, and periodontitis.

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The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

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In this study we aimed at evaluating the effect of the major polar constituents of the medicinal plant Lychnophora ericoides on the production of inflammatory mediators produced by LPS-stimulated U-937 cells. The 6,8-di-C-beta-glucosylapigenin (vicenin-2) presented no effect on tumor necrosis factor (TNF)-alpha production, but inhibited, in a dose-dependent manner, the production of prostaglandin (PG) E(2) without altering the expression of cyclooxygenase (COX) -2 protein. 3,5-Dicaffeoylquinic acid and 4,5-dicaffeoylquinic acid, at lower concentrations, had small but significant effects on reducing PG E, levels; at higher doses these compounds stimulated PGE(2) and also TNF-alpha production by the cells. All the caffeoylquinic acid derivatives, in a dose-dependent fashion, were able to inhibit monocyte chemoattractant protein-3 synthesis/release, with 4,5-DCQ being the most potent at the highest tested concentration. These results add important information on the effects of plant natural polyphenols, namely vicenin-2 and caffeoylquinic acid derivatives, on the production of inflammatory mediators by cultured cells.

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The synthesis, characterization and copper(II) coordination chemistry of three new cyclic peptide ligands, PatJ(1) (cyclo-(Ile -Thr- (Gly)Thz-lle-Thr(Gly)Thz)), PatJ(2) (cyclo-(Ile-Thr(Gly)Thz-(D)-Ile-Thr-(Gly)Thz)), and PatL (cyclo-(Ile-Ser-(Gly)Thz-Ile-Ser(Gly)Thz)) are reported. All of these cyclic peptides and PatN (cyclo-(Ile-Ser(Gly)Thz-Ile-Thr-(Gly)Thz)) are derivatives of patellamide A and have a [24]azacrown-8 macrocyclic structure. All four synthetic cyclic peptides have two thiazole rings but, in contrast to patellamide A, no oxazoline rings. The molecular structure of PatJ1, determined by X-ray crystallography, has a saddle conformation with two close-to-co-parallel thiazole rings, very similar to the geometry of patellamide D. The two coordination sites of PatJ1 with thiazole-N and amide-N donors are each well preorganized for transition metal ion binding. The coordination of copper(II) was monitored by UV/Vis spectroscopy, and this reveals various (meta)stable mono- and dinuclear copper(II) complexes whose stoichiometry was confirmed by mass spectra. Two types of dinuclear copper(II) complexes, [Cu-2(H4L)(OH2)(n)](2+) (n = 6, 8) and [Cu-2(H4L)(OH2)(n)] (n=4, 6; L=PatN, PatL, PatJ1, PatJ2) have been identified and analyzed structurally by EPR spectroscopy and a combination of spectra simulations and molecular mechanics calculations (MM-EPR). The four structures are similar to each other and have a saddle conformation, that is, derived from the crystal structure of PatJ(1) by a twist of the two thiozole rings. The small but significant structural differences are characterized by the EPR simulations.

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We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

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We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

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In this paper, two wind turbines equipped with a permanent magnet synchronous generator (PMSG) and respectively with a two-level or a multilevel converter are simulated in order to access the malfunction transient performance. Three different drive train mass models, respectively, one, two and three mass models, are considered in order to model the bending flexibility of the blades. Moreover, a fractional-order control strategy is studied comparatively to a classical integer-order control strategy. Computer simulations are carried out, and conclusions about the total harmonic distortion (THD) of the electric current injected into the electric grid are in favor of the fractional-order control strategy.

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Power converters play a vital role in the integration of wind power into the electrical grid. Variable-speed wind turbine generator systems have a considerable interest of application for grid connection at constant frequency. In this paper, comprehensive simulation studies are carried out with three power converter topologies: matrix, two-level and multilevel. A fractional-order control strategy is studied for the variable-speed operation of wind turbine generator systems. The studies are in order to compare power converter topologies and control strategies. The studies reveal that the multilevel converter and the proposed fractional-order control strategy enable an improvement in the power quality, in comparison with the other power converters using a classical integer-order control strategy. (C) 2010 Elsevier Ltd. All rights reserved.

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This paper is on variable-speed wind turbines with permanent magnet synchronous generator (PMSG). Three different drive train mass models and three different topologies for the power-electronic converters are considered. The three different topologies considered are respectively a matrix, a two-level and a multilevel converter. A novel control strategy, based on fractional-order controllers, is proposed for the wind turbines. Simulation results are presented to illustrate the behaviour of the wind turbines during a converter control malfunction, considering the fractional-order controllers. Finally, conclusions are duly drawn. Copyright (C) 2010 John Wiley & Sons, Ltd.

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We show that suspended nano and microfibres electrospun from liquid crystalline cellulosic solutions will curl into spirals if they are supported at just one end, or, if they are supported at both ends, will twist into a helix of one handedness over half of its length and of the opposite handedness over the other half, the two halves being connected by a short straight section. This latter phenomenon, known as perversion, is a consequence of the intrinsic curvature of the fibres and of a topological conservation law. Furthermore, agreement between theory and experiment can only be achieved if account is taken of the intrinsic torsion of the fibres. Precisely the same behaviour is known to be exhibited by the tendrils of climbing plants such as Passiflora edulis, albeit on a lengthscale of millimetres, i.e., three to four orders of magnitude larger than in our fibres. This suggests that the same basic, coarse-grained physical model is applicable across a range of lengthscales.

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For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.