161 resultados para Fractional Derivatives and Integrals


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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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The influence of the axial organic ligand R on the electrochemical oxidation of the compounds [RCoIII(salen)DMF)], where salen is bis(salicylaldehyde)ethylenediimine, and R CH3, C2H5, n-C3H7, n-C4H9, s-C4H9, i-C4H9, CH2Cl, CF3CH2, c-C6H11CH2, c-C6H11, C6H5, C6H5CH2, p-CH3C6H4CH2, and p-NO2C6H4CH2, was studied by means of cyclic voltametry in dimethylformamide (DMF), 0.2 M in tetraethylammonium perchlorate (TEAP), at 25 and -20°C, with a platinum disc working electrode. The above-mentioned compounds can be classified according to their electrochemical behavior. (a) The complexes with R CH3, C2H5, n-C3H7, n-C4H9, c-C6H11CH2, and C6H5 undergo a reversible one-electron oxidation in the 10-50 V s-1 potential scan range. At slower scan rates, the oxidized product decomposes chemically. At -20°C, this chemical step is slow, and a reversible one-electron electrochemical oxidation is observed. (b) The compounds with R CH2Cl, C6H5CH2, p-CH3C6H4CH2 and p-NO2C6H4CH2 undergo a quasi-reversible one-electron oxidation at room temperaure. At -20°C, the electrochemical process becomes more complex. A following chemical reactions is coupled to the quasi-reversible one-electron transfer. Two reduction peaks are observed. (c) The compounds with R i-C4H9, s-C4H9, and c-C6H11 undergo a reversible one-electron oxidation at -20°C. At room temperature, the irreversible chemical reaction following the electron transfer step is too fast to allow the isolation of the electrochemical step. (d) At -20°C, the derivatives with R C2H5, c-C6H11 CH2 and c-C6H11 are adsorbed at the electrode surface. Evidence indicates that the reagent in these reactions is the pentacoordinated species [RCoIII(salen)]. A linear free-energy relationship between E1/2 (for reversible processes) and the Taft polar parameters o* was obtained with a slope of ρ* = 0.25 ± 0.03. As expected, the benzyl derivatives which present mesomeric effects do not fit this polar correlation. The rated of the electrochemical oxidation is also affected by the nature of the ligand R. For the ligands which are strong electron-withdrawing groups and for the benzyl derivatives, the rate of the electrochemical oxidation of the metal ion decreases at room temperature. At lower temperatures, it is suggested that the oxidation to the CoIV-R species is followed by a chemical reaction in which this complex is partly transformed into a CoIII(R*) species, which is reduced at a much more cathodic potential than the Co(IV) species. © 1979.

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The complexes MeHgL and PhHgL (HL = 2-mercaptobenzothiazole) have been obtained from the reaction of the ligand with methylmercury hydroxide and phenylmercury acetate, respectively, in methanol. MeHgL, which has been characterized by single-crystal X-ray diffraction analysis (crystal data: triclinic, space group P1, with a = 8.009 (4) Å, b = 10.042 (4) Å, c = 13.074 (3) Å, α = 101.25 (2)°, β = 102.61(3)°, γ = 101.42 (3)°, R = 0.067), crystallizes with two independent molecules, I and I′, contained in each asymmetric unit with a coordination geometry based on the almost linear C-Hg-S group (Hg-S = 2.369 (6) Å, Hg-C = 2.06 (2) Å, and C-Hg-S = 177.7 (7)° for I; Hg-S = 2.375 (6) Å, Hg-C = 2.10 (3) Å, and C-Hg-S = 178.8 (6)° for I′). A secondary intramolecular interaction between the mercury atom and the C=N group of the ring and some weak intermolecular interactions between the metal and sulfur atoms were also found. The vibrational spectra of this compound and the phenylmercury(II) compound are discussed in light of the crystal structure. Diagnostic criteria of the bonding modes for the ligand are assessed. © 1985 American Chemical Society.

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Some derivatives of 2-mercaptobenzoxazole (HL) of the type MRnL [M = Hg or Tl, R = Me or Ph and n = 1 (Hg) or 2 (Tl)] have been prepared. The structure of HgMeL has been determined by an X-ray diffraction study; in the crystal there are two independent planar molecules in each asymmetric unit, with the ligand in its thiolic form and an almost linear CHgS linkage. Weak intramolecular and intermolecular secondary interactions complement the mercurysulphur bond. The spectroscopic (IR, Raman, mass, 13C-NMR), conductimetric, and dipolar properties of this and the other compounds are discussed. © 1991.

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Thin films of chemically synthesized polyaniline and poly(o-methoxyaniline) were exposed to ionizing X-ray radiation and characterized by radiation induced conductivity measurements, ultraviolet-visible spectroscopy, electron paramagnetic resonance, electrical conductivity and solubility measurements. Samples irradiated in vacuum or dry Oxygen atmosphere did not have their electronic spectra changed. However, under humid atmosphere the energy of the excitonic transition was decreased and accompanied by a great conductivity increase. The results indicate that doping of polyaniline can be induced by X-ray radiation which might be of great interest for applications on lithography and microelectronics.

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The crystal and molecular structures of the following molecules have been determined: 1-acetyl-indoline, 1-acetyl-5-nitro-indoline, 1-acetyl-5-nitro-7-bromo-indoline, 1-acetyl-5-bromo-7-nitro-indoline, and 1-acetyl-5-bromo-7-nitro-indol. Molecular orbital calculations are performed for these compounds and two related species.

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The negative-dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method gives solutions in different regions of external momenta simultaneously. Moreover, it is a technique whereby the difficulties associated with performing parametric integrals in the standard approach are transferred to a simpler solving of a system of linear algebraic equations, thanks to the polynomial character of the relevant integrands. We employ this method to evaluate a scalar integral for a massless two-loop three-point vertex with all the external legs off-shell, and consider several special cases for it, yielding results, even for distinct simpler diagrams. We also consider the possibility of NDIM in non-covariant gauges such as the light-cone gauge and do some illustrative calculations, showing that for one-degree violation of covariance (i.e. one external, gauge-breaking, light-like vector n μ) the ensuing results are concordant with the ones obtained via either the usual dimensional regularization technique, or the use of the principal value prescription for the gauge-dependent pole, while for two-degree violation of covariance - i.e. two external, light-like vectors n μ, the gauge-breaking one, and (its dual) n * μ - the ensuing results are concordant with the ones obtained via causal constraints or the use of the so-called generalized Mandelstam-Leibbrandt prescription. © 1999 Elsevier Science B.V.

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Strontium complexes of 5,7-dibromo-, 5,7-dichloro-, 7-iodo- and 5-chloro-7-iodo-8-hydroxyquinoline were precipitated from an aqueous ammonia and acetone medium. The complexes obtained were Sr[(C9H4ONBr2)2]·2.5H 2O; Sr[(C9H4ONCl2)(OH)]·1.5H2O; Sr[(C9H5ONI)2]·5H2O and Sr[(C9H4ONICl)(OH)]·1.25H2O. The residues of their thermal decomposition were SrBr2; a mixture of SrCl2, SrCO3 and SrO3 SrCO3, and SrCO3, respectively. All were characterized by means of thermogravimetry, differential thermal analysis, complexometry with EDTA, atomic absorption spectroscopy, IR spectroscopy and X-ray diffraction. © 1999 Akadémiai Kiadó.

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We apply the negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone, and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, regardless of which gauge choice that originated them. In the Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing to two-point functions without any kind of prescriptions, since NDIM can abandon such devices - this calculation is the first test of our prescriptionless method beyond one-loop order; and finally, for the Coulomb gauge we consider a four-propagator massless loop integral, in the split-dimensional regularization context. © 2001 Academic Press.

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The aim of the study was to investigate the anti-trypanocidal activities of natural chromene and chromene derivatives. Five chromenes were isolated from Piper gaudichaudianum and P. aduncum, and a further seven derivatives were prepared using standard reduction, methylation and acetylation procedures. These compounds were assayed in vitro against epimastigote forms of Trypanosoma cruzi, the causative agent of Chagas disease. The results showed that the most of the compounds, especially those possessing electron-donating groups as substituents on the aromatic ring, showed potent trypanocidal activity. The most active compound, [(2S)-methyl-2-methyl-8-(3″-methylbut-2″-enyl)-2- (4′-methylpent-3′-enyl)-2H-chromene-6-carboxylate], was almost four times more potent than benznidazole (the positive control) and showed an IC 50 of 2.82 μM. The results reveal that chromenes exhibit significant anti-trypanocidal activities and indicate that this class of natural product should be considered further in the development of new and more potent drugs for use in the treatment of Chagas disease. © 2008 Pharmaceutical Society of Japan.

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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)]. © 2009 Academic Journals.

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In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product where α >-1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative. © 2011 American Mathematical Society.

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This paper deals with a system involving a flexible rod subjected to magnetic forces that can bend it while simultaneously subjected to external excitations produces complex and nonlinear dynamic behavior, which may present different types of solutions for its different movement-related responses. This fact motivated us to analyze such a mechanical system based on modeling and numerical simulation involving both, integer order calculus (IOC) and fractional order calculus (FOC) approaches. The time responses, pseudo phase portraits and Fourier spectra have been presented. The results obtained can be used as a source for conduct experiments in order to obtain more realistic and more accurate results about fractional-order models when compared to the integer-order models. © Published under licence by IOP Publishing Ltd.

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In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems. © 2012 American Institute of Physics.