94 resultados para Simultaneous Diophantine approximations


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A method has been developed for the simultaneous determination of Al, As, Cu, Fe, Mn, and Ni in fuel ethanol by graphite furnace atomic absorption spectrometry (GFAAS) using a transversely heated graphite atomizer (THGA) with longitudinal Zeeman-effect background correction. The thermal behavior of analytes during the pyrolysis and atomization stages using the mixture Pd(NO3)(2) + Mg(NO3)(2) as the chemical modifier was investigated in 0.028 mol L-1 HNO3, 0.14 mol L-1 HNO3, and diluted ethanol (1 + 1, v/v) containing different nitric acid concentrations. With 5 rhog Pd + 3 mug Mg as the modifiers, pyrolysis and atomization temperatures of the heating program of the atomizer were fixed at 1200 C and 2200degreesC respectively. For 20 muL of diluted sample (10 muL ethanol + 10 muL of 0.28 mol L-1 HNO3) dispensed into the graphite tube, analytical curves in the 2.0 - 50 mug L-1 Al, As, Cu, Fe, Mn, Ni ranges were established. The calculated characteristic masses were - 37 pg Al, 73 pg As, 31 pg Cu, 16 pg Fe, 9 pg Mn, and 44 pg Ni, and the lifetime of the tube was around 2 50 firings. The limits of detection (LOD) based on integrated absorbance were 1.2 mug L-1 Al, 2.5 mug L-1 As. 0.22 mug L-1 Cu, 1.6 L-1 Fe 0.20 mug L-1 Mn 1.1 mug L-1 Ni. The relatively standard deviations (n = 12) were less than or equal to 3%, less than or equal to 6%, less than or equal to 2%, less than or equal to 3.4%, less than or equal to 1.3%, and less than or equal to 2% for Al, As, Cu, Fe, Mn, and Ni, respectively, the recoveries of Al, As, Cu, Fe, Mn and Ni added to fuel ethanol samples varied from 77% to 112%, 92% to 114%, 104% to 113%, 73% to 116%, 91% to 122% and 93% to 116%, respectively. Accuracy was checked for Al, As, Cu, Fe, Mn, and Ni determination in 20 samples purchased at local gas stations in Araraquara city, Brazil. A paired t-test showed that the results were in agreement at the 95% confidence level with those obtained by single-element GFAAS.

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A new, versatile, and simple method for quantitative analysis of zinc, copper, lead, and cadmium in fuel ethanol by anodic stripping voltammetry is described. These metals can be quantified by direct dissolution of fuel ethanol in water and subsequent voltammetric measurement after the accumulation step. A maximum limit of 20% (v/v) ethanol in water solution was obtained for voltammetric measurements without loss of sensitivity for metal species. Chemical and operational optimum conditions were analyzed in this study; the values obtained were pH 2.9, a 4.7-mum thickness mercury film, a 1,000-rpm rotation frequency of the working electrode, and a 600-s pre-concentration time. Voltammetric measurements were obtained using linear scan (LSV), differential pulse (DPV), and square wave (SWV) modes and detection limits were in the range 10(-9)-10(-8) mol L-1 for these metal species. The proposed method was compared with a traditional analytical technique, flame atomic absorption spectrometry (FAAS), for quantification of these metal species in commercial fuel ethanol samples.

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Iridium-, Ru-, and W-coated platforms were prepared by thermal treatment of the transversely heated graphite atomizer and investigated for the simultaneous determination of As, Bi, Pb, Sb, and Se in tap water by electrothermal atomic absorption spectrometry. The maximum pyrolysis temperature for As and Bi increased in a modifier sequence W < Ru < Ir. For Pb, Sb, and Se, this sequence was W < Ru, It. Calculated characteristic masses in the presence of It, Ru, and W were 35, 33, and 35 pg for As; 63, 51, and 52 pg for Bi; 50, 32, and 34 pg for Pb; 40, 35, and 31 pg for Sb; and 39, 39, and 93 pg for Se, respectively. Ruthenium was elected as the optimum modifier.Repeatability of the measurements was typically < 6%. Recoveries of As, Bi, Pb, Sb, and Se added to tap water samples varied from 79 to 109%. Accuracy was also checked by analysis of five certified reference materials (CRMs) from the National Institute of Standards and Technology (NIST1640 - Trace Elements in Natural Water; NIST 1643d Trace Elements in Water) and High Purity Standards (Trace Metals in Drinking Water Standards, lots #812708, #591107, and #710710). A paired t-test showed that the results for the CRMs were in agreement at the 95% confidence level with the certified values. The graphite tube lifetime was about 650 firings. multi-element determination is particularly challenging due to the necessity of carefully optimizing compromise conditions.Based on the considerations listed above, the aim of this paper was to evaluate the behavior of Ir, Ru, and W as permanent modifiers for the simultaneous determination of As, Bi, Pb, Sb, and Se. The performance of the proposed procedure was also verified after the ETAAS analysis of tap waters and reference materials.

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A method has been developed for the direct simultaneous determination of Cd and Pb in white and red wine by electrothermal atomic absorption spectrometry (ET-AAS) using a transversely heated graphite tube atomizer (THGA) with longitudinal Zeeman-effect background correction. The thermal behavior of both analytes during pyrolysis and atomization stages were investigated in 0.028 mol l(-1) HNO3 and in 1 + 1 v/v diluted wine using mixtures of Pd(NO3)(2) + Mg(NO3)(2) and NH4H2PO4 + Mg(NO3)(2) as chemical modifiers. With 5 mug Pd + 3 mug Mg as the modifiers and a two-step pyrolysis (10 s at 400 degreesC and 10 s at 600 degreesC), the formation of carbonaceous residues inside the atomizer was avoided. For 20 mul of sample (wine + 0.056 mol l(-1) HNO3, 1 + 1, v/v) dispensed into the graphite tube, analytical curves in the 0.10-1.0 mug l(-1) Cd and 5.0-50 mug l(-1) Pb ranges were established. The characteristic mass was approximately 0.6 pg for Cd and 33 pg for Pb, and the lifetime of the tube was approximately 400 firings. The limits of detection (LOD) based on integrated absorbance (0.03 mug l(-1) for Cd, 0.8 mug l(-1) for Pb) exceeded the requirements of Brazilian Food Regulations (decree #55871 from Health Department), which establish the maximum permissible level for Cd at 200 mug l(-1) and for Pb at 500 mug l(-1). The relative standard deviations (n = 12) were typically < 8% for Cd and < 6% for Pb. The recoveries of Cd and Pb added to wine samples varied from 88 to 107% and 93 to 103%, respectively. The accuracy of the direct determination of Cd and Ph was checked for 10 table wines by comparing the results with those obtained for digested wine using single-element ET-AAS, which were in agreement at the 95% confidence level. (C) 2001 Elsevier B.V. B.V. All rights reserved.

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The element-free Galerkin method (EFGM) is a very attractive technique for solutions of partial differential equations, since it makes use of nodal point configurations which do not require a mesh. Therefore, it differs from FEM-like approaches by avoiding the need of meshing, a very demanding task for complicated geometry problems. However, the imposition of boundary conditions is not straightforward, since the EFGM is based on moving-least-squares (MLS) approximations which are not necessarily interpolants. This feature requires, for instance, the introduction of modified functionals with additional unknown parameters such as Lagrange multipliers, a serious drawback which leads to poor conditionings of the matrix equations. In this paper, an interpolatory formulation for MLS approximants is presented: it allows the direct introduction of boundary conditions, reducing the processing time and improving the condition numbers. The formulation is applied to the study of two-dimensional magnetohydrodynamic flow problems, and the computed results confirm the accuracy and correctness of the proposed formulation. (C) 2002 Elsevier B.V. All rights reserved.

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The presence of trace basic organonitrogen compounds such as quinoline and pyridine in derivative petroleum fuels plays an important role in maintaining the engines of vehicles. However, these substances can contaminate the environment and so must be controlled because most of them are potentially carcinogenic and mutagenic. For these reasons, a reliable and sensitive method was developed for the determination of basic nitrogen compounds in fuel samples such as gasoline and diesel. This method utilizes preconcentration on an ion-exchange resin (Amberlyte IR - 120 H) followed by differential pulse voltammetry (DPV) on a glassy carbon electrode. The electrochemical behavior of quinoline and pyridine as studied by cyclic voltammetry (CV) suggests that their reduction occurs via a reversible electron transfer followed by an irreversible chemical reaction. Very well resolved diffusion-controlled voltammetric peaks were obtained in dimethylformamide (DMF) with tetrabutylammonium tetrafluoroborate (TBAF(4) 0.1 mol L-1) for quinoline (-1.95 V) and pyridine (-2.52 V) vs. Ag vertical bar AgCl vertical bar KClsat reference electrode. The proposed DPV method displayed a good linear response from 0.10 to 300 mg L-1 and a limit of detection (LOD) of 5.05 and 0.25 mu g L-1 for quinoline and pyridine, respectively. Using the method of standard additions, the simultaneous determination of quinoline and pyridine in gasoline samples yielded 25.0 +/- 0.3 and 33.0 +/- 0.7 mg L-1 and in diesel samples yielded 80.3 +/- 0.2 and 131 +/- 0.4 mg L-1, respectively. Spike recoveries were 94.4 +/- 0.3% and 10 +/- 0.5% for quinoline and pyridine, respectively, in the fuel determinations. This proposed method was also compared with UV-vis spectrophotometric measurements. Results obtained for the two methods agreed well based on F and t student's tests.

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A method was developed using the multi-element graphite furnace atomic absorption spectrometry technique for the direct and simultaneous determination of As, Cu, and Pb in Brazilian sugar cane spirit (cachaqa) samples. Also employed was the end-capped transversely heated graphite atomizer (THGA) with platforms pre-treated with W permanent modifier and co-injection of Pd/Mg(NO3)(2). Pyrolysis and atomization temperature curves were established in a cachaqa medium (1+1; v/v) containing 0.2% (v/v) HNO3 and spiked with 20 mu g L-1 As and Pb and 200 mu g L-1 Cu. The effect of the concentration of major elements usually present in cachaqa matrices (Ca, Mg, Na, and K) and ethanol on the absorbance of As, Cu, and Pb was investigated. Analytical working solutions of As, Cu, and Pb were prepared in 10% (v/v) ethanol plus 5.0 mg L-1 Ca, Mg, Na, and K. Acidified to 0.2% (v/v) HNO3, these solutions were suitable to build calibration curves by matrix matching. The proposed method was applied to the simultaneous determination of As, Cu, and Pb in commercial sugar cane spirits. The characteristic mass for the simultaneous determination was 16 pg As, 119 pg Cu, and 28 pg Pb. The pretreated tube lifetime was about 450 firings. The limit of detection (LOD) was 0.6 mu g L-1 As, 9.2 mu g L-1 Cu, and 0.3 pig L-1 Pb. The found concentrations varied from 0.81 to 4.28 mu g L-1 As, 0.28 to 3.82 mg L-1 Cu and 0.82 to 518 mu g L-1 Pb. The recoveries of the spiked samples varied from 94-112% (As), 97-111% (Cu), and 95-101% (Pb). The relative standard deviation (n=12) was 6.9%, 7.4%, and 7.7% for As, Cu, and Pb, respectively, present in a sample at 0.87 mu g L-1, 0.81 mg L-1, and 38.9 mu g L-1 concentrations.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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The Gaussian wave-packet phase-space representation is used to show that the expansion in powers of a of the quantum Liouville propagator leads, in the zeroth-order term, to results close to those obtained in the statistical quasiclassical method of Lee and Scully in the Weyl-Wigner picture. It is also verified that, propagating the Wigner distribution along the classical trajectories, the amount of error is less than that coming from propagating the Gaussian distribution along classical trajectories.

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In order to observe collagen and elastic fibers simultaneously, sections of human aorta, skin, lung, liver, and bladder were stained by Sirius red and analyzed by fluorescence microscopy. In all cases, the fibers of collagen presented the characteristic fluorescent red-orange color that results from the interaction of this extracellular protein with the dye, whereas elastic fibers showed strong green fluorescence (intrinsic fluorescence). This method efficiently detects collagen and elastic fibers when these two structures are present and could have valuable applications in processes that involves both fibers.

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The presence of trace neutral organonitrogen compounds as carbazole and indole in derivative petroleum fuels plays an important role in the car's engine maintenance. In addition, these substances contribute to the environmental contamination and their control is necessary because most of them are potentially carcinogenic and mutagenic. For those reasons, a reliable and sensitive method was proposed for the determination of neutral nitrogen compounds in fuel samples, such as gasoline and diesel using preconcentration with modified silica gel (Merck 70-230 mesh ASTM) followed by differential pulse voltammetry (DPV) technique on a glassy carbon electrode. The electrochemical behavior of carbazole and indole studied by cyclic voltammetry (CV) suggests that their reduction occurs via a reversible electron transfer followed by an irreversible chemical reaction. Very well resolved diffusion controlled voltammetric peaks were obtained in dimethylformamide (DMF) with tetrabutylammonium tetrafluoroborate (TBAF(4) 0.1 mol L-1) for indole (-2.27 V) and carbazole (-2.67 V) versus Ag vertical bar AgCl vertical bar KClsat reference electrode. The proposed DPV method showed a good linear response range from 0.10 to 300 mg L-1 and a limit of detection (L.O.D) of 7.48 and 2.66 mu g L-1 for indole and carbazole, respectively. The results showed that simultaneous determination of indole and carbazole presents in spiked gasoline samples were 15.8 +/- 0.3 and 64.6 +/- 0.9 mg L-1 and in spiked diesel samples were 9.29 +/- 1 and 142 +/- 1 mg L-1, respectively. The recovery was evaluated and the results shown the values of 88.9 +/- 0.4 and 90.2 +/- 0.8% for carbazole and indole in fuel determinations. The proposed method was also compared with UV-vis spectrophotometric measures and the results obtained for the two methods were in good agreement according to the F and t Student's tests. (C) 2007 Elsevier B.V. All rights reserved.

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A method is proposed for the simultaneous determination of Al, As, Cu, Fe, Mn, and Ni in fuel ethanol by electrothermal atomic absorption spectrometry (ETAAS) using W-Rh permanent modifier together with Pd(NO3)(2) + Mg(NO3)(2) conventional modifier. The integrated platform of a transversely heated graphite atomizer (THGA) was treated with tungsten, followed by rhodium, forming a deposit containing 250 mug W + 200 mug Rh. A 500-muL, volume of fuel ethanol was diluted with 500 muL, of 0.14 mol L-1 HNO3 in an autosampler cup of the spectrometer. Then, 20 muL, of the diluted ethanol was introduced into the pretreated graphite platform followed by the introduction of 5 mug Pd(NO3)(2) + 3 mug Mg(NO3)(2). The injection of this modifier was required to improve arsenic and iron recoveries in fuel ethanol. Calibrations were carried out using multi-element reference solutions prepared in diluted ethanol (1 + 1, v/v) acidified to 0. 14 mol L-1 HNO3. The pyrolysis and atomization temperatures of the heating program were 1200degreesC and 2200degreesC, respectively, which were obtained with multielement reference solutions in acidic diluted ethanol (1 + 1, v/v; 0. 14 mol L-1 HNO3). The characteristic masses for the simultaneous determination in ethanol fuel were 78 pg Al, 33 pg As, 10 pg Cu, 14 pg Fe, 7 pg Mn, and 24 pg Ni. The lifetime of the pretreated tube was about 700 firings. The detection limits (D.L.) were 1.9 mug L-1 Al, 2.9 mug L-1 As, 0.57 mug L-1.Cu, 1.3 mug L-1 Fe, 0.40 mug L-1 Mn, and 1.3 mug L-1 Ni. The relative standard deviations (n = 12) were 4%, 4%, 3%, 1.5%, 1.2%, and 2.2% for Al, As, Cu, Fe, Mn, and Ni, respectively. The recoveries of Al, As, Cu, Fe, Mn, and Ni added to the fuel ethanol samples varied from 81% to 95%, 80% to 98%, 97% to 109%, 85% to 107%, 98% to 106% and 97% to 103%, respectively. Accuracy was checked for the Al, As, Cu, Fe, Mn, and Ni determination in 10 samples purchased at a local gas station in Araraquara-SP City, Brazil. A paired t-test showed that at the 95% confidence level the results were in agreement with those obtained by single-element ETAAS.

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The error function is present in several equations describing eletrode processes. But, only approximations of this function are used. In this work, these and other approximations are studied and evaluated according to precision.