28 resultados para difference equation


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By using thermochemical data reported for a series of chelates of the type [Ln(thd)3], thd = 2, 2, 6, 6 ­ tetramethyl- 3,5-heptanedione and Ln = La, Pr, Nd, Sm, Gd, Tb, Ho, Er, Tm and Yb, empirical correlations were found involving thermochemical parameters (e.g. dissociation enthalpy) and the thermodynamic temperatures of the beginning of thermal degradation of the chelates, t i. It is shown that t i values are of capital importance in the study of this all class of coordination compounds. Among others, the empirical equation is obtained: r3+ = (-0,013.Z + 1,36)/0,005, that relates the lanthanide cation radius (pm) with the atomic number of the element. The remarkable fact is that this equation is achieved by using thermogravimetric and calorimetric parameters. Is also shown that t i values are related with the P(M) function values, which are very close related with the energy difference, deltaE, between the lowest electronic energy level of the f n s²d¹ configuration and the lowest energy level of the f n+1s² configuration in the neutral gaseous atoms.

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Saponins are natural soaplike foam-forming compounds widely used in foods, cosmetic and pharmaceutical preparations. In this work foamability and foam lifetime of foams obtained from Ilex paraguariensis unripe fruits were analyzed. Polysorbate 80 and sodium dodecyl sulfate were used as reference surfactants. Aiming a better data understanding a linearized 4-parameters Weibull function was proposed. The mate hydroethanolic extract (ME) and a mate saponin enriched fraction (MSF) afforded foamability and foam lifetime comparable to the synthetic surfactants. The linearization of the Weibull equation allowed the statistical comparison of foam decay curves, improving former mathematical approaches.

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The formalism of supersymmetric Quantum Mechanics can be extended to arbitrary dimensions. We introduce this formalism and explore its utility to solve the Schrödinger equation for a bidimensinal potential. This potential can be applied in several systems in physical and chemistry context , for instance, it can be used to study benzene molecule.

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In this work, a new mathematical equation correction approach for overcoming spectral and transport interferences was proposed. The proposal was applied to eliminate spectral interference caused by PO molecules at the 217.0005 nm Pb line, and the transport interference caused by variations in phosphoric acid concentrations. Correction may be necessary at 217.0005 nm to account for the contribution of PO, since Atotal217.0005 nm = A Pb217.0005 nm + A PO217.0005 nm. This may be easily done by measuring other PO wavelengths (e.g. 217.0458 nm) and calculating the relative contribution of PO absorbance (A PO) to the total absorbance (Atotal) at 217.0005 nm: A Pb217.0005 nm = Atotal217.0005 nm - A PO217.0005 nm = Atotal217.0005 nm - k (A PO217.0458 nm). The correction factor k is calculated from slopes of calibration curves built up for phosphorous (P) standard solutions measured at 217.0005 and 217.0458 nm, i.e. k = (slope217.0005 nm/slope217.0458 nm). For wavelength integrated absorbance of 3 pixels, sample aspiration rate of 5.0 ml min-1, analytical curves in the 0.1 - 1.0 mg L-1 Pb range with linearity better than 0.9990 were consistently obtained. Calibration curves for P at 217.0005 and 217.0458 nm with linearity better than 0.998 were obtained. Relative standard deviations (RSD) of measurements (n = 12) in the range of 1.4 - 4.3% and 2.0 - 6.0% without and with mathematical equation correction approach were obtained respectively. The limit of detection calculated to analytical line at 217.0005 nm was 10 µg L-1 Pb. Recoveries for Pb spikes were in the 97.5 - 100% and 105 - 230% intervals with and without mathematical equation correction approach, respectively.

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The arbitrary angular momentum solutions of the Schrödinger equation for a diatomic molecule with the general exponential screened coulomb potential of the form V(r) = (- a / r){1+ (1+ b )e-2b } has been presented. The energy eigenvalues and the corresponding eigenfunctions are calculated analytically by the use of Nikiforov-Uvarov (NU) method which is related to the solutions in terms of Jacobi polynomials. The bounded state eigenvalues are calculated numerically for the 1s state of N2 CO and NO

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The state of Ceará, Brazil, has 75% of its area covered by Brazilian semiarid, with its peculiar features. In this state, the dams are constituted in water structure of strategic importance, ensuring, both in time and space, the development and supply of water to population. However, construction of reservoirs results in various impacts that should be carefully observed when deciding on their implementation. One of the impacts identified as negative is the increased evaporation, which constitutes a major component of water balance in reservoirs, especially in arid regions. Several methods for estimating evaporation have been proposed over time, many of them deriving from the Penman equation. This study evaluated six different methods for estimating evaporation in order to determine the most suitable for use in hydrological models for water balance in reservoirs in the state of Ceará. The tested methods were proposed by Penman, Kohler-Nordenson-Fox, Priestley-Taylor, deBruim-Keijman, Brutsaert-Stricker and deBruim. The methods presented good performance when tested for water balance during the dry season, and the Priestley-Taylor was the most appropriate, since the data from de simulated water balance with evaporation estimated by this method were the closest of the water balance data observed from measures of reservoir level and the elevation-volume curve provided by the Company of Management of Water Resources of the state of Ceará - COGERH.

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This study aimed to propose methods to identify croplands cultivated with winter cereals in the northern region of Rio Grande do Sul State, Brazil. Thus, temporal profiles of Normalized Difference Vegetation Index (NDVI) from MODIS sensor, from April to December of the 2000 to 2008, were analyzed. Firstly, crop masks were elaborated by subtracting the minimum NDVI image (April to May) from the maximum NDVI image (June to October). Then, an unsupervised classification of NDVI images was carried out (Isodata), considering the crop mask areas. According to the results, crop masks allowed the identification of pixels with greatest green biomass variation. This variation might be associated or not with winter cereals areas established to grain production. The unsupervised classification generated classes in which NDVI temporal profiles were associated with water bodies, pastures, winter cereals for grain production and for soil cover. Temporal NDVI profiles of the class winter cereals for grain production were in agree with crop patterns in the region (developmental stage, management standard and sowing dates). Therefore, unsupervised classification based on crop masks allows distinguishing and monitoring winter cereal crops, which were similar in terms of morphology and phenology.

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The aim of this study was to generate maps of intense rainfall equation parameters using interpolated maximum intense rainfall data. The study area comprised Espírito Santo State, Brazil. A total of 59 intense rainfall equations were used to interpolate maximum intense rainfall, with a 1 x 1 km spatial resolution. Maximum intense rainfall was interpolated considering recurrence of 2; 5; 10; 20; 50 and 100 years, and duration of 10; 20; 30; 40; 50; 60; 120; 240; 360; 420; 660; 720; 900; 1,140; 1,380 and 1,440 minutes, resulting in 96 maps of maximum intense rainfall. The used interpolators were inverse distance weighting and ordinary kriging, for which significance level (p-value) and coefficient of determination (R²) were evaluated for the cross-validation data, choosing the method that presented better R² to generate maps. Finally, maps of maximum intense precipitation were used to estimate, cell by cell, the intense rainfall equation parameters. In comparison with literature data, the mean percentage error of estimated intense rainfall equations was 13.8%. Maps of spatialized parameters, obtained in this study, are of simple use; once they are georeferenced, they may be imported into any geographic information system to be used for a specific area of interest.

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Due to the lack of information concerning maximum rainfall equations for most locations in Mato Grosso do Sul State, the alternative for carrying out hydraulic work projects has been information from meteorological stations closest to the location in which the project is carried out. Alternative methods, such as 24 hours rain disaggregation method from rainfall data due to greater availability of stations and longer observations can work. Based on this approach, the objective of this study was to estimate maximum rainfall equations for Mato Grosso do Sul State by adjusting the 24 hours rain disaggregation method, depending on data obtained from rain gauge stations from Dourado and Campo Grande. For this purpose, data consisting of 105 rainfall stations were used, which are available in the ANA (Water Resources Management National Agency) database. Based on the results we concluded: the intense rainfall equations obtained by pluviogram analysis showed determination coefficient above 99%; and the performance of 24 hours rain disaggregation method was classified as excellent, based on relative average error WILMOTT concordance index (1982).

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Some studies have suggested that human immunodeficiency virus (HIV) infection modifies the natural history of hepatitis C virus (HCV) infection, accelerating the progression of fibrosis and the development of cirrhosis. Our objective was to evaluate the fibrosis progression rate (FPR) in HCV/HIV-co-infected patients, and to identify factors that may influence it. HCV-mono-infected and HCV/HIV-co-infected patients with a known date of HCV infection (transfusion or injection drug use) and a liver biopsy were included. The FPR was defined as the ratio between the fibrosis stage (Metavir score) and the estimated length of infection in years and the result was reported as fibrosis units per year. The factors studied were gender, age at infection, consumption of alcohol, aminotransferase levels, histological activity grade, HCV genotype and viral load, CD4 cell count, HIV viral load, and the use of antiretroviral therapy. Sixty-five HCV-infected (group 1) and 53 HCV/HIV-co-infected (group 2) patients were evaluated over a period of 19 months. The mean FPR of groups 1 and 2 was 0.086 ± 0.074 and 0.109 ± 0.098 fibrosis units per year, respectively (P = 0.276). There was a correlation between length of HCV infection and stage of fibrosis in both groups. The age at infection, the aspartate aminotransferase level (r = 0.36) and the inflammatory activity grade were correlated with the FPR (P < 0.001). No difference in FPR was found between HCV-mono-infected and HCV/HIV-co-infected patients.

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The aims of this study were to determine whether standard base excess (SBE) is a useful diagnostic tool for metabolic acidosis, whether metabolic acidosis is clinically relevant in daily evaluation of critically ill patients, and to identify the most robust acid-base determinants of SBE. Thirty-one critically ill patients were enrolled. Arterial blood samples were drawn at admission and 24 h later. SBE, as calculated by Van Slyke's (SBE VS) or Wooten's (SBE W) equations, accurately diagnosed metabolic acidosis (AUC = 0.867, 95%CI = 0.690-1.043 and AUC = 0.817, 95%CI = 0.634-0.999, respectively). SBE VS was weakly correlated with total SOFA (r = -0.454, P < 0.001) and was similar to SBE W (r = -0.482, P < 0.001). All acid-base variables were categorized as SBE VS <-2 mEq/L or SBE VS <-5 mEq/L. SBE VS <-2 mEq/L was better able to identify strong ion gap acidosis than SBE VS <-5 mEq/L; there were no significant differences regarding other variables. To demonstrate unmeasured anions, anion gap (AG) corrected for albumin (AG A) was superior to AG corrected for albumin and phosphate (AG A+P) when strong ion gap was used as the standard method. Mathematical modeling showed that albumin level, apparent strong ion difference, AG A, and lactate concentration explained SBE VS variations with an R² = 0.954. SBE VS with a cut-off value of <-2 mEq/L was the best tool to diagnose clinically relevant metabolic acidosis. To analyze the components of SBE VS shifts at the bedside, AG A, apparent strong ion difference, albumin level, and lactate concentration are easily measurable variables that best represent the partitioning of acid-base derangements.

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We assessed the 6-min walk distance (6MWD) and body weight x distance product (6MWw) in healthy Brazilian subjects and compared measured 6MWD with values predicted in five reference equations developed for other populations. Anthropometry, spirometry, reported physical activity, and two walk tests in a 30-m corridor were evaluated in 134 subjects (73 females, 13-84 years). Mean 6MWD and 6MWw were significantly greater in males than in females (622 ± 80 m, 46,322 ± 10,539 kg.m vs 551 ± 71 m, 36,356 ± 8,289 kg.m, P < 0.05). Four equations significantly overestimated measured 6MWD (range, 32 ± 71 to 137 ± 74 m; P < 0.001), and one significantly underestimated it (-36 ± 86 m; P < 0.001). 6MWD significantly correlated with age (r = -0.39), height (r = 0.44), body mass index (r = -0.24), and reported physical activity (r = 0.25). 6MWw significantly correlated with age (r = -0.21), height (r = 0.66) and reported physical activity (r = 0.25). The reference equation devised for walk distance was 6MWDm = 622.461 - (1.846 x Ageyears) + (61.503 x Gendermales = 1; females = 0); r2 = 0.300. In an additional group of 85 subjects prospectively studied, the difference between measured and the 6MWD predicted with the equation proposed here was not significant (-3 ± 68 m; P = 0.938). The measured 6MWD represented 99.6 ± 11.9% of the predicted value. We conclude that 6MWD and 6MWw variances were adequately explained by demographic and anthropometric attributes. This reference equation is probably most appropriate for evaluating the exercise capacity of Brazilian patients with chronic diseases.

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The effective diffusivity of clove essential oil in subcritical liquid CO2 was estimated. The experimental apparatus employed was a fixed-bed extractor. The fixed bed was formed with grounded (mesh -32 + 65) and compacted clove buds which were considered a solid element. The effective diffusion coefficient was evaluated by fitting the experimental concentration profile to the unsteady state mass balance equation for unidirectional diffusion in a finite solid medium. The diffusion coefficient was related to the concentration of oil in the solid by an exponential function. The estimated values of the effective diffusion coefficient varied from 3.64 to 5.22x10-10 m2/s. The average relative errors were lower than 3.1%.