951 resultados para Multilinear polynomial


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Cooling crystallization is one of the most important purification and separation techniques in the chemical and pharmaceutical industry. The product of the cooling crystallization process is always a suspension that contains both the mother liquor and the product crystals, and therefore the first process step following crystallization is usually solid-liquid separation. The properties of the produced crystals, such as their size and shape, can be affected by modifying the conditions during the crystallization process. The filtration characteristics of solid/liquid suspensions, on the other hand, are strongly influenced by the particle properties, as well as the properties of the liquid phase. It is thus obvious that the effect of the changes made to the crystallization parameters can also be seen in the course of the filtration process. Although the relationship between crystallization and filtration is widely recognized, the number of publications where these unit operations have been considered in the same context seems to be surprisingly small. This thesis explores the influence of different crystallization parameters in an unseeded batch cooling crystallization process on the external appearance of the product crystals and on the pressure filtration characteristics of the obtained product suspensions. Crystallization experiments are performed by crystallizing sulphathiazole (C9H9N3O2S2), which is a wellknown antibiotic agent, from different mixtures of water and n-propanol in an unseeded batch crystallizer. The different crystallization parameters that are studied are the composition of the solvent, the cooling rate during the crystallization experiments carried out by using a constant cooling rate throughout the whole batch, the cooling profile, as well as the mixing intensity during the batch. The obtained crystals are characterized by using an automated image analyzer and the crystals are separated from the solvent through constant pressure batch filtration experiments. Separation characteristics of the suspensions are described by means of average specific cake resistance and average filter cake porosity, and the compressibilities of the cakes are also determined. The results show that fairly large differences can be observed between the size and shape of the crystals, and it is also shown experimentally that the changes in the crystal size and shape have a direct impact on the pressure filtration characteristics of the crystal suspensions. The experimental results are utilized to create a procedure that can be used for estimating the filtration characteristics of solid-liquid suspensions according to the particle size and shape data obtained by image analysis. Multilinear partial least squares regression (N-PLS) models are created between the filtration parameters and the particle size and shape data, and the results presented in this thesis show that relatively obvious correlations can be detected with the obtained models.

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The most widespread literature for the evaluation of uncertainty - GUM and Eurachem - does not describe explicitly how to deal with uncertainty of the concentration coming from non-linear calibration curves. This work had the objective of describing and validating a methodology, as recommended by the recent GUM Supplement approach, to evaluate the uncertainty through polynomial models of the second order. In the uncertainty determination of the concentration of benzatone (C) by chromatography, it is observed that the uncertainty of measurement between the methodology proposed and Monte Carlo Simulation, does not diverge by more than 0.0005 unit, thus validating the model proposed for one significant digit.

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Extended Hildebrand Solubility Approach (EHSA) developed by Martin et al. was applied to evaluate the solubility of ketoprofen (KTP) in ethanol + water cosolvent mixtures at 298.15 K. Calculated values of molar volume and solubility parameter for KTP were used. A good predictive capacity of EHSA was found by using a regular polynomial model in order five to correlate the W interaction parameter and the solubility parameters of cosolvent mixtures (δmix). Nevertheless, the deviations obtained in the estimated solubilities with respect to the experimental solubilities were on the same order like those obtained directly by means of an empiric regression of the logarithmic experimental solubilities as a function of δmix values.

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In wireless communications the transmitted signals may be affected by noise. The receiver must decode the received message, which can be mathematically modelled as a search for the closest lattice point to a given vector. This problem is known to be NP-hard in general, but for communications applications there exist algorithms that, for a certain range of system parameters, offer polynomial expected complexity. The purpose of the thesis is to study the sphere decoding algorithm introduced in the article On Maximum-Likelihood Detection and the Search for the Closest Lattice Point, which was published by M.O. Damen, H. El Gamal and G. Caire in 2003. We concentrate especially on its computational complexity when used in space–time coding. Computer simulations are used to study how different system parameters affect the computational complexity of the algorithm. The aim is to find ways to improve the algorithm from the complexity point of view. The main contribution of the thesis is the construction of two new modifications to the sphere decoding algorithm, which are shown to perform faster than the original algorithm within a range of system parameters.

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Extended Hildebrand Solubility Approach (EHSA) was successfully applied to evaluate the solubility of Indomethacin in 1,4-dioxane + water mixtures at 298.15 K. An acceptable correlation-performance of EHSA was found by using a regular polynomial model in order four of the W interaction parameter vs. solubility parameter of the mixtures (overall deviation was 8.9%). Although the mean deviation obtained was similar to that obtained directly by means of an empiric regression of the experimental solubility vs. mixtures solubility parameters, the advantages of EHSA are evident because it requires physicochemical properties easily available for drugs.

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Classification of biodiesel by oilseed type using pattern recognition techniques is described. The spectra of the samples were performed in the Visible region, requiring noise removal by use of a first derivative by the Savitzky-Golay method, employing a second-order polynomial and a window of 21 points. The characterization of biodiesel was performed using HCA, PCA and SIMCA. For HCA and PCA methods, one can observe the separation of each group of biodiesel in a spectral region of 405-500 nm. SIMCA model was used in a test group composed of 28 spectral measurements and no errors are obtained.

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The quantum harmonic oscillator is described by the Hermite equation.¹ The asymptotic solution is predominantly used to obtain its analytical solutions. Wave functions (solutions) are quadratically integrable if taken as the product of the convergent asymptotic solution (Gaussian function) and Hermite polynomial,¹ whose degree provides the associated quantum number. Solving it numerically, quantization is observed when a control real variable is "tuned" to integer values. This can be interpreted by graphical reading of Y(x) and |Y(x)|², without other mathematical analysis, and prove useful for teaching fundamentals of quantum chemistry to undergraduates.

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Os deslocamentos químicos de RMN 13C de carbonos a , b , g e d de 17 conjuntos de haletos (F, Cl Br e I) alifáticos, inclusive compostos mono, bi e tricíclicos, podem ser reproduzidos por uma equação linear de duas constantes e duas variáveis do tipo : d R-X = A*d R-X1 + B*d R-X2 onde A e B são constantes obtidas por regressão multilinear a partir de deslocamentos químicos de 13C; d R-X, o deslocamento químico de 13C do composto com halogênio (R-X); d R-X1 e d R-X2 deslocamentos químicos de outros haletos. Para brometos (R-X) alifáticos a melhor correlação foi obtida com os dados de fluoretos (R-X1) e iodetos (R-X2) com R2 de 0,9989 e desvio médio absoluto (DM) de 0,39ppm. Para cloretos (R-X) a melhor correlação foi com dados de brometos (R-X1) e iodetos (R-X2) com R2 de 0,9960 e DM de 0,76ppm. Para fluoretos (R-X) a melhor correlação foi com brometos (R-X1) e iodetos (R-X2) com R2 de 0,9977 e DM de 1,10ppm e para iodetos (R-X) foi com fluoretos (R-X1) e brometos (R-X2) com R2 de 0,9972 e desvio médio absoluto de 0,60 ppm.

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Bauhinia x blakeana (B. purpurea x B. variegata) is a natural hybrid that has been cultivated in gardens, streets and parks. Due to its sterility, it must be vegetatively propagated. The objective of this work was to evaluate the viability of cuttings and grafting on its propagation. Semi-woody cuttings were collected during four seasons and treated with 0; 1,000; 2,000; and 3,000 mg L-1 of IBA. The experimental design was entirely randomized and the treatments were arranged in a 4x4 factorial scheme (four collecting times x four IBA concentrations) and five replications with 10 cuttings each, per collecting time and per IBA concentration. Characteristics of roots and shoots were evaluated after 90 days. The data means were compared by the Tukey test and submitted to the polynomial regression analysis. For the grafting experiment, B. variegata and B. variegata var. candida plants of six and 12 months were used as rootstocks and the splice graft and T-budding methods were tested. The experimental design was entirely randomized and the treatments were arranged in a 2x2x2 factorial scheme (two rootstock species x two grafting methods x two rootstock ages) and four replications with five plants each, per rootstock species, per grafting method and per rootstock age. Characteristics of shoots were evaluated after 90 days and the data means were compared by the Tukey test. B. x blakeana can be propagated by semi-woody cuttings collected in spring, without IBA application, or in summer, with the application of 3,000 mg L-1 of IBA. The tested grafting methods were not effective.

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The irrigation management based on the monitoring of the soil water content allows for the minimization of the amount of water applied, making its use more efficient. Taking into account these aspects, in this work, a sensor for measuring the soil water content was developed to allow real time automation of irrigation systems. This way, problems affecting crop yielding such as irregularities in the time to turn on or turn off the pump, and excess or deficit of water can be solved. To develop the sensors were used stainless steel rods, resin, and insulating varnish. The sensors measuring circuit was based on a microcontroller, which gives its output signal in the digital format. The sensors were calibrated using soil of the type “Quartzarenic Neosoil”. A third order polynomial model was fitted to the experimental data between the values of water content corresponding to the field capacity and the wilting point to correlate the soil water content obtained by the oven standard method with those measured by the electronic circuit, with a coefficient of determination of 93.17%, and an accuracy in the measures of ±0.010 kg kg-1. Based on the results, it was concluded that the sensor and its implemented measuring circuit can be used in the automation process of irrigation systems.

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Most studies on measures of transpiration of plants, especially woody fruit, relies on methods of heat supply in the trunk. This study aimed to calibrate the Thermal Dissipation Probe Method (TDP) to estimate the transpiration, study the effects of natural thermal gradients and determine the relation between outside diameter and area of xylem in 'Valencia' orange young plants. TDP were installed in 40 orange plants of 15 months old, planted in boxes of 500 L, in a greenhouse. It was tested the correction of the natural thermal differences (DTN) for the estimation based on two unheated probes. The area of the conductive section was related to the outside diameter of the stem by means of polynomial regression. The equation for estimation of sap flow was calibrated having as standard lysimeter measures of a representative plant. The angular coefficient of the equation for estimating sap flow was adjusted by minimizing the absolute deviation between the sap flow and daily transpiration measured by lysimeter. Based on these results, it was concluded that the method of TDP, adjusting the original calibration and correction of the DTN, was effective in transpiration assessment.

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This study aimed to evaluate the effect of horizontal plate meter with oblong holes operating with one or two seed outlets at different speeds over the accuracy of longitudinal distribution of common bean seeds (Phaseolus vulgaris L.). The experiment was performed in laboratory using the meter with one and two seed outlet points in relation to ten tangential disk plate speeds (0.03 to 0.30 m s-1). It was used a complete randomized design with four replications, summing up 80 experimental treatments. Tangential speed quantitative factor was estimated through a 2nd order polynomial regression. There was no significant difference in the behavior of the seed meter operating with one or two outlets in the metering of bean seeds in all tested speeds, with percentage of single seeds spacing over 60% in tangential speeds below of 0.24 m s-1.

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Water and fertilizer among the production factors are the elements that most restrict the production of cashew. The precise amount of these factors is essential to the success of the crop yield. This research aimed to determine the best factor-product ratio and analyze technical and economic indicators, of productivity of the cashew clone BRS 189 (Anacardium occidentale) to production factors water and potassium. The experiment was conducted from May 2009 to December 2009 in an experimental area of 56.0 m x 112.0 m in the irrigated Curu - Pentecoste, located in the municipality of Pentecoste, Ceará, Brazil. Production factors water (W) and potassium (K) were the independent variables and productivity (Y), the dependent variable. Ten statistical models that have proven satisfactory for obtaining production function were tested. The marginal rate of substitution was obtained through the ratio of the potassium marginal physical product and the water marginal physical product. The most suited model to the conditions of the experiment was the quadratic polynomial without intercept and interaction. Considering that the price of the water was 0.10 R$ mm -1, the price of the potassium 2.19 R$ kg -1 and the price of the cashew 0.60 R$ kg-1, the amounts of water and K2O to obtain the maximum net income were 6,349.1 L plant-1 of water and 128.7 g plant -1year, -1 respectively. Substituting the values obtained in the production function, the maximum net income was achieved with a yield of 7,496.8 kg ha-1 of cashew.

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The effects of starter diet (days 1 to 21) supplemented with arginine (Arg) on the production performance and duodenum and jejunum mucosa morphometry of broilers were studied. Male Cobb broiler chickens (990) were randomly assigned to one of five treatments in a complete random design. Measurements of 33 chicks per treatment were made in six repetitions. The treatments consisted of a basal diet with 1.390% digestible Arg (no supplementation) and four dietary levels (1.490%, 1.590%, 1.690%, and 1.790%), providing a relationship with lysine of 1.103; 1.183; 1.262; 1.341 and 1.421%, respectively. From the age of 22 days on, all birds received conventional grower diet. The data were submitted to regression analysis by polynomial decomposition of the degrees of freedom in relation to the levels of Arg. The Arg supplementation increased (P<0.05) the live weight and the feed conversion ratio without increasing the feed intake of the birds. However, no effect was observed (P>0.05) in the growth phase (days 22 to 42) in the absence of the Arg supplementation. The supplementation of Arg over of NRC recommendation during the starter phase may be necessary for the expression of the maximal weight gain potential in birds. No effect (P<0.05) of Arg dietary supplementation was observed either on small intestine weight and length at any age. However, the duodenum villus:crypt ratio increased and the crypt depth decreased in the first week in response to increasing dietary Arg. It is concluded that broiler Arg dietary supplementation in the starter diet improved production performance and small intestine morphometry, especially in the first week.

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This paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. The behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. A control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. The state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. General polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. This methodology is applied to systems with quadratic and cubic non-linearities. Strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. Numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. Numerical results emphasize the importance of considering time delay in the project of active structural control systems.