Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

THE GENERALIZED MAXIMUM LIKELIHOOD METHOD APPLIED TO HIGH PRESSURE PHASE EQUILIBRIUM

The generalized maximum likelihood method was used to determine binary interaction parameters between carbon dioxide and components of orange essential oil. Vapor-liquid equilibrium was modeled with Peng-Robinson and Soave-Redlich-Kwong equations, using a methodology proposed in 1979 by Asselineau, Bogdanic and Vidal. Experimental vapor-liquid equilibrium data on binary mixtures formed with carbon dioxide and compounds usually found in orange essential oil were used to test the model. These systems were chosen to demonstrate that the maximum likelihood method produces binary interaction parameters for cubic equations of state capable of satisfactorily describing phase equilibrium, even for a binary such as ethanol/CO2. Results corroborate that the Peng-Robinson, as well as the Soave-Redlich-Kwong, equation can be used to describe phase equilibrium for the following systems: components of essential oil of orange/CO2.

Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.

Determinação in Loco da difusividade térmica num solo da região de Caatinga (PB)

Um estudo experimental detalhado sobre transferências de calor e água no complexo solo - vegetação - atmosfera, em uma região de caatinga no semi-árido paraibano, mostrou que o comportamento termodinâmico do solo exerce papel fundamental no processo de evaporação do solo e nos fluxos de calor sensível. Este trabalho objetivou mostrar como a difusividade térmica do solo in loco foi determinada. Três métodos diferentes, embasados sobre hipóteses bem distintas, foram utilizados, e os seus resultados foram comparados. O método harmônico não se mostrou adequado para o tipo de solo encontrado. Para a camada superficial do solo (0-5 cm), o método CLTM (Corrected Laplace Transform Method) mostrou-se bem adaptado. Em todos os casos, o método NHS (método de Nassar & Horton), que considera variações verticais da difusividade térmica, apresentou uma dispersão elevada dos seus pontos, porém forneceu valores próximos dos valores estimados pelo método CLTM na camada superior e valores coerentes nas outras camadas. A umidade do solo, na profundidade média de 5 cm, foi medida por uma sonda TDR devidamente calibrada. Assim, pôde se determinar a relação entre a difusividade térmica e a umidade volumétrica para o solo estudado. Os valores muito baixos de difusividade constituem um condicionante importante do clima local.

Separação de espectros simulados e de luminescência total através do método generalizado de anulação do posto (GRAM)

A multivariate curve resolution method, "GENERALIZED RANK ANNIHILATION METHOD (GRAM)", is discussed and tested with simulated and experimental data. The analysis of simulated data provides general guidelines concerning the condition for uniqueness of a solution for a given problem. The second-order emission-excitation spectra of human and animal dental calculus deposits were used as an experimental data to estimate the performance of the above method. Three porphyrinic spectral profiles, for both human and cat, were obtained by the use of GRAM.

In-house ELISA method to analyze anti-Trypanosoma cruzi IgG reactivity for differential diagnosis and evaluation of Chagas disease morbidity

INTRODUCTION: The goal was to develop an in-house serological method with high specificity and sensitivity for diagnosis and monitoring of Chagas disease morbidity. METHODS: With this purpose, the reactivities of anti-T. cruzi IgG and subclasses were tested in successive serum dilutions of patients from Berilo municipality, Jequitinhonha Valley, Minas Gerais, Brazil. The performance of the in-house ELISA was also evaluated in samples from other relevant infectious diseases, including HIV, hepatitis C (HCV), syphilis (SYP), visceral leishmaniasis (VL), and American tegumentary leishmaniasis (ATL), and noninfected controls (NI). Further analysis was performed to evaluate the applicability of this in-house methodology for monitoring Chagas disease morbidity into three groups of patients: indeterminate (IND), cardiac (CARD), and digestive/mixed (DIG/Mix), based on their clinical status. RESULTS: The analysis of total IgG reactivity at serum dilution 1:40 was an excellent approach to Chagas disease diagnosis (100% sensitivity and specificity). The analysis of IgG subclasses showed cross-reactivity, mainly with NI, VL, and ATL, at all selected serum dilutions. Based on the data analysis, the IND group displayed higher IgG3 levels and the DIG/Mix group presented higher levels of total IgG as compared with the IND and CARD groups. CONCLUSIONS: These findings demonstrated that methodology presents promising applicability in the analysis of anti-T. cruzi IgG reactivity for the differential diagnosis and evaluation of Chagas disease morbidity.

Histopathological analysis of rat mesentery as a method for evaluating neutrophil migration: differential effects of dexamethasone and pertussis toxin

In the present study, histopathological analysis of rat mesentery was used to quantify the effect of two anti-inflammatory agents, dexamethasone (Dex) and pertussis toxin (Ptx), on leukocyte migration. The intravenous injection of Dex (1 mg/kg) and Ptx (1,200 ng) 1 h prior to the intraperitoneal injection of the inflammatory stimuli lipopolysaccharide (LPS) or formyl-methionyl-leucyl-phenylalanine (fMLP) significantly reduced the neutrophil diapedesis (LPS: Ptx = 0.86 ± 0.19 and Dex = 0.35 ± 0.13 vs saline (S) = 2.85 ± 0.59; fMLP: Ptx = 0.43 ± 0.09 and Dex 0.01 ± 0.01 vs S = 1.08 ± 0.15 neutrophil diapedesis/field) and infiltration (LPS: Ptx = 6.29 ± 1.4 and Dex = 3.06 ± 0.76 vs S = 15.94 ± 3.97; fMLP: Ptx = 3.85 ± 0.56 and Dex = 0.40 ± 0.16 vs S = 7.15 ± 1.17 neutrophils/field) induced by the two agonists in the rat mesentery. The inhibitory effect of Dex and Ptx was clearly visible in the fields nearest the venule (up to 200 µm), demonstrating that these anti-inflammatory agents act preferentially in the transmigration of neutrophils from the vascular lumen into the interstitial space, but not in cell movement in response to a haptotactic gradient. The mesentery of rats pretreated with Dex showed a decreased number of neutrophils within the venules (LPS: Dex = 1.50 ± 0.38 vs S = 4.20 ± 1.01; fMLP: Dex = 0.25 ± 0.11 vs S = 2.20 ± 0.34 neutrophils in the lumen/field), suggesting that this inhibitor may be acting at a step that precedes neutrophil arrival in the inflamed tissue. In contrast to that observed with Dex treatment, the number of neutrophils found in mesenteric venules was significantly elevated in animals pretreated with Ptx (LPS: Ptx = 9.85 ± 2.25 vs S = 4.20 ± 1.01; fMLP: Ptx = 4.66 ± 1.24 vs S = 2.20 ± 0.34 neutrophils in the lumen/field). This discrepancy shows that Ptx and Dex act via different mechanisms and suggests that Ptx prevents locomotion of neutrophils from the vascular lumen to the interstitial space. In conclusion, the method described here is useful for quantifying the inflammatory and anti-inflammatory effect of different substances. The advantage of this histopathological approach is that it provides additional information about the steps involved in leucocyte migration.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Acute generalized exanthematous pustulosis (AGEP). Case report

Acute Generalized Exanthematous Pustulosis (AGEP) is a drug-induced dermatosis characterized by an acute episode of sterile pustules over erythematous-edematous skin. It is accompanied by an episode of fever, which regresses a few days after discontinuation of the drug that caused the condition or as a result of corticosteroid treatment. The main triggering drugs are antibiotics, mainly beta-lactam ones. Other medications, such as antifungal agents, non steroid anti-inflammatory drugs, analgesics, antiarrhythmic, anticonvulsant and antidepressant drugs, may also be responsible. Histologically, it is characterized by the existence of vasculitis, associated with non-follicular subcorneal pustules. A case of a Caucasian female outpatient unit of Dermatology with AGEP, who presented with generalized pustulosis lesions after the use of cephalosporin for urinary infection is related. The diagnosis was confirmed by the clinical and pathological correlations, the resolution of the dermatosis after discontinuation of the drug and use of systemic corticosteroid treatment, and the recurrence of the disorder after the introduction of a similar drug. The importance of the recognition of this drug-induced dermatosis is given by its main differential clinical and histological diagnoses: generalized pustular psoriasis and subcorneal pustulosis.

Differential gene expression during Trypanosoma cruzi metacyclogenesis

The transformation of epimastigotes into metacyclic trypomastigotes involves changes in the pattern of expressed genes, resulting in important morphological and functional differences between these developmental forms of Trypanosoma cruzi. In order to identify and characterize genes involved in triggering the metacyclogenesis process and in conferring to metacyclic trypomastigotes their stage specific biological properties, we have developed a method allowing the isolation of genes specifically expressed when comparing two close related cell populations (representation of differential expression or RDE). The method is based on the PCR amplification of gene sequences selected by hybridizing and subtracting the populations in such a way that after some cycles of hybridization-amplification genes specific to a given population are highly enriched. The use of this method in the analysis of differential gene expression during T. cruzi metacyclogenesis (6 hr and 24 hr of differentiation and metacyclic trypomastigotes) resulted in the isolation of several clones from each time point. Northern blot analysis showed that some genes are transiently expressed (6 hr and 24 hr differentiating cells), while others are present in differentiating cells and in metacyclic trypomastigotes. Nucleotide sequencing of six clones characterized so far showed that they do not display any homology to gene sequences available in the GeneBank.

A cophenetic correlation coefficient for Tocher's method

The objective of this work was to propose a way of using the Tocher's method of clustering to obtain a matrix similar to the cophenetic one obtained for hierarchical methods, which would allow the calculation of a cophenetic correlation. To illustrate the obtention of the proposed cophenetic matrix, we used two dissimilarity matrices - one obtained with the generalized squared Mahalanobis distance and the other with the Euclidean distance - between 17 garlic cultivars, based on six morphological characters. Basically, the proposal for obtaining the cophenetic matrix was to use the average distances within and between clusters, after performing the clustering. A function in R language was proposed to compute the cophenetic matrix for Tocher's method. The empirical distribution of this correlation coefficient was briefly studied. For both dissimilarity measures, the values of cophenetic correlation obtained for the Tocher's method were higher than those obtained with the hierarchical methods (Ward's algorithm and average linkage - UPGMA). Comparisons between the clustering made with the agglomerative hierarchical methods and with the Tocher's method can be performed using a criterion in common: the correlation between matrices of original and cophenetic distances.

Combined application of continuous wavelet transform-zero crossing technique in the simultaneous spectrophotometric determination of perindopril and indapamid in tablets

Signal processing methods based on the combined use of the continuous wavelet transform (CWT) and zero-crossing technique were applied to the simultaneous spectrophotometric determination of perindopril (PER) and indapamide (IND) in tablets. These signal processing methods do not require any priory separation step. Initially, various wavelet families were tested to identify the optimum signal processing giving the best recovery results. From this procedure, the Haar and Biorthogonal1.5 continuous wavelet transform (HAAR-CWT and BIOR1.5-CWT, respectively) were found suitable for the analysis of the related compounds. After transformation of the absorbance vectors by using HAAR-CWT and BIOR1.5-CWT, the CWT-coefficients were drawn as a graph versus wavelength and then the HAAR-CWT and BIOR1.5-CWT spectra were obtained. Calibration graphs for PER and IND were obtained by measuring the CWT amplitudes at 231.1 and 291.0 nm in the HAAR-CWT spectra and at 228.5 and 246.8 nm in BIOR1.5-CWT spectra, respectively. In order to compare the performance of HAAR-CWT and BIOR1.5-CWT approaches, derivative spectrophotometric (DS) method and HPLC as comparison methods, were applied to the PER-IND samples. In this DS method, first derivative absorbance values at 221.6 for PER and 282.7 nm for IND were used to obtain the calibration graphs. The validation of the CWT and DS signal processing methods was carried out by using the recovery study and standard addition technique. In the following step, these methods were successfully applied to the commercial tablets containing PER and IND compounds and good accuracy and precision were reported for the experimental results obtained by all proposed signal processing methods.

Fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy and chemometric techniques for the determination of adulteration in petrodiesel/biodiesel blends

We propose an analytical method based on fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy to detect the adulteration of petrodiesel and petrodiesel/palm biodiesel blends with African crude palm oil. The infrared spectral fingerprints from the sample analysis were used to perform principal components analysis (PCA) and to construct a prediction model using partial least squares (PLS) regression. The PCA results separated the samples into three groups, allowing identification of those subjected to adulteration with palm oil. The obtained model shows a good predictive capacity for determining the concentration of palm oil in petrodiesel/biodiesel blends. Advantages of the proposed method include cost-effectiveness and speed; it is also environmentally friendly.

Reaction of wheat cultivars and differential lines to Puccinia triticina races in detached leaves

The method of preserving detached wheat leaves in Petri dish was used for the inoculation and development of the fungus Puccinia triticina, the causal agent of wheat leaf rust. The reaction of 26 wheat cultivars was compared by using seedlings cultivated in pots (in vivo) and detached leaves (in vitro) inoculated with four physiological races of the pathogen. After inoculation, the material was kept in a growth chamber for 15 days. The reaction was evaluated on the 15th day after inoculation. Results for each race in the evaluated genotypes confirmed the efficiency of the detached leaf method in assessing the reaction of wheat cultivars.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.