976 resultados para Laguerre orthogonal polynomials


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In the present paper we discuss the development of "wave-front", an instrument for determining the lower and higher optical aberrations of the human eye. We also discuss the advantages that such instrumentation and techniques might bring to the ophthalmology professional of the 21st century. By shining a small light spot on the retina of subjects and observing the light that is reflected back from within the eye, we are able to quantitatively determine the amount of lower order aberrations (astigmatism, myopia, hyperopia) and higher order aberrations (coma, spherical aberration, etc.). We have measured artificial eyes with calibrated ametropia ranging from +5 to -5 D, with and without 2 D astigmatism with axis at 45º and 90º. We used a device known as the Hartmann-Shack (HS) sensor, originally developed for measuring the optical aberrations of optical instruments and general refracting surfaces in astronomical telescopes. The HS sensor sends information to a computer software for decomposition of wave-front aberrations into a set of Zernike polynomials. These polynomials have special mathematical properties and are more suitable in this case than the traditional Seidel polynomials. We have demonstrated that this technique is more precise than conventional autorefraction, with a root mean square error (RMSE) of less than 0.1 µm for a 4-mm diameter pupil. In terms of dioptric power this represents an RMSE error of less than 0.04 D and 5º for the axis. This precision is sufficient for customized corneal ablations, among other applications.

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Research on molecular mechanisms of carcinogenesis plays an important role in diagnosing and treating gastric cancer. Metabolic profiling may offer the opportunity to understand the molecular mechanism of carcinogenesis and help to non-invasively identify the potential biomarkers for the early diagnosis of human gastric cancer. The aims of this study were to explore the underlying metabolic mechanisms of gastric cancer and to identify biomarkers associated with morbidity. Gas chromatography/mass spectrometry (GC/MS) was used to analyze the serum metabolites of 30 Chinese gastric cancer patients and 30 healthy controls. Diagnostic models for gastric cancer were constructed using orthogonal partial least squares discriminant analysis (OPLS-DA). Acquired metabolomic data were analyzed by the nonparametric Wilcoxon test to find serum metabolic biomarkers for gastric cancer. The OPLS-DA model showed adequate discrimination between cancer and non-cancer cohorts while the model failed to discriminate different pathological stages (I-IV) of gastric cancer patients. A total of 44 endogenous metabolites such as amino acids, organic acids, carbohydrates, fatty acids, and steroids were detected, of which 18 differential metabolites were identified with significant differences. A total of 13 variables were obtained for their greatest contribution in the discriminating OPLS-DA model [variable importance in the projection (VIP) value >1.0], among which 11 metabolites were identified using both VIP values (VIP >1) and the Wilcoxon test. These metabolites potentially revealed perturbations of glycolysis and of amino acid, fatty acid, cholesterol, and nucleotide metabolism of gastric cancer patients. These results suggest that gastric cancer serum metabolic profiling has great potential in detecting this disease and helping to understand its metabolic mechanisms.

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This study analyzed the variation in shape and size of Adzuki beans during soaking at different temperatures. In addition, different mathematical models were fitted to the experimental values of volumetric expansion, selecting the best one. Grains of Adzuki beans (Vigna angularis) with moisture content of approximately 0.25 (decimal d.b.) were manually harvested; they were, then, dried to 0.128 (decimal d.b.). The beans were subjected to soaking in distilled water at the temperatures 18 ± 1, 27 ± 1, 36 ± 1, and 45 ± 1 °C, in five repetitions. Recipients containing 80 mL of distilled water and 20 g of beans for each sample were used. The samples were periodically weighed in order to determine the water absorption. After that, the samples were removed from the recipients and placed on filter papers for two minutes to drain the surface water. Water absorption continued until the beans reached the saturation moisture content. It was concluded that, the form of the Adzuki beans was altered regularly, the orthogonal axes expanded differentially in the radial and axial directions, and that the linear model appropriately described the volumetric expansion of the Adzuki beans, among the series of models analyzed for the temperatures 18, 27, 36 and 45 °C.

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Orthogonal design was employed to study the effect of extraction time, temperature and liquid-to-solid ratio on the production of antioxidant polysaccharides from leaves of Gynura bicolor (PLG). Analysis of variance was performed on the data obtained. The most relevant variable was extraction time. A liquid-solid ratio of 30:1 (v/w), a temperature of 80 °C and an extraction time of 3 h were found to be optimal for PLG. The optimal extraction yield of 4.9% was obtained through additional verification test. Hydroxyl radical-scavenging activity, reducing power and ferrous ion chelating ability of PLG were determined. PLG possess concentration-dependent antioxidant potency and IC50 of PLG was 4.67, 0.24 and 4.31 mg/mL for hydroxyl radical-scavenging and ferric ion chelating abilities as well as reducing power, respectively. The results suggest that G. bicolor polysaccharides could be potential source of natural antioxidant and be contributor to the health benefits of G. bicolor.

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