Iterative process for G-multi degree reduction of Bézier curves

In this paper, the issue of multi-degree reduction of Bézier curves with C¹ and G²-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method.     

Multiple Degree Reduction and Elevation of Bézier Curves Using Jacobi–Bernstein Basis Transformations

In this article, we find the optimal r times degree reduction of Bézier curves with respect to the Jacobi-weighted L ₂-norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L ₁, L ₂, and L _∞-norms. We give some examples and figures to demonstrate these methods.     

In Vitro Gastric and Intestinal Digestions of Pulsed Light-Treated Shrimp Extracts

Pulsed ultraviolet light (PUV), a novel technology most commonly used for microbial inactivation, has recently been employed to effectively mitigate food allergens in peanuts, soybean, shrimp, and almond. Putative mechanisms for the efficacy of PUV in reducing allergen reactivity include photothermal, photochemical, and photophysical effects. To date, there are no published data highlighting the effects of in vitro simulated gastric and intestinal digestion on the stability of PUV reduced allergen reactivity of food. In this study, PUV-treated shrimp extracts were subjected to simulated gastric fluid containing pepsin and simulated intestinal fluid containing trypsin and chymotrypsin, and then tested for changes in allergen potency. SDS-PAGE showed no major band deviation between undigested and digested PUV-treated shrimp extracts. IgE binding to tropomyosin remained markedly decreased as seen in Western blot analysis. Total shrimp allergen reactivity remained unchanged following in vitro peptic digestion and was markedly reduced following in vitro intestinal digestion as illustrated in indirect ELISA. The PUV reduced shrimp allergens remained at a low level under the in vitro simulated digestive conditions. The results inferred that PUV could be a potential method to create less allergenic shrimp products that would remain at a low allergen level under human gastric and intestinal digestive conditions.     

Electron spin density distribution in the polymer phase of CsC60: assignment of the NMR spectrum

We present high resolution 133Cs-13C double resonance NMR data and 13C-13C NMR correlation spectra of 13C enriched samples of the polymeric phase of CsC60. These data lead to a partial assignment of the lines in the 13C NMR spectrum of CsC60 to the carbon positions on the C60 molecule. A plausible completion of the assignment can be made on the basis of an ab initio calculation. The data support the view that the conduction electron density is concentrated at the C60 "equator," away from the interfullerene bonds.     

Computing Derivatives of Jacobi Polynomials Using Bernstein Transformation and Differentiation Matrix

In this paper, we give a new, simple, and efficient method for evaluating the pth derivative of the Jacobi polynomial of degree n. The Jacobi polynomial is written in terms of the Bernstein basis, and then the pth derivative is obtained. The results are given in terms of both Bernstein basis of degree n ? p and Jacobi basis form of degree n ? p and presented in a matrix form. Numerical examples and comparisons with other well-known methods are presented.     

Antioxidant activities, total phenolics and HPLC analyses of the phenolic compounds of extracts from common Mediterranean plants

In this study, the total phenolic amounts and antioxidant activities of plant extracts obtained from some common Mediterranean plant species collected from different places in Jordan were determined. The phenolic constituents of these extracts were also determined using HPLC. The total phenolic amounts ranged from 52.8 to 876.9 mg GAE per 100 g dry material. The antioxidant activities were evaluated according to the 2,2-diphenyl-1-picrylhydrazyl radical scavenger method. Sage (Salvia officinalis) showed the highest antioxidant activity (91%), while the lowest (11.3%) was seen in parsley (Petroselinum crispum). A strong correlation (r = 0.85) between antioxidant activity and total phenolic content was found. The phenolic compounds identified by HPLC were gallic acid, protocatechuic acid, catechin, gentisic acid, chlorogenic acid, vanillic acid, syringic acid, caffeic acid, epicatechin and benzoic acid. All the investigated plants contain gallic acid, whose phenolic content ranged from 0.4 to 37.8 mg per 100 g, catechin (0.3-339.9 mg per 100 g), protocatechuic acid (0.3-41.9 mg per 100 g) and gentisic acid (0.3-35.8 mg per 100 g), while caffeic acid (0.3-2.6 mg per 100 g) was detected in six species only. These natural plant phenolics could thus be a good source of antioxidants for applications in food.