Repository logo

Browsing by Issue Date, starting with "2010-08-15"

Filter results by year or month
Now showing 1 - 2 of 2
  • Grid structure impact in sparse point representation of derivatives
    Publication . Domingues, Margarete O.; Ferreira, Paulo; Gomes, Sónia M.; Gomide, Anamaria; Pereira, José R.; Pinho, Pedro
    In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.
    2010-08-15Journal article Open access Show more
  • Essential oils of Origanum vulgare L. subsp glandulosum (Desf.) letswaart from Tunisia: chemical composition and antioxidant activity
    Publication . Mechergui, Kaouther; Coelho, Jose; Serra, Maria Celeste; Lamine, Sassia B.; BOUKHCHINA, SADOK; Khouja, Mohamed Larbi Arbi
    BACKGROUND: Characterisation of the essential oils from O. glandulosum collected in three locations of Tunisia, chemical composition and the evaluation of their antioxidant activities were carried out. RESULTS: The essential oils from Origanum vulgare L. subsp. glandulosum (Desf.) letswaart collected from three localities of north Tunisia - Krib, Bargou and Nefza - were obtained in yields of 2.5, 3.0 and 4.6% (v/w), respectively. The essential oils were analysed by GC and GC/MS and assayed for their total phenolics content, by the Folin-Ciocalteu method, and antioxidant effectiveness, using the 2,2-diphenyl-1-picrylhydrazil (DPPH) radical scavenging assay. The main components of these essential oils, from Nefza, Bargou and Krib, were p-cymene (36%, 40% and 46%), thymol (32%, 39% and 18%), gamma-terpinene (24%, 12% and 16%) and carvacrol (2%, 2% and 15%), respectively). The ability to scavenge the DPPH radicals, expressed by IC50, ranged from 59 to 80 mg L-1. The total phenolic content, expressed in gallic acid equivalent (GAE) g kg(-1) dry weight, varied from 9.37 to 17.70 g kg(-1) dw. CONCLUSIONS: A correlation was identified between the total phenolic content of the essential oils and DPPH radical scavenger capacity. The occurrence of a p-cymene chemotype of O. glandulosum in the northern region of Tunisia is demonstrated.
    2010-08-15Journal article Open access Show more