Grid structure impact in sparse point representation of derivatives

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.

Assessment of the impact of the European CO2 emissions trading scheme on the Portuguese chemical industry

This paper describes an assessment of the impact of the enforcement of the European carbon dioxide (CO2) emissions trading scheme on the Portuguese chemical industry, based on cost structure, CO2 emissions, electricity consumption and allocated allowances data from a survey to four Portuguese representative units of the chemical industry sector, and considering scenarios that allow the estimation of increases on both direct and indirect production costs. These estimated cost increases were also compared with similar data from other European Industries, found in the references and with conclusions from simulation studies. Thus, it was possible to ascertain the impact of buying extra CO2 emission permits, which could be considered as limited. It was also found that this impact is somewhat lower than the impacts for other industrial sectors.

Use of quantitative structure-property relationships to study the solvation process of 18-crown-6

Solution enthalpies of 18-crown-6 have been obtained for a set of 14 protic and aprotic solvents at 298.15 K. The complementary use of Solomonov's methodology and a QSPR-based approach allowed the identification of the most significant solvent descriptors that model the interaction enthalpy contribution of the solution process (Delta H-int(A/S)). Results were compared with data previously obtained for 1,4-dioxane. Although the interaction enthalpies of 18-crown-6 correlate well with those of 1,4-dioxane, the magnitude of the most relevant parameters, pi* and beta, is almost three times higher for 18-crown-6. This is rationalized in terms of the impact of the solute's volume in the solution processes of both compounds. (C) 2015 Elsevier B.V. All rights reserved.