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In this paper, multivariate polynomials in the Bernstein basis over a simplex (simplicial Bernstein representation) are considered. Two matrix methods for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, are presented. Also matrix methods for the calculation of the Bernstein coefficients over subsimplices generated by subdivision of the standard simplex are proposed and compared with the use of the de Casteljau algorithm. The evaluation of a multivariate polynomial in the power and in the Bernstein basis is considered as well. All the methods solely use matrix operations such as multiplication, transposition, and reshaping; some of them rely also on the bidiagonal factorization of the lower triangular Pascal matrix or the factorization of this matrix by a Toeplitz matrix. The latter one enables the use of the Fast Fourier Transform hereby reducing the amount of arithmetic operations.
The Kerala tourism model
(2017)
Sustainable tourism in Kerala is on the rise. Therefore, this South Indian state is assessed according to the sustainable tourism criteria of the Strasdas et al. (2007) framework. Kerala as a state does not qualify as a sustainable tourism destination, although individual success stories at the NGO and government level exist. This conceptual paper delivers a detailed analysis of the three dimensions of sustainability, i.e. ecology, economy and socio-cultural aspects, of the ‘Kerala tourism model’ and discusses the question of whether this model can be transferred to other developing countries. Copyright © 2016 John Wiley & Sons, Ltd and ERP Environment
Leadership in a global world
(2017)
R concretes with a proportion of recycled aggregates are standardized normal concretes which are allowed for use in Germany up to strength class C30/37. Because of the good technical properties and the ecological advantages, the article presents possible applications in the field of concrete products and precast concrete elements. Read part 2 of the paper.