Chebyshev, Legendre, Hermite and other orthonormal polynomials in D-dimensions

We propose a general method to construct symmetric tensor polynomials in the D-dimensional Euclidean space which are orthonormal under a general weight. The D-dimensional Hermite polynomials are a particular case of the present ones for the case of a gaussian weight. Hence we obtain generalizations of the Legendre and of the Chebyshev polynomials in D dimensions that reduce to the respective well-known orthonormal polynomials in D=1 dimensions. We also obtain new D-dimensional polynomials orthonormal under other weights, such as the Fermi-Dirac, Bose-Einstein, Graphene equilibrium distribution functions and the Yukawa potential. We calculate the series expansion of an arbitrary function in terms of the new polynomials up to the fourth order and define orthonormal multipoles. The explicit orthonormalization of the polynomials up to the fifth order (N from 0 to 4) reveals an increasing number of orthonormalization equations that matches exactly the number of polynomial coefficients indication the correctness of the present procedure.Comment: 20 page

Dynamic nonlinear analyses for the 4-storey infilled R/C frame: study of a retrofitting solution

A research project on assessment and retrofitting of R/C frame structures is currently being developed under the research programme of the ICONS TMR-research network. This paper presents and discusses the preliminary experimental results from a 4-storey bare frame representative of the common practice of 40~50 years ago in most south European countries and devotes special attention to the study of a retrofitting solution based on bracing and rubber dissipaters, which intends to increase stiffness and damping reducing consequently the earthquake deformation demands.O estudo aqui apresentado concentra-se numa solução de reforço de um pórtico utilizando contraventamentos (k-bracing) com perfis de aço em conjunto com elementos elastoméricos de dissipação. Os resultados das análises não lineares da estrutura com e sem alvenaria e com reforço são apresentados e discutidos. Na segunda parte da comunicação apresentam-se os resultados experimentais já disponíveis e discute-se o problema da modelação recorrendo aos resultados experimentais e comparando os resultados obtidos com diferentes tipos de modelos

Seismic analyses of a R/C building: study of a retrofitting solution

The preliminary experimental results from the tests on a 4-storey R/C frame structure are presented and discussed. The full-scale model is representative of the common practice of 40~50 years ago in most south European countries. Special attention is devoted to the study of a retrofitting solution based on bracing and rubber dissipaters, which intends to increase stiffness and damping reducing consequently the earthquake deformation demands

Recruiting business expatriates in Portugal: A surefooted endeavor?

Managerial discourses tend to portray work-related mobility practices in a positive light, presenting mobility assignments as a place of stimulus and differentiation. A conception of mobility as an opportunity, may contrast, in specific economies and business settings, with lived personal experiences. This article reports the results of a three-year study, aimed to question how multinational companies (MNCs) located in a small and developing European economy (Portugal) are building talent pools for expatriate assignments. Interaction effects, as proposed by the job demands-resources (JD-R) theory, are considered as lens to understand the interplay of company expatriate policies, willingness profiles and psychological contracts of expatriates. By using a Portuguese sample, the study examines whether prior findings in mature economies and consolidated MNCs can be generalized to less developed international business settings.info:eu-repo/semantics/publishedVersio

Fully dissipative relativistic lattice Boltzmann method in two dimensions

In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-J\"uttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grad's theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot