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Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

Publication . Pereira, P. J. S.; Lopes, Nuno David; Trabucho, L.

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

2015-10Journal article

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A spatial econometric analysis of the calls to the Portuguese National Health Line

Publication . Simões, Paula; Carvalho, M. Lucília; Aleixo, Sandra; Gomes, Sérgio; Natário, Isabel

The Portuguese National Health Line, LS24, is an initiative of the Portuguese Health Ministry which seeks to improve accessibility to health care and to rationalize the use of existing resources by directing users to the most appropriate institutions of the national public health services. This study aims to describe and evaluate the use of LS24. Since for LS24 data, the location attribute is an important source of information to describe its use, this study analyses the number of calls received, at a municipal level, under two different spatial econometric approaches. This analysis is important for future development of decision support indicators in a hospital context, based on the economic impact of the use of this health line. Considering the discrete nature of data, the number of calls to LS24 in each municipality is better modelled by a Poisson model, with some possible covariates: demographic, socio-economic information, characteristics of the Portuguese health system and development indicators. In order to explain model spatial variability, the data autocorrelation can be explained in a Bayesian setting through different hierarchical log-Poisson regression models. A different approach uses an autoregressive methodology, also for count data. A log-Poisson model with a spatial lag autocorrelation component is further considered, better framed under a Bayesian paradigm. With this empirical study we find strong evidence for a spatial structure in the data and obtain similar conclusions with both perspectives of the analysis. This supports the view that the addition of a spatial structure to the model improves estimation, even in the case where some relevant covariates have been included.

2017-06Journal article

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Ranks of monoids of endomorphisms of a finite undirected path

Publication . Dimitrova, Ilinka; Fernandes, Vítor Hugo; Koppitz, J.; Quinteiro, Teresa

In this paper, we study the widely considered endomorphisms and weak endomorphisms of a finite undirected path from monoid generators perspective. Our main aim is to determine the ranks of the monoids wEndPn and EndPn of all weak endomorphisms and all endomorphisms of the undirected path Pn with n vertices. We also consider strong and strong weak endomorphisms of Pn.

2020-03Journal article

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A method to minimize the sum of the variances of the estimators of the variance components in stair nested designs

Publication . Fernandes, Célia; Ramos, Paulo

Stair nested designs may be a good alternative to balanced nested designs since we can work with fewer observations and the amount of information for the different factors is more evenly distributed. In stair nested designs the number of treatments is the sum of the "actice" factor levels so these designs lead to a great economy. A method will be used to minimize the sum of the variances of the estimators of the variance components.

2017-10Journal article

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