Bounds and extremal domains for Robin eigenvalues with negative boundary parameter

We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking coordinate method, and a proof that in the fixed perimeter case the disk maximises the first eigenvalue for all values of the parameter. This is in contrast with what happens in the constant area problem, where the disk is the maximiser only for small values of the boundary parameter. We also present sharp upper and lower bounds for the first eigenvalue of the ball and spherical shells. These results are complemented by the numerical optimisation of the first four and two eigenvalues in 2 and 3 dimensions, respectively, and an evaluation of the quality of the upper bounds obtained. We also study the bifurcations from the ball as the boundary parameter becomes large (negative).Comment: 26 pages, 20 figure

Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian

We consider the problem of minimising the $n^{th}-$eigenvalue of the Robin Laplacian in $\mathbb{R}^{N}$. Although for $n=1,2$ and a positive boundary parameter $\alpha$ it is known that the minimisers do not depend on $\alpha$, we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on $\alpha$. We derive a Wolf-Keller type result for this problem and show that optimal eigenvalues grow at most with $n^{1/N}$, which is in sharp contrast with the Weyl asymptotics for a fixed domain. We further show that the gap between consecutive eigenvalues does go to zero as $n$ goes to infinity. Numerical results then support the conjecture that for each $n$ there exists a positive value of $\alpha_{n}$ such that the $n^{\rm th}$ eigenvalue is minimised by $n$ disks for all $0<\alpha<\alpha_{n}$ and, combined with analytic estimates, that this value is expected to grow with $n^{1/N}$

A CHECK-LIST OF FOSSIL CHONDRICHTHYES FROM BRIELAS (LANGHIAN, PORTUGAL)

Located in a slope of the Costa de Caparica motorway, in the peninsula of Setúbal, West Portugal, the outcrop of Brielas stand out as one of the best Miocene sections of the Lower Tagus Basin to collect a great diversity of fossil Chondrichthyes, which are cartilaginous fishes also known as selachians. The first mention regarding this outcrop was made by Antunes and Jonet (1970), in a study focused on the characterization of Serravalian to Tortonian shark fossil forms of Lisbon. The sediments present in Brielas can be correlated with the geological units Vc, VIa and VIIa traditionally used for the Miocene of Lisbon (Cotter in Dollfus et al., 1903-1904). The samples studied were taken from the unit Vc, with approximately four meters thick and characterized by sandy-silt banks, intercalated with fossiliferous biocalcarenites. Through 87Sr/86Sr dating (H. Elderfield) of a Pectinid shell it was determined that the Vc unit has an age of approximately 14 ± 0,4Ma (Antunes et al., 1999), and integrates the depositional sequence S1 (Antunes et al., 2000). The planktonic foraminifera association found by Legoinha (2001) portrays the unit Vc as part of the biozone N9, correlative of the Langhian. The present study aims to contribute to the improvement of the knowledge about Brielas section and its rich marine selachian faun

The exotic invasive plant Vincetoxicum rossicum is a strong competitor even outside its current realized climatic temperature range

Dog-strangling vine (Vincetoxicum rossicum) is an exotic plant originating from Central and Eastern Europe that is becoming increasingly invasive in southern Ontario, Canada. Once established, it successfully displaces local native plant species but mechanisms behind this plant’s high competitive ability are not fully understood. It is unknown whether cooler temperatures will limit the range expansion of V. rossicum, which has demonstrated high tolerance for other environmental variables such as light and soil moisture. Furthermore, if V. rossicum can establish outside its current climatic limit it is unknown whether competition with native species can significantly contribute to reduce fitness and slow down invasion. We conducted an experiment to test the potential of V. rossicum to spread into northern areas of Ontario using a set of growth chambers to simulate southern and northern Ontario climatic temperature regimes. We also tested plant-plant competition by growing V. rossicum in pots with a highly abundant native species, Solidago canadensis, and comparing growth responses to plants grown alone. We found that the fitness of V. rossicum was not affected by the cooler climate despite a delay in reproductive phenology. Growing V. rossicum with S. canadensis caused a significant reduction in seedpod biomass of V. rossicum. However, we did not detect a temperature x competition interaction in spite of evidence for adaptation of S. canadensis to cooler temperature conditions. We conclude that the spread of V. rossicum north within the tested range is unlikely to be limited by climatic temperature but competition with an abundant native species may contribute to slow it down

Numerical minimization of dirichlet laplacian eigenvalues of four-dimensional geometries

We develop the first numerical study in four dimensions of optimal eigenmodes associated with the Dirichlet Laplacian. We describe an extension of the method of fundamental solutions adapted to the four-dimensional context. Based on our numerical simulation and a postprocessing adapted to the identification of relevant symmetries, we provide and discuss the numerical description of the eighth first optimal domains.The work of the first author was partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific project PTDC/MATCAL/4334/2014. The work of the second author was supported by the ANR, through the projects COMEDIC, PGMO, and OPTIFORMinfo:eu-repo/semantics/publishedVersio

Causes of the Decline of Economic Growth in Italy and the Responsibility of EURO. A Balance-of-Payments Approach.

Some countries of the Euro-zone have experienced a declining economic growth more pronounced in the last recent years, like Italy. The aim of this paper is to investigate the causes of the poor growth performance in Italy and the responsibility of the Euro for this crisis. The theoretical approach applied is based on the balance-of-payments constraint hypothesis (known as Thirlwall’s Law) adapted to include internal and external imbalances. Our empirical analysis shows that both the extended model and the original Thirlwall’s Law over-predict the actual growth in Italy suggesting that there are supply constraints that encumber the economy from growing faster. Another conclusion is that part of the decline in economic growth is explained by the loss of competiveness during the Euro period. A scenarios analysis shows that a budget deficit and public debt discipline aiming at achieving the goals of the Stability Pact are not significant stimulus for faster growth. On the other hand, reducing the import dependence of the components of demand, or reducing the import and increasing the export shares in the economy are the most effective policies for fostering growth in Italy.Internal and External Imbalances, Import Elasticities of the Components of Demand, Equilibrium Growth Rates, 3SLS System Regressions.

Growth rates constrained by internal and external imbalances: a demand orientated approach.

Thirlwall’s Law considers that growth can be constrained by the balance-of-payments when the current account is in permanent deficit. The Law focuses on external imbalances as impediments to growth and does not consider the case where internal imbalances (budget deficits or public debt) can also constrain growth. The recent European public debt crisis shows that when internal imbalances are out of control they can constrain growth and domestic demand in a severe way. The aim of this paper is to fill this gap by developing a growth model in line with Thirlwall’s Law that takes into account both internal and external imbalances. The model is tested for Portugal that recently fell into a public debt crisis with serious negative consequences on growth. The empirical analysis shows that the growth rate in Portugal is in fact balance-of-payments constrained and the main drawback is the high import elasticity of the components of demand and in particular that of exports.internal and external imbalances, import elasticities of the components of demand, equilibrium growth rates, 3SLS system regressions.

Embodying Uncertainty in a Portuguese Borderland Village

UIDB/04038/2020 UIDP/04038/2020Focusing on the ritual of the Commending of the Souls in Penha Garcia (Portugal), this article analyzes how its recasting as heritage is re-inventing a declining rurality and aiding an uncertain future. A renewed vernacular engagement with the ritual, along with the local use of heritage policy to render it intangible heritage is 1) generating a vernacularization of Portuguese Catholicism (analogous to “religious pluralization”), and 2) construing heritage-making as an efficacious technique of religious belief. This article argues that the collective engagement of local actors in the processes of vernacularization and transforming of this ritual into heritage is (re-)enchanting the virtuosity of their local religiosity, which embodies and suspends a structural uncertainty.publishersversionpublishe

Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives

In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.P.A. is partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific projects PEstOE/MAT/UI0208/2013 and PTDC/MAT-CAL/4334/2014. R.F. was supported by the “Fundação para a Ciência e a Tecnologia (FCT)” through the program “Investigador FCT” with reference IF/01345/2014.info:eu-repo/semantics/publishedVersio