New roles for farming in a differentiated countryside: the Portuguese example

Throughout Europe, the role of farming as the private provider of public goods and services increasingly valuated by society is today generally acknowledged. Furthermore, in the turn towards rural development concerns, multifunctionality as an attribute of rural space has emerged, justifying the territorial approach of farming. The situation facing the multifunctionality demand is nevertheless not the same in all European regions, which by all means is getting strengthened in the transition towards post-productivism. In some regions, there is a productivist orientation and production has a dominant economic role, while others will need to be supported on other functions to survive economically and socially, or may be best suited to environmental functions alone. The vocation of the rural territories is different, and thus also the functions they are able to support. This paper discusses the concept of multifunctionality of the rural areas, and defines a possible methodological approach towards the identification of the different types of rural areas in Europe, based on the identification of ideal types, through the analysis of selected indicators. The empirical application has been developed for the Portuguese Ministry of Agriculture, aiming at assessing the differentiated characteristics and dynamics of the Portuguese rural territory. Analyzing data from 1990 and 2000, at municipal level, three dimensions have been considered: the land cover, the agricultural sector and the rural community. Combining the three analyses, it was possible to identify different vocations of the rural space, and the role that farming could have in the future for the multifunctionality of the territory. Accordingly, the municipalities have been grouped in types, pre-defined as ideal types. This was a first attempt to understand the differentiation of the rural territory in Portugal. For decision-making it should be further developed. It nevertheless shows that there is clear differentiation concerning the possible landscape functions to be developed between regions and a possible way to assess. It also shows that a territorial approach to agriculture may be the key for the maintenance of the sector in many areas where production by itself, as it has been know until now, may be severely threatened

On the convergence to critical scaling profiles in submonolayer deposition models

In this work we study the rate of convergence to similarity profiles in a mean field model for the deposition of a submonolayer of atoms in a crystal facet, when there is a critical minimal size $n\geq 2$ for the stability of the formed clusters. The work complements recently published related results by the same authors in which the rate of convergence was studied outside of a critical direction $x=\tau$ in the cluster size $x$ vs. time $\tau$ plane. In this paper we consider a different similarity variable, $\xi := (x-\tau)/\sqrt{\tau}$, corresponding to an inner expansion of that critical direction, and prove the convergence of solutions to a similarity profile $\Phi_{2,n}(\xi)$ when $x, \tau\to +\infty$ with $\xi$ fixed, as well as the rate at which the limit is approached.Comment: Dedicated to the memory of Jack Car

The Redner - Ben-Avraham - Kahng cluster system

We consider a coagulation model first introduced by Redner, Ben-Avraham and Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J. Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that the reaction between a j-cluster and a k-cluster results in the creation of a |j-k|-cluster, and not, as in Smoluchowski's model, of a (j+k)-cluster. In this paper we prove existence and uniqueness of solutions under reasonably general conditions on the coagulation coefficients, and we also establish differenciability properties and continuous dependence of solutions. Some interesting invariance properties are also proved. Finally, we study the long-time behaviour of solutions, and also present a preliminary analysis of their scaling behaviour.Comment: 24 pages. 2 figures. Dedicated to Carlos Rocha and Luis Magalhaes on the occasion of their sixtieth birthday

Steps in modular specifications for concurrent modules

© 2015 Published by Elsevier B.V.The specification of a concurrent program module is a difficult problem. The specifications must be strong enough to enable reasoning about the intended clients without reference to the underlying module implementation. We survey a range of verification techniques for specifying concurrent modules, in particular highlighting four key concepts: auxiliary state, interference abstraction, resource ownership and atomicity. We show how these concepts combine to provide powerful approaches to specifying concurrent modules

Rates of convergence to scaling profiles in a submonolayer deposition model and the preservation of memory of the initial condition

We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modelling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies in a change of variables that allows for the decoupling of the original infinite system of ordinary differential equations into a closed two-dimensional nonlinear system for the monomer--bulk dynamics and a lower triangular infinite dimensional linear one for the cluster dynamics. The detailed knowledge of the long time monomer concentration, which was obtained earlier by Costin et al. in (O. Costin, M. Grinfeld, K.P. O'Neill and H. Park, Long-time behaviour of point islands under fixed rate deposition, Commun. Inf. Syst. 13, (2), (2013), pp.183-200) using asymptotic methods and is rederived here by center manifold arguments, is then used for the asymptotic evaluation of an integral representation formula for the concentration of $j$-clusters. The use of higher order expressions, both for the Stirling expansion and for the monomer evolution at large times allow us to obtain, not only the similarity limit, but also the rate at which it is approached.Comment: Revised according to referee's suggestions; to be published in SIAM J. Math. Ana

The Redner - Ben-Avraham - Kahng coagulation system with constant coefficients: the finite dimensional case

We study the behaviour as $t\to\infty$ of solutions $(c_j(t))$ to the Redner--Ben-Avraham--Kahng coagulation system with positive and compactly supported initial data, rigorously proving and slightly extending results originally established in [4] by means of formal arguments.Comment: 13 pages, 1 figur