In this paper we consider three submonoids of the dihedral inverse monoid DI_n, namely its submonoids OPDI_n, MDI_n and ODI_n of all orientation-preserving, monotone and order-preserving transformations, respectively. For each of these three monoids, we compute the cardinal, give descriptions of Green's relations and determine the rank.

Em Portugal, existe uma ausência de formalização da ciência para assuntos políticos em que a procura de aconselhamento é, em grande medida, informal.

In this paper we consider the monoid DPC_n of all partial isometries of a n-cycle graph C_n. We show that DPC_n is the submonoid of the monoid of all oriented partial permutations on a n-chain whose elements are precisely all restrictions of a dihedral group of order 2n. Our main aim is to exhibit a presentation of DPC_n. We also describe Green's relations of DPC_n and calculate its cardinality and rank.

In this paper we consider the monoid DPSn of all partial isometries of a star graph Sn with n vertices. Our main objectives are to determine the rank and to exhibit a presentation of DPSn. We also describe Green’s relations of DPSn and calculate its cardinal.

In this paper we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid wEndP_n of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid O_n of all order-preserving transformations of a n-chain. Also, we describe the regular elements of wEndP_n and calculate its size and number of idempotents.

Following the new description of an oriented full transformation on a finite chain given recently by Higgins and Vernitsk,
in this short note we present a refinement of this description which is extendable to partial transformations and to injective partial transformations.

This paper aims at contributing towards a better understanding of the non-uniform elastoplastic torsion mechanism of I-section beams. The particular case of cantilevers subjected to an end torque is analysed, which constitutes a simple yet interesting problem, since the maximum torque is very close to the so-called Merchant upper bound (MUB), with added independent maximum bishear and Saint-Venant torques. Consequently, it turns out that the maximum torque can be significantly higher than that for uniform plastic torsion. Besides the MUB, several solutions are presented and compared, namely (i) a stress resultant-based solution stemming from the warping beam theory differential equilibrium equation and (ii) solutions obtained with several beam finite elements that allow for a coarse/refined description of warping. It is found that all models are in very close agreement in terms of maximum torque (including the MUB) and stress resultants. However, the beam finite elements that allow for bishear, even with a simplified warping function, are further capable of reproducing quite accurately the stress field, as a comparison with a 3D solid finite element solution shows. Although the paper is primarily concerned with the small displacement case, the influence of considering finite rotations is also addressed.

A large fraction of the current environmental crisis derives from the large rates of human-driven biodiversity loss. Biodiversity conservation questions human practices towards biodiversity and, therefore, largely conflicts with ordinary societal aspirations. Decisions on the location of protected areas, one of the most convincing conservation tools, reflect such a competitive endeavor. Operations Research (OR) brings a set of analytical models and tools capable of resolving the conflicting interests between ecology and economy. Recent technological advances have boosted the size and variety of data available to planners, thus challenging conventional approaches bounded on optimized solutions. New models and methods are needed to use such a massive amount of data in integrative schemes addressing a large variety of concerns. This study provides an overview on the past, present and future challenges that characterize spatial conservation models supported by OR. We discuss the progress of OR models and methods in spatial conservation planning and how those models may be optimized through sophisticated algorithms and computational tools. Moreover, we anticipate possible panoramas of modern spatial conservation studies supported by OR and we explore possible avenues for the design of optimized interdisciplinary collaborative platforms in the era of Big Data, through consortia where distinct players with different motivations and services meet. By enlarging the spatial, temporal, taxonomic and societal horizons of biodiversity conservation, planners navigate around multiple socioecological/environmental equilibria and are able to decide on cost-effective strategies to improve biodiversity persistence under complex environments.