n/a

Given graphs G and H and a positive number b, a weighted (H,b)-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms an H-subgraph. We assign a weight of b to each H-subgraph in the decomposition and a weight of 1 to single edges. The total weight of the decomposition is the sum of the weights of all elements in the decomposition. Let f(n,H,b) be the the smallest number such that any graph G of order n admits an (H,b)-decomposition with weight at most f(n,H,b). The value of the function f(n,H,b) when b=1 was determined, for large n, by Pikhurko and Sousa [Pikhurko, O. and Sousa, T., Minimum H-Decompositions of Graphs, Journal of Combinatorial Theory, B, 97 (2007), 1041--1055.Here we determine the asymptotic value of f(n,H,b)for any fixed bipartite graph H and any value of b as n tends to infinity.

No património edificado português as rochas granulares assumem importância relevante nos elementos construtivos presentes no património histórico e cultural, nomeadamente as pedras graníticas e areníticas. Tendo por objectivo a avaliação do comportamento mecânico de rochas granulares presentes no património edificado histórico foi realizado um estudo de investigação experimental sobre amostras dos litótipos seleccionados e que são representativos de rochas presentes no próprio edificado, em termos de propriedades petrográficas, físicas e mecânicas. Neste artigo apresenta-se um modelo analítico definido com base em ensaios experimentais que permite efectuar a simulação do comportamento das rochas em compressão uniaxial (diagramas de tensão-deformação), função de propriedades físicas e mecânicas obtidas através de ensaios não destrutivos e quasi não destrutivos. Este modelo permite desta forma a avaliação do comportamento mecânico de rochas granulares sem afectar a integridade do património histórico.

Eleven new tracks from the Upper Jurassic of Portugal are described and attributed to the stegosaurian ichnogenus Deltapodus. One track exhibits exceptionally well−preserved impressions of skin on the plantar surface, showing the stegosaur foot to be covered by closely spaced skin tubercles of ca. 6 mm in size. The Deltapodus specimens from the Aalenian of England represent the oldest occurrence of stegosaurs and imply an earlier cladogenesis than is recognized in the body fossil record.

We prove that given a finite (zero) exact right decomposition (M, T) of a semigroup S, if M is defined by a finite complete presentation, then S is also defined by a finite complete presentation. Exact right decompositions are natural generalizations to semigroups of coset decompositions in groups. As a consequence, we deduce that any Zappa–Szép extension of a monoid defined by a finite complete presentation, by a finite monoid, is also defined by such a presentation.

It is also proved that a semigroup M^0[A; I, J; P], where A and P satisfy some very general conditions, is also defined by a finite complete presentation.

We give an example of a monoid with finitely many left and right ideals, all of whose Schützenberger groups are presentable by finite complete rewriting systems, and so each have finite derivation type, but such that the monoid itself does not have finite derivation type, and therefore does not admit a presentation by a finite complete rewriting system. The example also serves as a counterexample to several other natural questions regarding complete rewriting systems and finite derivation type. Specifically it allows us to construct two finitely generated monoids M and N with isometric Cayley graphs, where N has finite derivation type (respectively, admits a presentation by a finite complete rewriting system) but M does not. This contrasts with the case of finitely generated groups for which finite derivation type is known to be a quasi-isometry invariant. The same example is also used to show that neither of these two properties is preserved under finite Green index extensions.

n/a

Optimized supply chains, both economically as well as environmentally, are significant instruments to be adopted by companies if they want to succeed in the current competitive world. However, without the support of decision tools to help, at least approximately, the integration of these two aspects in the company’s decision making such aim is difficult to reach. The purpose of this study is to develop a mixed integer linear programming model (MILP), which allows the optimization of closed loop supply chains, considering not only economical aspects, but also environmental ones. The model developed was applied to a Portuguese company where their logistic network structure was redesigned.

The efficient design and operation of supply chains with return flows represent a major optimization challenge, given the high number of factors involved and their intricate interactions. In particular, the quality level of the return products has strong economic and societal implications and depends greatly on the type of product (glass, paper, electronic, oil, etc) and on the degree of consumers’ readiness, frequently promoted by various kinds of awareness raising campaigns. A multi-product multi-period model was previously developed by the authors [1] for the closed-loop supply chain (CLSC) design and planning, where strategic and tactical decisions were comprehensively considered. This model is now being extended to handle the uncertainty related to the quality of the returned products, which at this stage is modeled by a two-stage scenario-based stochastic approach. General strategies to solve optimization problems involving uncertainty tend to exhibit poor computational performance, due to the problem NP-hard complexity, which tends to worsen with the problem size. Therefore and, in addition, a model performance solution enhancement is also being explored. To increase the efficiency of the solution approach, an alternative representation to some of the integer variables employed in the mathematical formulation was developed, which is tested by means of computational experiments being performed on illustrative real sized examples.

n/a

n/a