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.

This paper intends to determine whether the lean, agile, resilient and green paradigms are applied and combined in the actual environment of supply-chain management. A structured literature review on the state of the art was carried out, thus providing a comprehensive understanding on supply-chain management. A classification scheme of supply-chain paradigms was developed where five databases were used to find how these paradigms were being integrated. The research developed provided the confirmation that papers combining more than two paradigms were rare. To date, academicians have not studied the merging of these paradigms in supply-chain management at significant depth.

We analysed the changes in the metabolites of Lupinus albus organs (leaf-blades, petioles, apexes, hypocotyls and roots) as a consequence of B deficiency. The deficiency did not affect malate concentration and induced only minor changes in the sugar content, suggesting that the carbohydrate metabolism is little affected by the deficiency. Contrarily, marked changes in the content of free amino acids were observed, with some specific variations associated with the different organs. These changes indicate that various aspects of metabolism implicated in the amino acid accumulation were affected by B deficiency. Most of the detected changes appear to have implications with some stress responses or signalling processes. Asparagine and proline that increase in many stresses also accumulated in petioles, apexes and hypocotyls. Accumulation of gamma-aminobutyric acid shunt amino acids, indicative of production of reactive oxygen species, occurs in the same three organs and also the roots. The increase in the branched-chain amino acids, observed in all organs, suggests the involvement of B with the cytoskeleton, whereas glycine decrease in leaf-blades and active growing organs (apexes and roots) could be associated with the proposed role of this amino acids in plant signalling in processes that might be associated with the decreased growth rates observed in B deficiency. Despite the admitted importance of free amino acids in plant metabolism, the available information on this matter is scarce. So our results bring new information concerning the effects of B deficiency in the metabolism of the several L. albus organs.

The European Union directive for electric and electronic waste, published in 2003, enforced all European countries to meet some targets concerning the recycling and recovery of these products. This directive was transposed to the Portuguese legislation in 2004. Following this, a group of EEE producers set up an organization (Amb3e) whose mission was to design and manage a nationwide recovery network for WEEE, which will be the subject matter of this work. A generic MILP model is proposed to represent this network, which is applied to its design and planning, where the best locations for collection and sorting centres are chosen simultaneously with the definition of a tactical network planning. Several analyses are performed to provide further insights regarding the selection of these alternative locations. The results gave support to the company strategic expansion plans for a high number of centres to be opened and to their location near the major WEEE sources.

Theoretical expressions for ionization cross sections by electron impact based on the binary encounter Bethe (BEB) model, valid from ionization threshold up to relativistic energies, are proposed.The new modified BEB (MBEB) and its relativistic counterpart (MRBEB) expressions are simpler than the BEB (nonrelativistic and relativistic) expressions because they require only one atomic parameter, namely the binding energy of the electrons to be ionized, and use only one scaling term for the ionization of all sub-shells.The new models are used to calculate the K-, L- and M-shell ionization cross sections by electron impact for several atoms with Z from 6 to 83.Comparisons with all, to the best of our knowledge, available experimental data show that this model is as good or better than other models, with less complexity.

We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights \(\varphi_{t,\gamma}(\tau)=|(\tau-t)^\gamma|\), where \(\gamma\) is a complex number, over arbitrary Carleson curves. If the curve has different spirality indices at the point $t$ and \(\gamma\) is not real, then \(\varphi_{t,\gamma}\) is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko.