Full analogy of Sharkovsky's theorem for lower semicontinuous maps

A full analogy of the celebrated Sharkovsky cycle coexistence theorem is established for lower semicontinuous (multivalued) maps on metrizable linear continua. This result is further extended to triangular maps.     

Scheduling production of multiple part-types in a system with pre-known demands and deterministic inactive time intervals

We introduce and formalise a scheduling problem that consists in determining an optimum policy (i.e. one that minimises total inventory holding costs) to produce n part-types using a system that is able to share its capacity at all times among these part-types and that switches between an active and an inactive state for pre-known periods of time. Consequently, when active the system must produce enough reserves to meet the demand during the inactive interval. We show that there is always a simple optimum policy in which the production of the part-types is prioritised and, provided the units are properly defined, the optimum priority ordering corresponds to a non-decreasing sequence of the unit holding costs of the part-types.     

A proposal for a hybrid meta-strategy for combinatorial optimization problems

In this paper, we propose an algorithm named BDS (Bound-Driven Search) that combines features of exact and approximate methods. The proposed procedure may be seen as a local search algorithm that systematically explores (in a branch-and bound sense) the most promising nodes, thus preventing solutions from being reevaluated. Additionally, it can be regarded as an exact method as it may be able to guarantee that the solution found is optimal. We present the application of this new algorithm to a specific problem domain: the permutation flow shop scheduling problem with makespan objective. The subsequent computational experiments are encouraging, as the algorithm is able to yield exact or near exact solutions to most instances of the problem. Furthermore, the algorithm outperforms one of the best state-of-the-art algorithms for the problem.     

On comparison of ℓ-stable vector optimization results

Two papers with similar optimality conditions were published by I. Ginchev, and by D. Bedna?ík and K. Pastor independently in Nonlinear Analysis in 2011. We compare these results. We also show the equivalence of two definitions of ?-stability of vector functions. Moreover, we generalize another result given by I. Ginchev and V. I. Ivanov [J. Math. Anal. Appl. 340 (2008), 646–657] and compare it with the previously mentioned optimality conditions.     

Effect of precipitation procedure and detection technique on particle size distribution of CaCO3

The deposition of inorganic salts (“scales”) such as calcium carbonate is an important flow assurance problem during crude oil production. The knowledge of the features of the precipitated solids, mainly the particle size and morphology, is crucial to understand the nature of the solids and to avoid or reduce the effect of their deposition. For instance, the use of additives is one of the most usual procedures to mitigate this problem. Additives interact with scale-forming substances either by increasing the induction time, or by inhibiting crystal growth, changing the morphology of solids.     

On uniqueness of fractional powers of multi-valued linear operators and the incomplete Cauchy problem

We obtain uniqueness of additive families {A _t } _t>0 of fractional powers of a multi-valued sectorial linear operator A ?? A ₁ in a Banach space, satisfying a certain kind of continuity with respect to the exponent and a spectral property, from uniqueness of the solutions of the second-order incomplete Cauchy problem associated with A. We show the close relationship between the multiplicativity and the uniqueness of fractional powers.     

Calculation of the electronic properties of neutral and ionized divalent-metal clusters

The electronic properties of neutral and ionized divalent-metal clusters have been studied using a microscopic theory, which takes into account the interplay between van der Waals (vdW) and covalent bonding in the neutral clusters, and the competition between hole delocalization and polarization energy in the ionized clusters. By calculating the ground-state energies of neutral and ionized Hg _n clusters, we determine the size dependence of the bond character and the ionization potentialI _p (n). For neutral Hg _n clusters we obtain a transition from van der Waals to covalent behaviour at the critical sizen _c ～10–20 atoms. Results forI _p (Hg _n ) withn≤20 are in good agreement with experiments, and suggest that small Hg _n ⁺ clusters can be viewed as consisting of a positive trimer core Hg ₃ ⁺ surrounded byn?3 polarized neutral atoms.     

The quantitative electrochemical generation of bromine in acetic acid

The quantitative electrochemical generation of bromine at a platinum electrode in acetic acid is described. Coulometric methods for the determination of hydroquinone and 2-methylhydroquinone are reported. The best results are obtained with 0.7–1.1 M potassium acetate solutions as supporting electrolyte, and biamperometric end-point detection. The effects of water and acetic anhydride on the accuracy of titrations are discussed. Determination of the formal redox potential of the Br₂/Br^- system in a 0.9 M potassium acetate solution in acetic acid showed that bromide is oxidized directly to bromine at a platinum electrode with 100% current efficiency.