On Free Energies of the Ising Model on the Cayley Tree

We present, for the Ising model on the Cayley tree, some explicit formulae of the free energies (and entropies) according to boundary conditions (b.c.). They include translation-invariant, periodic, Dobrushin-like b.c., as well as those corresponding to (recently discovered) weakly periodic Gibbs states. The weakly periodic measures are defined through a partition of the Cayley tree that induces a 4-edge-coloring on that tree. We compute the density of each color. We use these densities for computations of free energies corresponding to a weakly periodic b.c.     

Cyclic coordinate descent in hydrothermal nonsmooth problems

In this paper we present an algorithm, inspired by the cyclic coordinate descent method, which allows the solution of hydrothermal optimization problems involving pumped-storage plants. The proof of the convergence of the succession generated by the algorithm was based on the use of an appropriate adaptation of Zangwill’s global theorem of convergence. Finally, the algorithm proposed is implemented using the Mathematica Package and is applied to an example to illustrate the results obtained.     

Ranking ranges in cross-efficiency evaluations

The existence of alternate optima for the DEA weights may reduce the usefulness of the cross-efficiency evaluation, since the ranking provided depends on the choice of weights that the different DMUs make. In this paper, we develop a procedure to carry out the cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into consideration all the possible choices of weights that all the DMUs can make, and yields for each unit a range for its possible rankings instead of a single ranking. This range is determined by the best and the worst rankings that would result in the best and the worst scenarios of each unit across all the DEA weights of all the DMUs. This approach might identify good/bad performers, as those that rank at the top/bottom irrespective of the weights that are chosen, or units that outperform others in all the scenarios. In addition, it may be used to analyze the stability of the ranking provided by the standard cross-efficiency evaluation.     

Crystallization of the mesomorphic form and control of the molecular structure for tailoring the mechanical properties of isotactic polypropylene

The combination of the control of the concentration of stereodefects in isotactic polypropylene using metallocene catalysts and the crystallization via the mesophase is a strategy to tailor the mechanical properties. Stiff materials, flexible materials, and thermoplastic elastomers can be produced depending only on the concentration of rr stereodefects. Modulus, ductility, and strength can be modulated through the crystallization of α and γ forms or of the mesophase. Different morphologies are observed depending on the stereoregularity and conditions of crystallization. Crystals of the mesomorphic form always exhibit a nodular morphology, accounting for the similar good deformability of all quenched samples, whatever the concentration of stereodefects. The mesophase transforms by thermal treatments into the α form preserving the nodular morphology, with increase of strength while maintaining the ductility typical of the mesophase. Annealing of the mesophase permits a precise adjustment of crystallinity and size of nodular crystals offering additional options to modify the mechanical properties. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 677–699     

On an algorithm to adapt spline approximations to the presence of discontinuities

Numerical Algorithms - Interpolatory splines are usually useful to reconstruct data that present certain regularity. This paper is devoted to the construction and analysis of a new technique that...