On a proximal point method for convex optimization in banach spaces

We analyze the behavior of a parallel proximal point method for solving convex optimization problems in reflexive Banach spaces. Similar algorithms were known to converge under the implicit assumption that the norm of the space is Hilbertian. We extend the area of applicability of the proximal point method to solving convex optimization problems in Banach spaces on which totally convex functions can be found. This includes the class of all smooth uniformly convex Banach spaces. Also, our convergence results leave more flexibility for the choice of the penalty function involved in the algorithm and, in this way, allow simplification of the computational procedure.     

Existence of a solution for a thermoelectric model with several phase changes and a Carathéodory thermal conductivity

We present an existence result for the time domain eddy current model for electromagnetic field, coupled with a Stefan problem for temperature. We have extended the existence result proved by Bermúdez et al. (2005) [40] to the case of materials with several phase changes and thermal conductivity depending on both position and temperature.The new proof starts from a totally implicit time discretization of a truncated system. The thermal part can be rewritten as a variational inequality of the second kind. Then, a priori estimates independent of the truncation parameter are obtained for the solution of the truncated problem, using a technique that adapts the method of Boccardo and Gallouët (1989)  [28] to the case of materials with several phase changes.     

Analysis of breakdown process at U50 voltage for plane rod discharges by means of Neural Networks

The influence of many parameters on the electric discharges at U50% can only be correlated by means of an analysis of a large amount of experimental data. The 50% probability of breakdown is considered a random process. We have investigated how to find relevant statistical differences leading to breakdown or withstanding during an impulse voltage test under the same conditions for a plane high voltage electrode and a grounded electrode configuration. An analysis based on Neural Network discrimination has been developed which indicates that measurements do contain some relevant information test at early stages in a reduced time frame.     

Inexact Proximal Point Methods for Equilibrium Problems in Banach Spaces

We introduce two inexact proximal-like methods for solving equilibrium problems in reflexive Banach spaces and establish their convergence properties, proving that the sequence generated by each one of them converges to a solution of the equilibrium problem under reasonable assumptions.     

Phosphine‐Stabilized Diiododiborenes: Isolable Diborenes with Six Labile Bonds

The lability of B=B, B?P, and B–halide bonds is combined in the syntheses of the first diiododiborenes. In a series of reactivity tests, these diiododiborenes undergo cleavage of all six of their central bonds in different ways, leading to products of B=B hydrogenation and dihalogenation as well as halide exchange.     

Hierarchical Functionalized Polymeric‐Ceramic Coatings on Mg‐Ca Alloys for Biodegradable Implant Applications

Magnesium‐based implants present several advantages for clinical applications, in particular due to their biocompatibility and degradability. However, degradation products can affect negatively the cell activity. In this work, a combined coating strategy to control the implant degradation and cell regulation processes is evaluated, including plasma electrolytic oxidation (PEO) that produces a 13 µm‐thick Ca, P, and Si containing ceramic coating with surface porosity, and breath figures (BF) approach that produces a porous polymeric poly(ε‐caprolactone) surface. The degradation of PCL‐PEO‐coated Mg hierarchical scaffold can be tailored to promote cell adhesion and proliferation into the porous structure. As a result, cell culture can colonize the inner PEO‐ceramic coating structure where higher amount of bioelements are present. The Mg/PEO/PCL/BF scaffolds exhibit equally good or better premyoblast cell adhesion and proliferation compared with Ti CP control. The biological behavior of this new hierarchical functionalized scaffold can improve the implantation success in bone and cardiovascular clinical applications.     

GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55 microm

We haves realized and measured a GaAs nanocavity in a slab photonic crystal based on the design by Kuramochi et al. [Appl. Phys. Lett. 88, 041112 (2006)]. We measure a quality factor Q=700,000, which proves that ultrahigh Q nanocavities are also feasible in GaAs. We show that owing to larger two-photon absorption in GaAs nonlinearities appear at the microwatt level and will be more functional in gallium arsenide than in silicon nanocavities.     

Ring Opening Polymerization of Lactide under Solvent‐Free Conditions Catalyzed by a Chlorotitanium Calix[4]arene Complex

A novel chlorotitanium calix[4]arene complex was synthesized and tested, without activator, as catalyst for the polymerization of L ‐ and rac‐lactide under solvent‐free conditions. The catalyst displayed high activity, which depended on the monomer‐to‐catalyst molar ratio, and led to highly isotactic PLLA. Despite concomitant transesterification during the polymerization, polylactide formation was well‐controlled, the molar mass distribution indexes remaining in the restricted range of 1.2–1.4.