A vanishing result for strictly p-convex domains

In view of Andreotti and Grauert (Bull Soc Math France 90:193–259, 1962) vanishing theorem for \(q\) -complete domains in \(\mathbb C ^{n}\) , we reprove a vanishing result by Sha (Invent Math 83(3):437–447, 1986), and Wu (Indiana Univ Math J 36(3):525–548, 1987), for the de Rham cohomology of strictly \(p\) -convex domains in \(\mathbb R ^n\) in the sense of Harvey and Lawson (The foundations of \(p\) -convexity and \(p\) -plurisubharmonicity in riemannian geometry. arXiv:1111.3895v1 [math.DG]). Our proof uses the \({L}^2\) -techniques developed by Hörmander (An introduction to complex analysis in several variables, 3rd edn. North-Holland Publishing Co, Amsterdam 1990), and Andreotti and Vesentini (Inst Hautes Études Sci Publ Math 25:81–130, 1965).     

Adaptive and multi-mining versions of the DM-GRASP hybrid metaheuristic

Metaheuristics represent an important class of techniques to solve, approximately, hard combinatorial optimization problems for which the use of exact methods is impractical. Some researches have been combining machine learning techniques with metaheuristics to adaptively guide and improve the search for near optimal solutions. An example of such development is the DM-GRASP, a hybrid version of the Greedy Randomized Adaptative Search Procedures (GRASP) metaheuristic which incorporates a data mining process. In this hybrid proposal, after executing half of the total number of iterations, the data mining process extracts patterns from an elite set of sub-optimal solutions for the optimization problem. These patterns present characteristics of near optimal solutions and can be used to guide the following half GRASP iterations in the search through the solution space. In this work, we explore new versions of the DM-GRASP metaheuristic to experiment, not a single activation, but multiple and adaptive executions of the data mining process during the metaheuristic execution. We also applied the data mining technique into a reactive GRASP to show that a more sophisticated and not memoryless GRASP approach can also benefit from the use of this technique. In order to evaluate these new proposals, we adopted the server replication for reliable multicast problem since the best known results for this problem were obtained by GRASP and DM-GRASP implementations. The computational experiments, comparing traditional GRASP, DM-GRASP, and the new proposals, showed that multiple and adaptive executions of the data mining process can improve the results obtained by the DM-GRASP hybrid metaheuristic—the new proposals were able to find better results in less computational time for the reliable multicast problem.     

Principal differential analysis of the Aneurisk65 data set

We explore the use of principal differential analysis as a tool for performing dimensional reduction of functional data sets. In particular, we compare the results provided by principal differential analysis and by functional principal component analysis in the dimensional reduction of three synthetic data sets, and of a real data set concerning 65 three-dimensional cerebral geometries, the AneuRisk65 data set. The analyses show that principal differential analysis can provide an alternative and effective representation of functional data, easily interpretable in terms of exponential, sinusoidal, or damped-sinusoidal functions and providing a different insight to the functional data set under investigation. Moreover, in the analysis of the AneuRisk65 data set, principal differential analysis is able to detect interesting features of the data, such as the rippling effect of the vessel surface, that functional principal component analysis is not able to detect.     

Crystallization of glasses in the germanium-tellurium-sulphur system

The glasses of the germanium-tellurium-sulphur ternary system were investigated in order to determine the formation and crystallization processes. Vitreous samples were prepared by quenching. The vitreous transition and crystallization temperatures, together with microhardnesses, were measured throughout the vitreous region. The latter was sub-divided into several zones, and the behaviour of the glasses in each of these zones was analyzed separately.     

Thermal analysis of hair treated with oxidative hair dye under influence of conditioners agents

This research aimed the effect on Caucasian hair tresses treated with oxidative hair dye, either incorporated or not with conditioners agents, analyzed by Differential Scanning Calorimetry (DSC) and Thermogravimetric analysis (TG). The formulations of hair dyes were emulsions oil-in-water with light blond color containing or not the conditioners agents: silanetriol and panthenol; PEG-12 dimethicone; hydrolyzed silk, hydrolyzed milk protein, and lactose. Each dye (1.5 g) was applied in the hair tress (2.0 g/20.0 cm of length of Caucasian light-brown), previously treated, more 1.5 g of hydrogen peroxide 20 vol during 40 min. Evaluation of mass loss of the different hair sample demonstrates that these chemical hair treatments impair the hair fibers, reduced their moisture content with respect to the untreated hair. The incorporation of conditioners agents (silanetriol and panthenol; PEG-12 dimethicone; hydrolyzed silk, hydrolyzed milk protein, and lactose) in oxidative hair dyes types did not decrease the damage caused on the tresses by the coloring process quantified by TG/DTG. However, the DSC curves demonstrated those conditioners agents (silanetriol and panthenol; PEG-12 dimethicone) dislocated the beginning of the third event in 20 °C and they inhibited the presence of the fourth event, having characterized thermal protection to the hair.     

Characterization of high heating rate chars of biomass fuels

Data on biomass chars obtained under conditions similar to those of practical applications (high heating rate and low residence time) are required for co-combustion and gasification plants. A methodological procedure is developed and applied to two biomass fuels (cacao shells and olive cake) for producing high heating rate chars and characterizing their reactivity and morphology after the first steps of devolatilization. Different chars are produced in a drop tube reactor (rapid pyrolysis) by varying the nominal temperature and the residence time. Oxidation in air is performed to compare typical temperatures and kinetic parameters and evaluate the effect of the operating conditions on char reactivity. A detailed SEM analysis allows to assess the structural variations during the pyrolysis and detect the main phenomena (softening, swelling, melting, formation of bubbles). A quantitative morphological study is also performed to provide size and shape (important for biomasses) distributions of the parent fuel and the chars. These data are more significant than average values in advanced model to correctly simulate the fluid dynamic behaviour of each dimensional class of particles in large scale furnaces and gasifiers and predict a more reliable residence time of the particles.     

Stopping criteria for inner iterations in inexact potential reduction methods: a computational study

We focus on the use of adaptive stopping criteria in iterative methods for KKT systems that arise in Potential Reduction methods for quadratic programming. The aim of these criteria is to relate the accuracy in the solution of the KKT system to the quality of the current iterate, to get computational efficiency. We analyze a stopping criterion deriving from the convergence theory of inexact Potential Reduction methods and investigate the possibility of relaxing it in order to reduce as much as possible the overall computational cost. We also devise computational strategies to face a possible slowdown of convergence when an insufficient accuracy is required.