Cohomology of classes of symbols and classi cation of traces on corresponding classes of operators with non positive order

This thesis is devoted to the classification issue of traces on classical pseudo-differential operators with fixed non positive order on closed manifolds of dimension $n>1$. We describe the space of homogeneous functions on a symplectic cone in terms of Poisson brackets of appropriate homogeneous functions, and we use it to find a representation of a pseudo-differential operator as a sum of commutators. We compute the cohomology groups of certain spaces of classical symbols on the $n$--dimensional Euclidean space with constant coefficients, and we show that any closed linear form on the space of symbols of fixed order can be written either in terms of a leading symbol linear form and the noncommutative residue, or in terms of a leading symbol linear form and the cut-off regularized integral. On the operator level, we infer that any trace on the algebra of classical pseudo-differential operators of order $a\in\Z$ can be written either as a linear combination of a generalized leading symbol trace and the residual trace when $-n+1\leq2a\leq0$, or as a linear combination of a generalized leading symbol trace and any linear map that extends the $L^2$--trace when $2a\leq-n\leq a$. In contrast, for odd class pseudo-differential operators in odd dimensions, any trace can be written as a linear combination of a generalized leading symbol trace and the canonical trace. We derive from these results the classification of determinants on the Fr\'echet Lie group associated to the algebras of classical pseudo-differential operators with non positive integer order

Control of the chemical composition and thickness of deposited coatings over carbon nanotubes using acrylic acid plasma

In this study, it is demonstrated that the surface of carbonnanotubes can be coated with a polymer nanometer size film (nanocoating) with tailored surface polar behavior when treated with acrylic acid plasma. The polar behavior of the polymer nanocoating can be hydrophilic or hydrophobic depending deposition and erosion processes caused by ionized species in the plasma. In turn, deposition and erosion can be controlled by plasma power. Deposition dominates at 20 W power, where a significant amount of polymer nanocoating is produced with carboxylic acid functional groups in the surface thus having an hydrophilic behavior. On the contrary, a smaller amount of polymer nanocoating with hydrophobic behavior (i.e. without any functional groups on its surface) suggests that erosion isthe dominant process when 40 W power is used. Finally, a competition between deposition and erosion processes results in different polar behavior and amount of polymer nanocoating depending of the treatment time

Critical Behavior of Disordered Systems with a Free Surface

The behavior of homogeneous and disordered systems with a free boundary is described on the basis of group theory in the two-loop approximation directly in three-dimensional space. The effect of the free boundary on the regime of the bulk critical behavior is revealed. It is shown that the boundedness of the system slightly affects the regime of the bulk critical behavior in the case of the ordinary transition, whereas this effect is more noticeable in the case of the special transition. Surface critical phenomena are described for homogeneous and disordered systems, and the critical exponents are calculated in the two-loop approximation. It is shown that the effect of impurities is insignificant in the special phase transition, whereas it is more noticeable in the ordinary phase transition. The derived critical exponents are compared with the computer-simulation results.Comment: 19 pages, 2 figure

Late Bronze Age Hoard studied by PIXE

The hoards of metallic objects belonging to the Late European Bronze Age can be interpreted differently depending on the type, number and composition of the artefacts. PIXE analysis has been performed in nine items from the Hoard of Freixanda in Portugal comprising 4 socket axes, a palstave axe, a ring, a chisel, a dagger, and a casting debris. Besides the composition of the main matrix elements, that is Cu and Sn, the amount of trace elements of interest like, As, Pb, Ni and Ag has been determined using this ion beam technique. The high tin content alloy and the high purity of the metals from the Freixanda hoard are characteristic of the Portuguese and Spanish Late Bronze Age metallurgy, supporting the idea of a regional production

Effect of pH and temperature on the morphology and phases of co-precipitated hydroxyapatite

This paper reports a high-yield process to fabricate biomimetic hydroxyapatite nano-particles or nano-plates. Hydroxyapatite is obtained by simultaneous dripping of calcium chloride and ammonium hydrogen phosphate solutions into a reaction vessel. Reactions were carried out under various pH and temperature conditions. The morphology and phase composition of the precipitates were investigated using scanning electron microscope and X-ray diffraction. The analyses showed that large plates of calcium hydrophosphate are formed at neutral or acidic pH condition. Nanoparticles of hydroxyapatite were obtained in precipitates prepared at pH 9–11. Hydroxyapatite plates akin to seashell nacre were obtained at 40 °C and pH 9. This material holds promise to improve the strength of hydroxyapatite containing composites for bone implant or bone cement used in orthopaedic surgeries. The thermodynamics of the crystal growth under these conditions was discussed. An assembly mechanism of the hydroxyapatite plates was proposed according to the nanostructure observations

First spaceborne observation of sea surface height using GPS-reflectometry

An analysis of spaceborne Global Positioning System reflectometry (GPS-R) data from the TechDemoSat-1 (TDS-1) satellite is carried out to image the ocean sea surface height (SSH). An SSH estimation algorithm is applied to GPS-R delay waveforms over two regions in the South Atlantic and the North Pacific. Estimates made from TDS-1 overpasses during a 6 month period are aggregated to produce SSH maps of the two regions. The maps generally agree with the global DTU10 mean sea surface height. The GPS-R instrument is designed to make bistatic measurements of radar cross section for ocean wind observations, and its altimetric performance is not optimized. The differences observed between measured and DTU10 SSH can be attributed to limitations with the GPS-R instrument and the lack of precision orbit determination by the TDS-1 platform. These results represent the first observations of SSH by a spaceborne GPS-R instrument

Immersiveness of ubiquitous computing environments prototypes: A case study

The development of ubiquitous computing (ubicomp) environments raises several challenges in terms of their evaluation. Ubicomp virtual reality prototyping tools enable users to experience the system to be developed and are of great help to face those challenges, as they support developers in assessing the consequences of a design decision in the early phases of development. Given the situated nature of ubicomp environments, a particular issue to consider is the level of realism provided by the prototypes. This work presents a case study where two ubicomp prototypes, featuring different levels of immersion (desktop-based versus CAVE-based), were developed and compared. The goal was to determine the cost/benefits relation of both solutions, which provided better user experience results, and whether or not simpler solutions provide the same user experience results as more elaborate one.Fundação para a Ciência e a Tecnologia (FCT) through Projecto Estratégico – LA 9 – 2014-2015 (PEst-OE/EEI/LA0009/201

Developing serious games for cultural heritage: a state-of-the-art review

Although the widespread use of gaming for leisure purposes has been well documented, the use of games to support cultural heritage purposes, such as historical teaching and learning, or for enhancing museum visits, has been less well considered. The state-of-the-art in serious game technology is identical to that of the state-of-the-art in entertainment games technology. As a result, the field of serious heritage games concerns itself with recent advances in computer games, real-time computer graphics, virtual and augmented reality and artificial intelligence. On the other hand, the main strengths of serious gaming applications may be generalised as being in the areas of communication, visual expression of information, collaboration mechanisms, interactivity and entertainment. In this report, we will focus on the state-of-the-art with respect to the theories, methods and technologies used in serious heritage games. We provide an overview of existing literature of relevance to the domain, discuss the strengths and weaknesses of the described methods and point out unsolved problems and challenges. In addition, several case studies illustrating the application of methods and technologies used in cultural heritage are presented

Living with chronic migraine: a qualitative study on female patients' perspectives from a specialised headache clinic in Spain

OBJECTIVES: The aim of this study was to explore the views and experiences of a group of Spanish women suffering from chronic migraine (CM). SETTING: Headache clinic at a university hospital in Madrid (Spain). PARTICIPANTS: Purposeful sampling of patients that attended a specialised headache clinic for the first time between June 2016 and February 2017 was performed. The patients included were females aged 18–65 and with positive diagnoses of CM according to the International Classification of Headache disorders (third edition, beta version), with or without medication overuse. Accordingly, 20 patients participated in the study with a mean age of 38.65 years (SD 13.85). DESIGN: Qualitative phenomenological study. METHODS: Data were collected through in-depth interviews, researchers’ field notes and patients’ drawings. A thematic analysis was performed following appropriate guidelines for qualitative research. RESULTS: Five main themes describing the significance of suffering emerged: (a) the shame of suffering from an invisible condition; (b) treatment: between need, scepticism and fear; (c) looking for physicians’ support and sincerity and fighting misconceptions; (d) limiting the impact on daily life through self-control; and (e) family and work: between understanding and disbelief. The disease is experienced as an invisible process, and the journey to diagnosis can be a long and tortuous one. Drug prescription by the physician is greeted with distrust and scepticism. Patients expect sincerity, support and the involvement of their doctors in relation to their disease. Pain becomes the main focus of the patient’s life, and it requires considerable self-control. The disease has a strong impact in the work and family environment, where the patient may feel misunderstood. CONCLUSIONS: Qualitative research offers insight into the way patients with CM experience their disease and it may be helpful in establishing a more fruitful relationship with these patients