Abstract:
The present article comprehensively reviews the thoracic outlet syndrome (TOS), its etiology and assessment, with reference to the usual conservative treatment and surgical therapy, highlighting new definitions and reporting obsolete tests. The syndrome affects about 8% of the population, with higher prevalence in females, and rarely affects the children. Conservative, non-surgical treatment produces good results, and it becomes important to know which specific areas need to be treated. Currently, there is no rehabilitation scheme, either osteopathic or chiropractic, considered as a valid tool for a precise localization of the pathologic condition, probably due to the lack of a manual assessment process to evaluate bones and muscular components of the thoracic outlet. In this situation, the manual treatment performed is usually generic. The present article proposes a manual evaluation that can be used to identify the anatomical area which needs to be treated. This hypothesis of assessment should be carried out after the clinician has ruled out the necessity of surgery with instrumental examinations.

Abstract:
The purpose of this paper was to analyze specialization and convergence of European countries and regions, within the framework of integration in the EU. This is important not only for long-term real convergence processes, but also for a proper functioning of the monetary union (in the line of research on the OCA's criteria, asymmetry of shocks and synchronization of business cycles). The position of new member states is particularly delicate, also considering the forthcoming adoption of the euro by some of them. As indicated by the EU Treaty, economic growth should be balanced with economic and social cohesion that includes a careful consideration of regional disparities. Our empirical investigation focuses on the regions of EU25, further broken up into other relevant groupings (EU15, EMU, and the new members' EU10 group), over the period from 1980 (or 1990 for EU10) to 2005. This paper considers a rather fine regional disaggregation (NUTS-2 level), counting 250 regions. The analysis of different indices of specialisation point to a prevalent increase of homogeneity of sector structures across European regions, although in some cases (especially in the industrial sector and in some services) specialisation has increased. For convergence, a sigma convergence's analysis confirms a reduction of disparities, both at a country and regional level. However, a trade-off between fast national growth and internal distribution has emerged in the early stages of development, as in the case of new members. Moreover, beta convergence has also been established - regarding per capita income, employment and productivity - for almost all territorial aggregates (excluding the new members since 1999). The addition of structural variables, following a beta-conditional approach, indicates a positive role for services and a negative impact of agriculture. Finally, some preliminary results have been obtained by the innovative inclusion of specialisation indices within convergence regressions.

Abstract:
More than 40 years after the discovery of Isolated Neutron Stars, the comprehension of their physics is still rather poor. This thesis is based on a program of multiwavelength observations of pulsars which yielded new and important pieces of information about the overall proprieties of this class of sources. The thesis is organized as follows: - In chapter 1 we give a very brief overview of the current status of the understanding of Isolated Neutron Stars. We also talk about the Fermi revolution that occurred in the last three years, focusing on the Fermi contribution to the knowledge of neutron stars. Then, we describe the results led by the synergy between X-ray and gamma-ray bands. - In chapter 2 we report two of our published papers containing the surprising results we obtained for two different radio-quiet pulsars. Such neutron stars, J0007+7303 and J0357+3205, can be considered "extreme" in the Fermi pulsars' zoo due to their energetics and ages. Both the X-ray observations and analyses are very different so that they can be considered as the standing-up examples of all the following analyses. - In chapter 3 we describe the analysis we done in the X-ray band and briefly report the obtained spectra of each pulsar and its nebula, if present. Then, we study the X-ray and gamma-ray pulsars' luminosities as a function of their rotational energies and ages in order to find any relationship between these values and any difference between the two populations of radio-quiet and radio-loud pulsars. - In chapter 4 we report the "identity card" of all Fermi pulsars, the detailed description of the analyses done and results obtained for each pulsar. Finally, in appendix we report our accepted proposals of the most significative X-ray observations used in this thesis plus the article on the X-ray behaviour of Fermi/LAT pulsars we published on the Astrophyisical Journal.

Abstract:
Motivated by mirror symmetry, we consider a Lagrangian fibration $X\to B$ and Lagrangian maps $f:L\hookrightarrow X\to B$, when $L$ has dimension 2, exhibiting an unstable singularity, and study how their caustic changes, in a neighbourhood of the unstable singularity, when slightly perturbed. The integral curves of $\nabla f_x$, for $x\in B$, where $f_x(y)=f(y)-x\cdot y$, called ``gradient lines'', are then introduced, and a study of them, in order to analyse their bifurcation locus, is carried out.

Abstract:
Given, in the Lagrangian torus fibration $R^4\to R^2$, a Lagrangian submanifold $L$, endowed with a trivial flat connection, the corresponding mirror object is constructed on the dual fibration by means of a family of Morse homologies associated to the generating function of $L$, and it is provided with a holomorphic structure. Morse homology, however, is not defined along the caustic $C$ of $L$ or along the bifurcation locus $B$, where the family does not satisfy the Morse-Smale condition. The holomorphic structure is extended to the subset $C\cup B$, except cusps, yielding the so called quantum corrections to the mirror object.

Abstract:
Given the Lagrangian fibration $T^4\to T^2$ and a Lagrangian submanifold, exhibiting an elliptic umbilic and supporting a flat line bundle, we study, in the context of mirror symmetry, the ``quantum'' corrections necessary to solve the monodromy of the holomorphic structure of the mirror bundle on the dual fibration.

Abstract:
Motivated by mirror symmetry, we consider the Lagrangian fibration $\R^4\to\R^2$ and Lagrangian maps $f:L\hookrightarrow \R^4\to \R^2$, exhibiting an unstable singularity, and study how the bifurcation locus of gradient lines, the integral curves of $\nabla f_x$, for $x\in B$, where $f_x(y)=f(y)-x\cdot y$, changes when $f$ is slightly perturbed. We consider the cases when $f$ is the germ of a fold, of a cusp and, particularly, of an elliptic umbilic.

Abstract:
This article describes the design and general outcome of applying a computer system that includes interactive activities to the topics of ratio and proportion. The work was undertaken with Mexican students attending primary school grade six (11 year olds). In designing the activities, our work was based on the studies of researchers who have focused on such topics, as well as on the work of researchers in the field of computer sciences and education technology. Support of the activities designed is found in psycho-pedagogy, in knowledge of mathematics and in the fields of computer sciences and education technology.

Abstract:
This article is derived from the research project registered under number 20110343 (Ruiz, 2011), and developed in Escuela Superior de Cómputo del Instituto Politécnico Nacional (IPN) (School of Computer Sciences of the National Poly-technical Institute of Mexico). The article reports on the problems found among Engineering students with respect to their resistance to using different representation registers when solving optimization problems in the Calculus Learning Unit. Use of such registers could help the students to build mathematics know
ledge and to solve calculus problems. As a didactic strategy, simulations are used in an electronic environment in order to support the students by fostering their use of tabular, graphical and algebraic representation registers. Interviews are undertaken of six of the professors who give the calculus courses, and a diagnostic questionnaire is applied to 68 students prior to and after working with the proposal. As for the theoretical framework, the work reported by Duval and Hitt is salient in this report, particularly their emphasis of the fact that working on activities by way of one single representation system is not sufficient. From the first responses provided by the students, one can conclude that the algebraic register is preferred by the majority of students. It is however used in a mechanical fashion without affording any meaning to the content of the problem and to the process of solving it. Another conclusion reported is that implementing tasks in the classroom in which the mathematics activity requires coherent use of different representations is necessary.

Abstract:
This study investigated elementary and secondary teachers’ understanding and pedagogical strategies applied to students making errors in finding a missing length in similar rectangles. It was revealed that secondary teachers had better understanding of ratio and proportion in similar rectangles than elementary teachers. While all secondary teachers solved the similar rectangles problems correctly, a large portion of elementary teacher struggled with the problem. In explaining their solution strategies, and even though similar strategies appeared both from elementary teachers and secondary teachers, a majority of secondary teachers pointed out the underlying idea of similarity, whereas less than half of the elementary teachers explained their reasoning for using ratios and proportion. This article is derived from the research project registered under number 20110343 (Ruiz, 2011), and developed in Escuela Superior de Cómputo del Instituto Politécnico Nacional (IPN) (School of Computer Sciences of the National Poly-technical Institute of Mexico)