On the different convex hulls of sets involving singular values

We give a representation formula for the convex, polyconvex and rank one convex hulls of a set of n × n matrices with prescribed singular value

Equations de type implicite avec contraintes

In this thesis we will treat the Dirichlet problem for systems of implicit equations, i.e. where Ω ⊂ Rn is an open set, u : Ω → Rm, Fi : Ω × Rm × Rm×n → R, m,n ≥ 1, are continuous functions and φ, the boundary datum, is given. At first we will be interested in the study of problems of the type (1) under constraints. We will show theorems of existence of Lipschitz solutions using an approach based on Baire category theorem. As corollaries of our abstract results, we will give two theorems related to the constraints det Du > 0 and det Du = 1, the constraints most closely related to the applications. Indeed, the constraints det Du > 0 and det Du = 1 come from nonlinear elasticity and represent respectively the conditions of non interpenetration of matter and incompressibility. In the second part of this study, we will focus on the applications. We will treat many examples such as the case of singular values, potential wells under the incompressibility constraint (i.e. det Du = l), the problem of confocal ellipses, the problem of nematic elastomers, particularly related to the fields of nonlinear elasticity, the microstructure of the crystals and the optimal design, as well as the complex eikonal equation (application related to geometric optics). From the mathematical point of view, we will give sufficient conditions of solvability of the system (1). These conditions consist in characterizing the different convex hulls. Indeed, the possibility of representing these sets, in algebraic terms, gives one of the conditions which the boundary datum must satisfy so that a problem of the type (1) admits a solution. Finally we will extend to polyconvex sets properties such as the gauge, the characterization of the extreme points and the Choquet function, all of which are well-known tools within the framework of classical convex analysis

Eyes Of Darwin : une fenêtre ouverte sur l'évolution du logiciel

De nos jours, les logiciels doivent continuellement évoluer et intégrer toujours plus de fonctionnalités pour ne pas devenir obsolètes. C'est pourquoi, la maintenance représente plus de 60% du coût d'un logiciel. Pour réduire les coûts de programmation, les fonctionnalités sont programmées plus rapidement, ce qui induit inévitablement une baisse de qualité. Comprendre l’évolution du logiciel est donc devenu nécessaire pour garantir un bon niveau de qualité et retarder le dépérissement du code. En analysant à la fois les données sur l’évolution du code contenues dans un système de gestion de versions et les données quantitatives que nous pouvons déduire du code, nous sommes en mesure de mieux comprendre l'évolution du logiciel. Cependant, la quantité de données générées par une telle analyse est trop importante pour être étudiées manuellement et les méthodes d’analyses automatiques sont peu précises. Dans ce mémoire, nous proposons d'analyser ces données avec une méthode semi automatique : la visualisation. Eyes Of Darwin, notre système de visualisation en 3D, utilise une métaphore avec des quartiers et des bâtiments d'une ville pour visualiser toute l'évolution du logiciel sur une seule vue. De plus, il intègre un système de réduction de l'occlusion qui transforme l'écran de l'utilisateur en une fenêtre ouverte sur la scène en 3D qu'il affiche. Pour finir, ce mémoire présente une étude exploratoire qui valide notre approche.Software must continuously evolve and integrate more functionalities to remain useful. Consequently, more than 60% of a software system's cost is related to maintenance. To reduce this cost, programming must performed faster, witch leads to a decrease of the system code's quality. Therefore, understanding software evolution is becoming a necessity to prevent code decay and to increase the system life span. To ease software understanding, we perform a cross analysis of the historical data extracted from a version control system, with quantitative data that we obtain from the source code. However, the significant amount of data generated by this kind of analysis makes it necessary to have tools to support the maintainer’s analysis. First, tools help because examining them manually is impossible. Second, they help because automatics methods are not accurate enough. We present a new semiautomatic approach to help analysis. Our 3D visualization system, Eyes Of Darwin, uses a cityscape metaphor to show software's evolution on a single view. It integrates an occlusion reduction system, witch turns the screen to an open window on the 3D world. We conclude, with an exploratory study in order to validate our approach

Dialettica del fantastico. Il (mobile) confine tra noto e ignoto in Guy de Maupassant

Maupassant, a writer of a largely positivist background, considers the problem of the relationship between the known and the unknown and rationalistically deals with this issue in several texts, both of a narrative and a theoretical nature. With an approach in some measure similar to Zola’s, he claims for the writer the right and the capacity to explore the unlimited scope of the still unknown to discover its darkest and most mysterious areas. Within his wide literary production it is possible to highlight a “fantastic” line of reasoning that develops alongside his literary creativity and is characterized by a singular dialectic between a rational and positivistic instance and a tension towards the unknown and supernatural. Both items co-exist and intermingle to combine in different blends. Such a dialectic tension between two opposites – positivistic rationalism and fantastic irrationalism – is often synthesized in Maupassant’s works and is represented in characters who have an extremely rational forma mentis and a deeply rational intellectual frame. These characters, in an extent a projection of the author himself, are forced to admit that the unknown is ‘real’ and its being real is somehow reinforced by their scepticism. We can find evidence of this typology of characters in Magnétisme, La Peur (1882), Lui?, La Main among others; however the profoundly contradictory mental and spiritual attitude, explicitly expressed in such texts, is the basis and a characteristic feature of almost all the writer’s fantasy production, as his masterpiece in this genre, Le Horla, shows.Maupassant, a writer of a largely positivist background, considers the problem of the relationship between the known and the unknown and rationalistically deals with this issue in several texts, both of a narrative and a theoretical nature. With an approach in some measure similar to Zola’s, he claims for the writer the right and the capacity to explore the unlimited scope of the still unknown to discover its darkest and most mysterious areas. Within his wide literary production it is possible to highlight a “fantastic” line of reasoning that develops alongside his literary creativity and is characterized by a singular dialectic between a rational and positivistic instance and a tension towards the unknown and supernatural. Both items co-exist and intermingle to combine in different blends. Such a dialectic tension between two opposites – positivistic rationalism and fantastic irrationalism – is often synthesized in Maupassant’s works and is represented in characters who have an extremely rational forma mentis and a deeply rational intellectual frame. These characters, in an extent a projection of the author himself, are forced to admit that the unknown is ‘real’ and its being real is somehow reinforced by their scepticism. We can find evidence of this typology of characters in Magnétisme, La Peur (1882), Lui?, La Main among others; however the profoundly contradictory mental and spiritual attitude, explicitly expressed in such texts, is the basis and a characteristic feature of almost all the writer’s fantasy production, as his masterpiece in this genre, Le Horla, shows

Detection of ground movements in Montjuïc (Barcelona) using TerraSAR-X data

In this study, 28 StripMap TerraSAR-X images were processed using a Persistent Scatterer Interferometry technique in order to detect and analyze superficial deformation phenomena affecting the hill of Montjuic in Barcelona between December 2007 and November 2009. The results show significant displacement values in two main areas affected by different types of superficial displacements, specifically compaction in a former quarry refill and sliding processes. Displacement values of up to 12 mm/ year along the line of sight of the satellite were detected in the area near the Perez de Rozas baseball stadium whereas values of up to 7 mm/year were found in the vicinity of Costa i Llobera gardens. For each deformation area, high resolution deformation velocity data were analyzed and integrated with historical images and field data to interpret the detected phenomena