Title: Approximation, numerical realization and qualitative analysis of contact problems with friction Author: Tomáš Ligurský Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Jaroslav Haslinger, DrSc., Department of Numerical Mathe- matics Abstract: This thesis deals with theoretical analysis and numerical realization of dis- cretized contact problems with Coulomb friction. First, discretized 3D static contact prob- lems with isotropic and orthotropic Coulomb friction and solution-dependent coefficients of friction are analyzed by means of the fixed-point approach. Existence of at least one solution is established for coefficients of friction represented by positive, bounded and con- tinuous functions. If these functions are in addition Lipschitz continuous and upper bounds of their values together with their Lipschitz moduli are sufficiently small, uniqueness of the solution is guaranteed. Second, properties of solutions parametrized by the coefficient of friction or the load vector are studied in the case of discrete 2D static contact problems with isotropic Coulomb friction and coefficient independent of the solution. Conditions under which there exists a local Lipschitz continuous branch of solutions around a given reference point are established due to two variants of the...

La recherche ainsi entamée nous a toutefois réservé des surprises de taille qui nous ont contraint à sortir de la seule sphère successorale pour élargir notre réflexion à d’autres domaines du droit civil, et à formuler ainsi une structure de thèse plus étendue et plus complexe.La thèse que nous proposons de défendre est que la saisine héréditaire n’est en réalité que l’une des déclinaisons d’un concept beaucoup plus vaste, qui traverse tout le champ du droit civil, celui de « saisine ». Nous défendrons la thèse selon laquelle ce concept transversal, méconnu de notre Code civil, se manifeste au travers de ses deux facultés principales, que nous qualifierons de saisine statique et de saisine dynamique. La saisine comprise dans sa faculté statique est précisément révélée dans notre droit par la saisine héréditaire et prend la forme d’un droit réel de posséder, dont nous proposons de démontrer l’existence et que nous mettrons à l’épreuve. L’autre faculté du concept de saisine, que nous qualifierons de saisine dynamique, consiste en la remise en cause du transfert solo consensu par la reconnaissance du caractère dual de la mécanique du transfert de propriété. Notre thèse est ici de démontrer que les droits français et belge connaissent, à l’instar du droit romain et du droit positif allemand, une mécanique de transfert duale, où l’acte translatif est distinct du contrat obligationnel. Nous démontrerons que la saisine, comprise dans sa faculté dynamique, est précisément l’acte translatif nécessaire au transfert du droit réel. Fort de ces enseignements nécessaires à sa compréhension causale, la thèse sera enfin recentrée sur son objet initial, la saisine héréditaire. Sur le fondement des analyses précitées, nous proposerons une théorie nouvelle de la saisine héréditaire, droit réel de posséder inclus dans la propriété de l’hérédité, selon laquelle le premier doit suivre la seconde, aux fins d’éviter les insécurités juridiques nombreuses générées par l’organisation de lege lata de l’institution. Nous proposerons enfin une harmonisation entre l’analyse causale de la saisine héréditaire, telle que nous l’aurons développée, et l’analyse fonctionnelle traditionnelle de l’institution. / Doctorat en Sciences juridiques / info:eu-repo/semantics/nonPublished

[pt] Seja F uma função definida de um espaço de Banach real X para um espaço de Banach real Y e g um ponto pertencente a Y. Descrevemos um algoritmo para calcular as soluções u da equação F de u igual a g. Inicialmente, o algoritmo parte de uma curva c no domínio, a qual é escolhida de modo a interceptar substancialmente o conjunto crítico de F. Calculamos através de métodos de continuação uma componente da imagem inversa de F de c e definimos essa componente de forma abstrata: grafo completamente espelhado. Claramente, os métodos de continuação padrão têm melhores chances de sucesso em diferentes pontos iniciais. Fornecemos argumentos geométricos para a abundância ocasional de soluções e uma busca estruturada dessas. Três exemplos são considerados detalhadamente. O primeiro é uma função do plano no plano, em que podemos validar os resultados com auxílio de um software. O segundo conjunto de exemplos é obtido a partir da discretização de um problema de Sturm-Liouville não linear com um número inesperado de soluções. Por último, calculamos as seis soluções aproximadas de um problema estudado por Solimini. / [en] Let F be a definite function from a real Banach space X to a real Banach space Y and g a point belonging to Y. We describe an algorithm for calculating the solutions u of the equation F of u equal to g. Initially, the algorithm starts from a curve c in the domain, which is chosen so as to substantially intercept the critical set of F. We calculate through continuation methods a component of the inverse image of F of c and define this component in an abstract way: graph completely mirrored. Clearly, standard continuation methods have better chances of success at different starting points. We provide geometric arguments for the occasional abundance of solutions and a structured search for these. Three examples are considered in detail. The first is a function of the plan in the plan, in which we can validate the results with the help of software. The second set of examples is obtained from the discretization of a non-linear Sturm-Liouville problem with an unexpected number of solutions. Finally, we calculate the six approximate solutions of a problem studied by Solimini.

We study a free quantum scalar field in the BTZ spacetime as a model of the AdS/CFT correspondence for black holes, and show the essential steps in computing Bogolyubov coefficients between modes on either side of the wormhole. As background, we review the BTZ geometry in standard, Kruskal and Poincaré coordinates, holographic renormalisation of the dual field theory and canonical quantisation in curved spacetime. / Vi studerar ett fritt skalärt kvantfält i BTZ-rumtiden som en modell av AdS/CFT-dualiteten för svarta hål och visar huvudstegen i beräkningen av Bogolyubov-koefficienter mellan moder på olika sidor av maskhålet. Som bakgrund redogör vi för BTZ-geometrin i standard-, Kruskal- och Poincarékoordinater, holografisk renormering av den duala fältteorin och kanonisk kvantisering i krökt rumtid.

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Ces travaux s'articulent autour du calcul des solutions périodiques dans les systèmes dynamiques non linéaires, au moyen de méthodes numériques de continuation. La recherche de solutions périodiques se traduit par un problème avec conditions aux limites périodiques, pour lequel nous avons implémenté deux méthodes d'approximation : - Une méthode spectrale dans le domaine fréquentiel : l'équilibrage harmonique d'ordre élevé, qui repose sur une formulation quadratique des équations. Nous proposons en outre une formulation originale permettant d'étendre cette méthode aux cas de non-linéarités non rationnelles. - Une méthode pseudo-spectrale par éléments dans le domaine temporel : la collocation à l'aide fonctions polynômiales par morceaux. Ces méthodes transforment le problème continu en un système d'équations algébriques non linéaires, dont les solutions sont calculées par continuation à l'aide de la méthode asymptotique numérique. L'ensemble de ces outils, intégrés au code de calcul MANLAB et complétés d'une analyse linéaire de stabilité, sont alors utilisés pour l'étude des régimes périodiques d'une classe particulière de systèmes dynamiques non linéaires : les instruments de musique auto-oscillants. Un modèle physique non-régulier de clarinette est étudié en détail : à partir de la branche de solutions statiques et ses bifurcations, on calcule les différentes branches de solutions périodiques, ainsi que leur stabilité et leurs bifurcations. Ce modèle est ensuite adapté au cas du saxophone, pour lequel on intègre une caractérisation acoustique expérimentale, afin de mieux tenir compte de la géométrie complexe de l'instrument. Enfin, nous étudions un modèle physique simplifié de violon, avec une non-régularité liée frottement de Coulomb. Cette dernière application illustre ainsi la polyvalence des outils développés face aux différents types de non-régularité.

My study explores the underlying factors that allow systemic structural issues to exist within continuation high schools which result in the low educational performance of low-income Latinx continuation students. My study focuses on educators’ experiences, as I conducted 20 in-depth, semi-structured interviews with Southern California continuation high school teachers. I focused on the following areas of study: the teacher’s career, the teacher’s interactions with students, and the teacher’s opinions regarding their accessibility to funding and resources. My findings indicate that teachers, the outer community, and school-board administrators utilize cultural deficit thinking and stigmatization as tools of total erasure to exchange low-income Latinx students’ social identities with racist and classist stereotypes; in consequence, these mechanisms allow the district to impose invisibility on students’ academic and emotional needs in order to justify the formation and maintenance of institutional challenges for administrators’ fiscal benefit. Overall, these results reaffirm that our educational system reproduces social inequality; the total erasure of low-income Latinx continuation students’ academic and emotional needs permits the persistence of systemic structural issues informed by racist and classist stereotypes. My research calls for avenues of communication between administrators, teachers, and the outer community to address institutional barriers and, subsequently, establish equitable funding distributions to promote continuation high school students’ educational success with an understanding of the increased academic, emotional, and social needs of low-income Latinx students.

My project explores the role of teachers at Southern California continuation high schools as it relates to serving low-income students of color in the face of the institutional barriers within alternative education. My study focuses on the teachers’ career, interactions with students, and opinions on accessibility to resources and funding. I have examined their experiences through twenty in-depth, semi-structured interviews with teachers from three districts. My findings indicate that district members’ misconceptions of Latinx students as inherently deviant and academically unengaged drive institutional issues creating financial burden for which teachers are forced to compensate. My study highlights that continuation high schools implement unjust policies, limit teaching materials and resources, reduce funding, and restrict the hiring of ancillary staff. My research pushes for more avenues of communication between the district and teachers to fulfill students’ needs through adequate funding allocation. These results extend existing literature in revealing the untold narratives of California continuation high school teachers, the structural issues within alternative education, and the needs of Latinx continuation high school students.

This study explored pre-existing quantitative data for 55 students when they were in the seventh grade who eventually attended a continuation high school years later. There were 101 students at a particular continuation high school, and this research explored pre-existing data looking solely at the students who were in the same district while they were in seventh grade. Attendance and grades from the pre-existing data in the district’s software system were analyzed using a descriptive methodology followed by a cluster analysis through SPSS. Attendance findings for the 55 students revealed that nine students (16%) were absent with a frequency of 10 or more days in each semester. Reasons given for some absences were bereavement for four students (7%) and suspensions for 10 students (18%). Eight out of these 10 students (80%) declined in their grades from the first semester to the second semester. Overall, 33 students (60%) declined in their grades from the first semester to the second semester regardless. Findings related to grades looked at the number of Fs over the two semesters of the seventh-grade school year and at the number of Fs earned in each course. Forty-four students (80%) earned at least one F either semester. Language Arts was the highest failed academic class second semester, with 32 out of 55 students (58%), and Computer Applications was the highest failed elective class for 5 out of 9 students (56%) who took this class second semester. Other findings related to grades were that 0 students (0%) failed only the elective, and only 2 students (4%) failed Physical Education. Additional findings through cluster analysis revealed a connection between failing an elective in combination with failing Language Arts: 81.8% first semester (9 out of 11 students) and 83.3% second semester (5 out of 6 students). Using a cross-tabulation, the highest pattern between the two semesters was for 10 students of the overall 55 (18%) with no Fs both semesters, and the second-highest pattern was for 6 students (11%) with no Fs first semester and 1 F second semester.