Étude du spectre discret de perturbations d'opérateurs de la physique mathématique

The topic of this thesis concern the discrete spectrum of non-selfadjoint operators defined by relatively compact perturbation of selfadjoint operators.These selfadjoint operators are choosen among classical operators of quantum mechanics.These are the Dirac operator, the Klein-Gordon operator, and the fractional laplacianwho generalize the Schroedinger operator usually studied for such issues.The main method is based on a theorem of complex analysis which gives Blaschke-type condition on the zeros of a holomorphic function on the unit disc.This Blaschke condition gives informations on the behaviour of eigenvalues of the perturbed operator by mean of Lieb-Thirring-type inequalities.Another method using functional analysis is also used to obtain these kind of inequalities and both methods are compared to each other.L'objet de cette thèse est d'obtenir des informations sur le spectre discret d'opérateurs non auto-adjoints définis par des perturbations relativement compactes d'opérateurs auto-adjoints. Ces opérateurs auto-adjoints sont choisit parmi les opérateurs classique de mécanique quantique. Il s'agit des opérateurs de Dirac, de Klein-Gordon et le laplacien fractionnaire qui généralise l'étude de l'opérateur de Schroedinger habituellement considéré pour de tels problèmes.La principale méthode utilisée ici relève d'un théorème d'analyse complexe donnant une condition de type Blaschke sur les zéros d'une fonction holomorphe du disque unité.Cette condition traduit le comportement des valeurs propres de l'opérateur perturbésous forme d'inégalités de type Lieb-Thirring.Une autre méthode venant d'analyse fonctionnelle a été employée pour obtenir de telles inégalités et les deux méthodes sont comparées entre elles

Laparoscopic repair of vaginal vault prolapse by lateral suspension with mesh

Background: To evaluate the long-term outcomes of laparoscopic lateral suspension using mesh reinforcement for symptomatic posthysterectomy vaginal vault prolapse. Materials and methods: We analyzed in a prospective cohort study all the women treated by laparoscopic lateral suspension with mesh for symptomatic vaginal vault prolapse between January 2004 and September 2010. In this procedure, the mesh is laterally suspended to the abdominal wall, posterior to the anterior superior iliac spine. We performed systematic follow-up examinations at 4weeks, 6months and yearly postoperatively. Clinical evaluation of pelvic organ support was assessed by the pelvic organ prolapse quantification (POP-Q) grading system. Main outcome measures were recurrence rate, reoperation rate for symptomatic recurrence or de novo prolapse, mesh erosion rate, reoperation rate for mesh erosion, total reoperation rate. Observations and results: Of the 73 patients seen at a mean 17.5months follow-up, recurrent vaginal vault prolapse was registered in only one woman (success rate of 98.6%). When considering all vaginal sites, we observed a total of 13 patients with recurrent or de novo prolapse (17.8%). The non-previously treated posterior compartment was involved in eight cases (new appearance rate of 11%). Of these 13 women, only 6 were symptomatic, requiring surgical management (reoperation rate for genital prolapse of 8.2%). Four patients presented with mesh erosion into the vagina (5.5%). Two required partial vaginal excision of the mesh in the operating room (2.7%). There were no mesh-related infections. The total reoperation rate was 11%. Conclusion: Laparoscopic lateral suspension with mesh interposition is a safe and effective technique for the treatment of vaginal vault prolapse. This approach represents an alternative procedure to the laparoscopic sacrocolpopex