Ολοκληρωσιμότητα Αρνητικών Δυνάμεων Λύσεων Του Προβλήματος Saint Venant

Σε αυτήν την εργασία θα ασχοληθούμε με την ανισότητα \int_{\Omega} u(x)^{-\beta}<+\infty, όπου Ω ανοικτό $\subseteq \mathbb{R}^n$ και $u(x)$ η λύση του προβλήματος \textlatin{Saint Venant} \left\{ \begin{array}{ll} \Delta u=-1 , & \mbox{στο $\Omega$,} \\ u=0, & \mbox{στο $\partial\Omega$}. \end{array} \right. Το κύριο θέμα που εντοπίζουμε είναι πως για τον προσδιορισμό της σταθεράς \beta >0 για τις προαναφερθήσες συνθήκες, σημαντικό ρόλο παίζει η ομαλότητα του Ω και η φύση της σταθεράς $C(\Omega ,\beta)$, από την οποία μπορούμε σε κάθε περίπτωση να φράξουμε το ολοκλήρωμα. Σύνολα στα οποία εφαρμόζεται η μελέτη μας είναι τμηματικά $C^1$ χωρία στο $\mathbb{R}^n$, με κωνικές ιδιομορφίες, πολύεδρα στον $\mathbb{R}^{3}$ καθώς και τοπικά φραγμένα $C^2$ χωρία.\textlatin{In this master thesis we initiate the study of the finiteness condition} \int_{\Omega} u(x)^{-\beta}\leq C(\Omega, \beta)<+\infty\textlatin{where} $\Omega \subseteq \mathbb{R}^{n}$\textlatin{ is an open set and} $u$ \textlatin{is the solution of the Saint Venant problem} \left\{ \begin{array}{ll} \Delta u=-1 , & \mbox{\textlatin{in} $ \Omega$,} \\ u=0 , & \mbox{\textlatin{on} $\partial\Omega$}. \end{array} \right. \textlatin{The central issue which we address is that of determining the range of values of the parameter } \beta>0 \textlatin{for which the aforementioned condition holds under various hypotheses on the smoothness of }$\Omega$ \textlatin{and demands on the nature of the constant} $C(\Omega, \beta).$ \textlatin{Classes of domains for which our analysis applies include bounded piecewise} $C^{1}$ \textlatin{domains in } $\mathbb{R}^{n}, n \geq 2$ \textlatin{, with conical singularities (in particular polygonal domains in the plane), polyhedra in } $\mathbb{R}^3$\textlatin{, and bounded domains which are locally of class} $C^2$ \textlatin{and which have (finitely many) outwardly pointing cusps.

Pathophysiology and Biomechanics of the Aging Spine

Aging of the spine is characterized by two parallel but independent processes: the reduction of bone mineral density and the development of degenerative changes. The combination of degeneration and bone mass reduction contribute, to a different degree, to the development of a variety of lesions. This results in a number of painful and often debilitating disorders. The present review constitutes a synopsis of the pathophysiological processes that take place in the aging spine as well as of the consequences these changes have on the biomechanics of the spine. The authors hope to present a thorough yet brief overview of the process of aging of the human spine

Cystic Echinococcosis of the Pelvic Bone with Recurrences: A Case Report

Hydatid cysts commonly affect the liver and the lung. However, they rarely involve bones with vertebral column. We hereby report a case of a female patient with cystic echinococcosis of the hip bone and ilium. She presented with a long history of frequent recurrences highlighting the dismal prognosis at this rare site. Resection of the hydatid cyst from the sacroiliac region was done with allograft and autograft (rib graft) with lumbosacroiliac fixation. Follow-up of the patient at 6 months showed no detectable abnormality on radiology and the patient was doing well

Recurrent intra-articular osteoid osteoma of the hip after radiofrequency ablation: a case report and review of the literature

We present a case of a 53-year-old woman with recurrent intra-articular osteoid osteoma of the hip 6 months after initial treatment with percutaneous radiofrequency ablation. En bloc surgical excision of the osteoid osteoma and prophylactic internal fixation for impending stress fracture was performed. The patient is pain free, has returned to normal function and there is no sign of recurrence at the one-year follow-up. Intraarticular osteoid osteoma, present a diagnostic challenge and often they are misdiagnosed. Minimally invasive ablation techniques can fail in significant percentage and then surgical excision with histological confirmation remains the definitive treatment of choice

Cement leakage in a symptomatic vertebral hemangioma: a case report and review of the literature

We present the case of a 50-year-old male with consistent back pain, not resolving with conservative treatment. Plain radiograms demonstrated a lytic lesion at the level of the 8th thoracic vertebra. Thorough examination with computerized tomography and magnetic resonance imaging revealed a hemangioma extending to the posterior third of the vertebral body, compressing the spinal cord at the level of 8th thoracic vertebra. A percutaneous vertebroplasty was performed. The post-operative computerized tomography scan demonstrated cement leakage. After thorough cement removal combined with extensive decompression and posterior stabilization, the patient reported gradual improvement of his symptoms and was able to return successfully to his work a few months later

Suicide Attempts from Height and Injury Patterns: An Analysis of 64 Cases

Falls from height are a common cause of death and disability. A majority of free falls occur accidentally and only a minority result from suicidal behaviour. Adolescents in many countries show high rates of suicide attempts and their repetition is a common feature. We describe the demographic characteristics of these patients, their psychiatric diagnosis at the time of the attempt and the injury patterns. We present 64 patients who sustained injuries as a result of a fall from height. They were divided into those without mental disorders (n = 32, group I) and those with mental disorders (n = 32, group II). The mean height from which the fall occurred was 5.4 m (range, 3–25 m). The mean injury severity score was 19 (range, 6–58) for all fall victims. Upper extremity fractures were found in 37 patients, while pelvic and lower extremity fractures were found in 198 cases. Spinal fractures were noted in 32 patients. Head injuries were revealed by CT scan in 16 patients. Patients following a suicidal high fall mostly had lower limb fractures, pelvis fractures, spinal fractures and head injuries

Posterior Instrumentation for Occipitocervical Fusion

Since 1995, 29 consecutive patients with craniocervical spine instability due to several pathologies were managed with posterior occipitocervical instrumentation and fusion. Laminectomy was additionally performed in nineteen patients. The patients were divided in two groups: Group A which included patients managed with screw-rod instrumentation, and Group B which included patients managed with hook-and-screw-rod instrumentation. The patients were evaluated clinically and radiographically using the following parameters: spine anatomy and reconstruction, sagittal profile, neurologic status, functional level, pain relief, complications and status of arthrodesis. The follow-up was performed immediately postoperatively and at 2, 6, 12 months after surgery, and thereafter once a year. Fusion was achieved in all but one patient. One case of infection was the only surgery related complication. Neurological improvement and considerable pain relief occurred in the majority of patients postoperatively. There were neither intraoperative complications nor surgery related deaths. However, the overall death rate was 37.5% in group A, and 7.7% in group B. There were no instrument related failures. The reduction level was acceptable and was maintained until the latest follow-up in all of the patients. No statistical difference between the outcomes of screw-rod and hook-and-screw-rod instrumentation was detected. Laminectomy did not influence the outcome in either group. Screw-rod and hook-and-screw-rod occipitocervical fusion instrumentations are both considered as safe and effective methods of treatment of craniocervical instability