A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Avaliação da tonopaquimetria como exame de rastreio de glaucoma primário de ângulo aberto

Mestrado em Gestão e Avaliação de Tecnologias em Saúde

Estudo comparativo entre o tonómetro de aplanação de Goldmann e o tonómetro de não contacto em pacientes com glaucoma primário de ângulo aberto

Mestrado em Gestão e Avaliação de Tecnologias em Saúde

Unusual cause for smoldering dysphagia

A 30-year-old black woman presented with heartburn and odynophagia. She had a 2-year history of Behçet’s disease and systemic lupus erythematosus and had been treated with colchicine, hydroxychloroquine, and sucralfate. Odynophagia was not related to the presence of oral ulcers as they were painless and when they were in remission the patient would still intermittently complain of substernal pain. The patient underwent upper digestive endoscopy that revealed only small mucosal irregularities in the upper third of the esophagus. Biopsies of these segments showed marked acanthosis and papillomatosis of the squamous epithelium as well as intense lymphoplasmacytic infiltrate with an increased number of intraepithelial lymphocytes (IEL). There were neither granulocytes nor signs of viral infection. The endoscopic findings were then attributed to regenerative changes of the epithelium and the patient was started on a proton pump inhibitor (PPI), assuming gastroesophageal reflux disease (GERD). During the following years there were flare-ups of rheumatologic disease activity due to the patient’s lack of adherence to therapy. However, there was no correlation of the patient’s maintained (although scarce) complaints of transitory dysphagia and substernal pain.