Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Local resection of metanephric adenoma with kidney preservation

Metanephric adenoma (MA) is a rare renal neoplasm present at any age. Usually, a total nephrectomy is performed. Some successful partial nephrectomies or selective tumor resections are described in adults but not in children. We present here the case of a 15-month-old boy, the youngest patient yet to be reported with an MA. We performed a local resection of the tumor. Today, 2 1/2 years after surgery, we can document a favorable clinical course and normal ultrasound findings in the follow-up of the operated kidney. This case gives further evidence that organ-sparing resection of MA is feasible in selected cases. A close clinical and ultrasound follow-up is mandatory for this approach.

Lions-type compactness and Rubik actions on the Heisenberg group

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group TeX is provided by the unitary group U(n) × {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein’s horizontal Sobolev space TeX. As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

Local pain and spreading hyperalgesia induced by intramuscular injection of nerve growth factor are not reduced by local anesthesia of the muscle

Injections with local anesthesia for therapeutic and diagnostic purposes are common clinical practice. This double-blind placebo controlled study explores the rational of local anesthetic blocks for the detection of muscle pain as the primary generator in spreading hyperalgesic conditions.

Intraoperative Patient-Specific Reconstruction of Partial Bone Flap Defects After Convexity Meningioma Resection

OBJECTIVE: To evaluate implant accuracy and cosmetic outcome of a new intraoperative patient-specific cranioplasty method after convexity meningioma resection. METHODS: The patient's own bone flap served as a template to mold a negative form with the use of polymethyl methacrylate (PMMA). The area of bone invasion was determined and broadly excised under white light illumination with a safety margin of at least 1 cm. The definitive replica was cast within the remaining bone flap frame and the imprint. Clinical and radiologic follow-up examinations were performed 3 months after surgery. RESULTS: Four women and two men (mean age 51.4 years ± 12.8) underwent reconstruction of bone flap defects after meningioma resection. Mean duration of intraoperative reconstruction of the partial bone flap defects was 19 minutes ± 4 (range 14-24 minutes). Implant sizes ranged from 17-35 cm(2) (mean size 22 cm(2) ± 8). Radiologic and clinical follow-up examinations revealed excellent implant alignment and favorable cosmesis (visual analogue scale for cosmesis [VASC] = 97 ± 5) in all patients. CONCLUSIONS: Patient-specific reconstruction of partial bone flap defects after convexity meningioma resection using the presented intraoperative PMMA cast method resulted in excellent bony alignment and a favorable cosmetic outcome. Relatively low costs and minimized operation time for adjustment and insertion of the cranioplasty implant justify use of this method in small bony defects as well.

[Local treatment of chronic skin wounds in a Swiss out-patient wound centre 2010]

In Switzerland around 30,000 patients suffer from chronic skin wounds. Appropriate topical wound care along with treatment of the causes of the wounds enables to heal a lot of these patients and to avoid secondary disease such as infections. Thereby, the final goal of wound care is stable reepithelisation. Based on experience with chronic leg ulcers mainly in our out-patient wound centre, we give a survey of the wound dressings we actually use and discuss their wound-phase adapted application. Furthermore, we address the two tissue engineering products reimbursed in Switzerland, Apligraf and EpiDex, as well as the biological matrix product Oasis. The crucial question, which treatment options will be offered in future to the wound patients by our health regulatory and insurance systems, is open to debate.