Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order. We establish a first global theory of existence and regularity for this shock diffraction problem. In particular, we establish that the optimal regularity for the solution is $C^{0,1}$ across the degenerate sonic boundary. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.Comment: 50 pages;7 figure

ARIA 2016: Care pathways implementing emerging technologies for predictive medicine in rhinitis and asthma across the life cycle

The Allergic Rhinitis and its Impact on Asthma (ARIA) initiative commenced during a World Health Organization workshop in 1999. The initial goals were (1) to propose a new allergic rhinitis classification, (2) to promote the concept of multi-morbidity in asthma a

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo