Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations

Q-conditional symmetries (nonclassical symmetries) for a general class of two-component reaction-diffusion systems with constant diffusivities are studied. Using the recently introduced notion of Q-conditional symmetries of the first type (R. Cherniha J. Phys. A: Math. Theor., 2010. vol. 43., 405207), an exhaustive list of reaction-diffusion systems admitting such symmetry is derived. The form-preserving transformations for this class of systems are constructed and it is shown that this list contains only non-equivalent systems. The obtained symmetries permit to reduce the reaction-diffusion systems under study to two-dimensional systems of ordinary differential equations and to find exact solutions. As a non-trivial example, multiparameter families of exact solutions are explicitly constructed for two nonlinear reaction-diffusion systems. A possible interpretation to a biologically motivated model is presented

Infinite square-well, trigonometric P\"oschl-Teller and other potential wells with a moving barrier

Using mainly two techniques, a point transformation and a time dependent supersymmetry, we construct in sequence several quantum infinite potential wells with a moving barrier. We depart from the well known system of a one-dimensional particle in a box. With a point transformation, an infinite square-well potential with a moving barrier is generated. Using time dependent supersymmetry, the latter leads to a trigonometric P\"oschl-Teller potential with a moving barrier. Finally, a confluent time dependent supersymmetry transformation is implemented to generate new infinite potential wells, all of them with a moving barrier. For all systems, solutions of the corresponding time dependent Schr\"odinger equation fulfilling boundary conditions are presented in a closed form

Pre-operative pulmonary assessment for patients with hip fracture

Hip fracture is a common injury among the elderly. Although patients who receive hip fracture surgery carry the best functional recovery compared to other treatment modalities, the presence of postoperative pulmonary complications, such as atelectasis, pneumonia, and pulmonary thromboembolism, may contribute to increased length of hospital stay, perioperative morbidity, and mortality. This review aims to provide evidence-based recommendations for preoperative assessment and perioperative strategies to reduce the risk of pulmonary complications after hip fracture surgery. Clinical assessment and basic laboratory results are sufficient to stratify the risk of postoperative pulmonary complications. Well-documented risk factors for pulmonary complications include advanced age, poor general health status, current infections, pre-existing cardiopulmonary diseases, hypoalbuminemia, and impaired renal function. Apart from optimizing the patient's medical conditions, interventions such as lung expansion maneuvers and thromboprophylaxis have been proven to be effective in reducing the risk of pulmonary complications after hip fracture surgery