114 research outputs found
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
Lie group analysis and similarity solutions for hydro-magnetic Maxwell fluid through a porous medium
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