Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
CatalysisCatalysis (kəˈtæləsɪs) is the process of change in rate of a chemical reaction by adding a substance known as a catalyst (ˈkætəlɪst). Catalysts are not consumed by the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quickly, very small amounts of catalyst often suffice; mixing, surface area, and temperature are important factors in reaction rate. Catalysts generally react with one or more reactants to form intermediates that subsequently give the final reaction product, in the process of regenerating the catalyst.
PneumoniaPneumonia is an inflammatory condition of the lung primarily affecting the small air sacs known as alveoli. Symptoms typically include some combination of productive or dry cough, chest pain, fever, and difficulty breathing. The severity of the condition is variable. Pneumonia is usually caused by infection with viruses or bacteria, and less commonly by other microorganisms. Identifying the responsible pathogen can be difficult. Diagnosis is often based on symptoms and physical examination.
Community-acquired pneumoniaCommunity-acquired pneumonia (CAP) refers to pneumonia (any of several lung diseases) contracted by a person outside of the healthcare system. In contrast, hospital-acquired pneumonia (HAP) is seen in patients who have recently visited a hospital or who live in long-term care facilities. CAP is common, affecting people of all ages, and its symptoms occur as a result of oxygen-absorbing areas of the lung (alveoli) filling with fluid. This inhibits lung function, causing dyspnea, fever, chest pains and cough.
