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In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, [1] introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of ...
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]
Within chemistry, a Job plot, otherwise known as the method of continuous variation or Job's method, is a method used in analytical chemistry to determine the stoichiometry of a binding event. The method is named after Paul Job and is also used in instrumental analysis and advanced chemical equilibrium texts and research articles.
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field.
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
Directed evolution is a mimic of the natural evolution cycle in a laboratory setting. Evolution requires three things to happen: variation between replicators, that the variation causes fitness differences upon which selection acts, and that this variation is heritable.
Indonesia was easily one of the most memorable trips of my life. I went to Bali, Nusa Penida, and the Gili Islands, and all the locals I met were incredibly kind and helpful. The cuisine was ...
John Venables, "The Variational Principle and some applications". Dept of Physics and Astronomy, Arizona State University, Tempe, Arizona (Graduate Course: Quantum Physics) Andrew James Williamson, "The Variational Principle-- Quantum monte carlo calculations of electronic excitations". Robinson College, Cambridge, Theory of Condensed Matter ...