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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 ...
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. Accordingly, the necessary condition of extremum ( functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf .
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.
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The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
Directional selection can change the genotypic and phenotypic variation of a population and cause a trend toward one specific phenotype. [6] This selection is an important mechanism in the selection of complex and diversifying traits, and is also a primary force of speciation. [ 7 ]
According to the Times, the study found that “in two-thirds, it was the direct cause of death, mostly in combination with other drugs.” It was a misreading of the study. Its author, Tor Seldén of Sweden’s National Board of Forensic Medicine, told The Huffington Post in an email that the Times’ claim “is not supported by our findings.”
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