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The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters of the model curve (,) so that the sum of the squares of the deviations () is minimized:
The exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...
An integral over [a, b] must be changed into an integral over [−1, 1] before applying the Gaussian quadrature rule. This change of interval can be done in the following way: = (+ +)
In combinatorial mathematics, the hook length formula is a formula for the number of standard Young tableaux whose shape is a given Young diagram.It has applications in diverse areas such as representation theory, probability, and algorithm analysis; for example, the problem of longest increasing subsequences.
Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,
The Burmese python (Python bivittatus) is one of the largest species of snakes. It is native to a large area of Southeast Asia and is listed as Vulnerable on the IUCN Red List . [ 1 ] Until 2009, it was considered a subspecies of the Indian python , but is now recognized as a distinct species . [ 3 ]