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If the 3/8 rule is applied to n equal subdivisions of the integration range [a, b], one obtains the composite Simpson's 3/8 rule. Simpson's 1/3 and 3/8 rules are two special cases of closed Newton–Cotes formulas .
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
n-vector is a one-to-one representation, meaning that any surface position corresponds to one unique n-vector, and any n-vector corresponds to one unique surface position. As a Euclidean 3D vector, standard 3D vector algebra can be used for the position calculations, and this makes n-vector well-suited for most horizontal position calculations.
In the tensor calculus formulation, the electromagnetic tensor F αβ is an antisymmetric covariant order 2 tensor; the four-potential, A α, is a covariant vector; the current, J α, is a vector; the square brackets, [ ], denote antisymmetrization of indices; ∂ α is the partial derivative with respect to the coordinate, x α.
The Helmholtz decomposition in three dimensions was first described in 1849 [9] by George Gabriel Stokes for a theory of diffraction. Hermann von Helmholtz published his paper on some hydrodynamic basic equations in 1858, [10] [11] which was part of his research on the Helmholtz's theorems describing the motion of fluid in the vicinity of vortex lines. [11]
The longest increasing subsequence problem is closely related to the longest common subsequence problem, which has a quadratic time dynamic programming solution: the longest increasing subsequence of a sequence is the longest common subsequence of and , where is the result of sorting.
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix, the algorithm will produce a number , which is the greatest (in absolute value) eigenvalue of , and a nonzero vector , which is a corresponding eigenvector of , that is, =.
A unit vector means that the vector has a length of 1, which is also known as normalized. Orthogonal means that the vectors are all perpendicular to each other. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis.