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A vector field V defined on an open set S is called a gradient field or a conservative field if there exists a real-valued function (a scalar field) f on S such that = = (,,, …,). The associated flow is called the gradient flow , and is used in the method of gradient descent .
In the study of mathematics, and especially of differential geometry, fundamental vector fields are instruments that describe the infinitesimal behaviour of a smooth Lie group action on a smooth manifold. Such vector fields find important applications in the study of Lie theory, symplectic geometry, and the study of Hamiltonian group actions.
Vector field reconstruction [1] is a method of creating a vector field from experimental or computer-generated data, usually with the goal of finding a differential equation model of the system. Definition
The optics that produced the laser were placed at the end of a silver coated spiral which helped amplify the beam and increase convergence. The energy to power the laser was provided by a generator and an auxiliary battery system. The lenses themselves were able to operate in different environments by moving metal caps closer to protect the lens.
A (,)-tensor field is a differential -form, a (,)-tensor field is a vector field, and a (,)-tensor field is -vector field. While differential forms are widely studied as such in differential geometry and differential topology , multivector fields are often encountered as tensor fields of type ( 0 , k ) {\displaystyle (0,k)} , except in the ...
It is the generator of the little group of the Poincaré group, that is the maximal subgroup (with four generators) leaving the eigenvalues of the four-momentum vector P μ invariant. [ 3 ] Definition
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A lamellar vector field is a special case given by vector fields with zero curl. The adjective "lamellar" derives from the noun "lamella", which means a thin layer. The lamellae to which "lamellar vector field" refers are the surfaces of constant potential, or in the complex case, the surfaces orthogonal to the vector field.
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