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With an introduction written by Zeus A. Salazar, Agpalo’s book is a “major contribution” to Filipinology that covers important areas of political science in the Philippines, including political dynamics, comparative government, comparative politics, Philippine government, Philippine politics, political philosophy, political theory ...
Here, () is the set of smooth vector fields on , and is the Lie derivative along the vector field . Examples of symplectomorphisms include the canonical transformations of classical mechanics and theoretical physics , the flow associated to any Hamiltonian function, the map on cotangent bundles induced by any diffeomorphism of manifolds, and ...
In the study of mathematics and especially differential geometry, fundamental vector fields are an instrument that describes 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.
The first formulation of this field theory used vector fields to describe the electric and magnetic fields. With the advent of special relativity, a more complete formulation using tensor fields was found. Instead of using two vector fields describing the electric and magnetic fields, a tensor field representing these two fields together is used.
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 .
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A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according to whether the represented physical quantity is a scalar, a vector, a spinor, or a tensor, respectively. A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field ...
Conrado de Quiros (27 May 1951 – 6 November 2023) was a Filipino journalist, columnist, and writer who covered Philippine politics from the 1980s to the early decades of the 21st century. Early life and education