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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 ...
This work is in the public domain in the Philippines and possibly other jurisdictions because it is a work created by an officer or employee of the Government of the Philippines or any of its subdivisions and instrumentalities, including government-owned and/or controlled corporations, as part of their regularly prescribed official duties ...
This work is in the public domain in the Philippines and possibly other jurisdictions because it is a work created by an officer or employee of the Government of the Philippines or any of its subdivisions and instrumentalities, including government-owned and/or controlled corporations, as part of their regularly prescribed official duties ...
(For vector fields the curves can be taken to be the integral curves of a local flow.) In this way any vector field X on M can be lifted to a vector field X* on F satisfying [32] X* is a vector field on F; the map X ↦ X* is C ∞ (M)-linear; X* is K-invariant and induces the vector field X on C ∞ (M) C ∞ (F).
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.
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Adams applied homotopy theory and topological K-theory [2] to prove that no more independent vector fields could be found. Hence ρ ( n ) − 1 {\displaystyle \rho (n)-1} is the exact number of pointwise linearly independent vector fields that exist on an ( n − 1 {\displaystyle n-1} )-dimensional sphere.
This work is in the public domain in the Philippines and possibly other jurisdictions because it is a work created by an officer or employee of the Government of the Philippines or any of its subdivisions and instrumentalities, including government-owned and/or controlled corporations, as part of their regularly prescribed official duties ...