Geography of the Philippines the Philippines, the Sierra Madre, stretching from Quezon province in the south to Cagayan in the north. 80 percent of the mountain range is tropical rainforest, which is diminishing from rampant illegal logging activity. The range serves as the eastern wall of Luzon Island that protects inhabitants from tropical cyclones usually coming from the Pacific Ocean. The largest plain of the nation is situated in the Central Luzon region and produces most of the national rice supply, earning itself the nickname ""Rice Bowl of the Philippines"". The plains encompass the provinces of Bulacan, Nueva Ecija, Pampanga, Tarlac and Pangasinan. South
Lie group Lie groups are called "isomorphic" if there exists a bijective homomorphism between them whose inverse is also a Lie group homomorphism. Equivalently, it is a diffeomorphism which is also a group homomorphism. Isomorphic Lie groups necessarily have isomorphic Lie algebras; it is then reasonable to ask how isomorphism classes of Lie groups relate to isomorphism classes of Lie algebras. The first result in this direction is Lie's third theorem, which states that every finite-dimensional, real Lie algebra is the Lie algebra of some (linear) Lie group. One way to prove Lie's third theorem is to use Ado's theorem, which says