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 algebra correspondence simply denoted by formula_77.) The homomorphisms theorem (mentioned above as part of the Lie group-Lie algebra correspondence) then says that if formula_78 is the simply connected Lie group whose Lie algebra is formula_56, "every" representation of formula_56 comes from a representation of "G". The assumption that "G" be simply connected is essential. Consider, for example, the rotation group SO(3), which is not simply connected. There is one irreducible representation of the Lie algebra in each dimension, but only the odd-dimensional representations of the Lie algebra come from representations of the group. (This observation is related to the distinction between integer