Environmental issues in the Philippines Environmental issues in the Philippines The Philippines' evident risk to natural disasters is due to its location. Being a country that lies in the Pacific Ring of Fire, it is prone to earthquake and volcanic eruptions. In addition, the country is surrounded by large bodies of water and faces the Pacific Ocean where 60% of the world's typhoons are made. One of the most devastating typhoons that hit the Philippines in 2013 was Typhoon Haiyan, or "Yolanda", that killed over 10,000 people and destroyed over a trillion pesos worth of properties and damage to various sectors. Other environmental problems that
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