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 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