Problem: Since the launch of the "Reinvent the Toilet Challenge", more than a dozen research teams, mainly at universities in the U.S., Europe, India, China and South Africa, have received grants to develop innovative on-site and off-site waste treatment solutions for the urban poor. The grants were in the order of 400,000 USD for their first phase, followed by typically 1-3 million USD for their second phase; many of them investigated resource recovery or processing technologies for excreta or fecal sludge.
What did many investigate
The answer is the following: many of them investigated resource recovery or processing technologies for excreta or fecal sludge.

Problem: Somali people in the Horn of Africa are divided among different countries (Somalia, Djibouti, Ethiopia, and northeastern Kenya) that were artificially and some might say arbitrarily partitioned by the former imperial powers. Pan-Somalism is an ideology that advocates the unification of all ethnic Somalis once part of Somali empires such as the Ajuran Empire, the Adal Sultanate, the Gobroon Dynasty and the Dervish State under one flag and one nation. The Siad Barre regime actively promoted Pan-Somalism, which eventually led to the Ogaden War between Somalia on one side, and Ethiopia, Cuba and the Soviet Union on the other.
In what geographic portion of Kenya can Somali people be found?
The answer is the following: northeastern

Problem: As aircraft started to be used against ground targets on the battlefield, the AA guns could not be traversed quickly enough at close targets and, being relatively few, were not always in the right place (and were often unpopular with other troops), so changed positions frequently. Soon the forces were adding various machine-gun based weapons mounted on poles. These short-range weapons proved more deadly, and the "Red Baron" is believed to have been shot down by an anti-aircraft Vickers machine gun. When the war ended, it was clear that the increasing capabilities of aircraft would require better means of acquiring targets and aiming at them. Nevertheless, a pattern had been set: anti-aircraft weapons would be based around heavy weapons attacking high-altitude targets and lighter weapons for use when they came to lower altitudes.
What was mounted on poles by forces?
The answer is the following: machine-gun based weapons

Problem: Another energy-related concept is called the Lagrangian, after Joseph-Louis Lagrange. This formalism is as fundamental as the Hamiltonian, and both can be used to derive the equations of motion or be derived from them. It was invented in the context of classical mechanics, but is generally useful in modern physics. The Lagrangian is defined as the kinetic energy minus the potential energy. Usually, the Lagrange formalism is mathematically more convenient than the Hamiltonian for non-conservative systems (such as systems with friction).
What is another energy-related concept?
The answer is the following:
Lagrangian