the equivalent noise level in large cities has been growing due to the population growth, uncontrolled production of cars, and the existence of worn out cars. on the other hand, heavy traffic has increased the amount of noise problems for residents of medical and educational centers, research institutes and residential area (or sensitive centers to noise) built in highway bounds and it has also...

Consider a rectangular art gallery divided into n rectangular rooms, such that any two rooms sharing a wall in common have a door connecting them. How many guards need to be stationed in the gallery so as to protect all of the rooms in our gallery? Notice that if a guard is stationed at a door, he will be able to guard two rooms. Our main aim in this paper is to show that Èn/2 ̆ guards are alway...