Sharif Digital Repository

The aim of this thesis is to introduce some algebraic topologies methods and apply them on fining the chromatic number of some famous graphs and also hypergraphs. In the first part, we will use a mixture of two well-known technics, Tucker lemma and Discrete Morse theory to find an upper bound for the chromatic number of s-stable Kneser for some specific vector s. to find the sharper upper bound, we will deviate our strategy and use another approach by finding an edge-labeling and apply some theorems in POSET algebraic topology. In this way, we also find a connection between Young diagrams and the numbers of spheres in the box complex related to Kneser graphs and hypergraph. Actually, we can... 

Motion is an impartible component of our physical environment and the most obvious consequence of motion is collision. Diverse applications of collision detection algorithms in various real world simulated environments have led to numerous solutions to this problem from different aspects of computer science. Within computational geometry, kinetic data structure is the well-known framework to detect collisions of moving objects.This thesis will look into the problem of collision detection for a number of disjoint disks moving freely in 2D plane. To this end, we will provide a kinetic data structure (KDS) that uses O(n) storage and under the assumption of pseudo algebraic motion plans,... 

Fossil fuels provide the most needs of the world's energy, however, continues to lead to two key problems. The first problem is their limitation, and the second problem is the creation of serious environmental issues. Therefore, the need for renewable energy sources is felt more than ever.As an energy source, hydrogen is the lightest, most efficient and cleanest fuel. One of its unique properties is efficiency, the production of electricity by fuel cells through the electrochemical process, has far greater efficiency than of mechanical energy production from fossil fuels in internal combustion engines or energy production in thermal power plants. A fuel cell is a device that converts...