Sharif Digital Repository

Let E be a semi-stable elliptic curve over Q with conductor N and L(E,s) as its L-function. We say that E is modular if there exists an eigenform of weight 2 and level N over X_0(N) such that L(E,s) equals the L-function of f or L(E,s)=L(f,s). Wilse's method to prove this was by proving that the Galois representations induced by E and f are equivalent. First we will discuss that equivalency of those representations is equivalent to equality of L-functions and after that we will use deformation theory for Galois representations to overlook the main ideas of the proof of the modularity theorem. Wiles using the idea of deformation of Galois representaions proved that under proper conditions... 

Finding a proper and fair schedule for sport competitions has been an important issue, especially these days which professional sports has became a large scale business and profitability of sport competitions depends on the quality of the schedule.
Hence in the last three decades sport scheduling has been considered by computer science and operation research scientists.
Professional soccer league consists of many teams which compete in one round or double round robin tournament every year. In round robin tournaments each team has two matches, one at their own place and the other one at the competitors place. The main issues of the sport scheduling are the round and the host of... 

To date, the plasmonic properties of many metallic and semi-conducting materials have been investigated and used in various industries. One of the plasmonic material categories that have always been considered is polycyclic aromatic hydrocarbon or PAH, whose plasmonic resonance energy depends on the charge state of the molecule. In this regard, it is easy to change the plasmonic resonance energy via changing the induced charge, which is a unique feature of the mentioned materials. In addition, plasmonic structures with excitations in the infrared region are able to enhance the vibration intensity of absorbed molecules by increasing the electric field around themselves. Therefore, they have... 

In this thesis, a method has been exploited to couple the atomistic domain with the coarse-grained domain. Since molecular dynamics has a high computational cost when a large number of atoms exist, coarse-grained molecular dynamics was used in which a number of atoms are assumed as a bigger bid and interatomic potential is modified for bids so that the material’s mechanical properties remain constant. This method not only reduces the computational cost of calculating forces in molecular dynamics simulation but also, the time step used in Coarse-Grained Methods can be more than atomistic simulations as the frequency of occurring phenomena in CG scale is less than atomistic scale.The advantage... 

Wettability alteration is the main mechanism for enhancing oil recovery in carbonate reservoirs during low salinity or engineered water flooding (LS/EWF), though it is a complex process due to the high heterogeneity of rock. During LS/EWF, wettability alteration occurs as a result of electrochemical interactions at the interface between carbonate rock and brine. One of the most critical factors affecting these interactions, and the wettability alteration process, is the presence of anhydrite impurities in the carbonate rock. Therefore, the success of LS/EWF in carbonate reservoirs lies on understanding the role of impurities like anhydrite from both geochemical and dissolution perspectives....