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... 

At high speeds, cavitation bubbles form at the sharp edges of the submerged body or in situations where the pressure falls below the fluid vapor pressure. By placing a suitable cavitator in the nose of the body, the cavitation bubbles are cobined by increasing the speed and the whole body is placed inside the cavity. The formation of a supercavity leads to a significant reduction in the drag force of the vehicle. The submersible device is in contact with the fluid at two points, the cavitator and the fins, and due to the location of the cavitator in the nose of the body, the forces acting on it play an important role in the stability and control of the device.The main goal of current... 

In this study, a nonlinear aeroelastic model for an aircraft with fully flexible wings is obtained. This aeroelastic model is based on system identification and is created using the beam model for the structure and the three-dimensional panel method for aerodynamic analysis. The model intended for the structure is a nonlinear beam with exact geometry with initial deformation and rigid motion. The model intended for aerodynamics is an unsteady three-dimensional panel method for the airplane’s body, wings, and tail. The desired aeroelasticity model is a reduced-order model based on system identification using the time-domain/frequency-domain aerodynamic response under forced vibrations in the... 

In this Thesis hydroelastic analysis of 3D hydrofoil is investigated while partial sheet cavitation effects are considered. To this aim, first steady cavity boundary must be recognized.This region is calculated by means of conventional iterative procedure, stood upon potential flow theorem. In the second step, the reduced order fluid dynamics equations are derived based on potential flow theorem along with finite element method. This procedure is done in a way that real time system of equations are derived and iterative algorithm of conventional methods is omitted. To this aim, it is assumed that amplitude and frequency of the body oscillations are altered so that the cavity length in...