This study shows how to create different types of crack and discontinuities by using isogeometric analysis approach (IGA) and extended finite element method (XFEM). In this contribution, two unique features of isogeometric analysis approach are utilized to create discontinuous zones. Discontinuities consist of crack and cohesive zone. In isogeometric analysis method NURBS is used to approximate...

  We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly.   Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creat...

throughout this dissertation r is a commutative ring with identity and m is a unitary r-module. in this dissertation we investigate submodules of multiplication , prufer and dedekind modules. we also stat the equivalent conditions for which is ring , wher l is a submodule of afaithful multiplication prufer module. we introduce the concept of integrally closed modules and show that faithful mu...