In this paper, first, we introduced a quantum system and how to create a quantum dot-paid and then with regard to the calculation of a quantum system uses quantum dots define a Hamiltonian for a Coulomb potential is caused by an electric dipole special functions particularly well as it could have obtained the relevant amounts. Finally, using a numerical method to compare the two discussed.

In this paper, the problem of Diagonalization of the autocovariance matrices of stationary processes is discussed. Basically, there is no explicit form for the diagonal matrices. An analytic solution has been provided for stationary ARMA models based on Band matrices. The results have been compared with Dargahi-Noubary and Fuller in a numerical study. It has been demonstrated that the results are more accurate compared to Dargahi-Noubary and Fuller approaches.

In the present work, the exact Diagonalization method had been implemented to calculate the ground state energy of shallow donor impurity located at finite distance along the growth axis in GaAs/AlGaAs heterostructure in the presence of a magnetic field taken to be along z direction. The impurity binding energy of the ground state had been calculated as a function of confining frequency and magnetic field strength. We found that the ground state donor binding energy (BE) calculated at c ω =2R * and * 0 ω = 5. 421R, decreases from BE=7. 59822 R * to BE=2. 85165 R *, as we change the impurity position from d=0. 0 a* to d=0. 5 a*, respectively. In addition, the combined effects of pressure and temperature on the binding energy, as a function of magnetic field strength and impurity position, had been shown using the effective-mass approximation. The numerical results show that the donor impurity binding energy enhances with increasing the pressure while it decreases as the temperature decreases.

This paper provides sufficient conditions that guarantee the existence of positive solutions to a boundary value problem of a nonlinear fractional differential equation on the half line. Our analysis takes advantage of a theory on cones and mixed monotone operators combined with the Diagonalization method. The paper also contains some examples that are numerically solved by the Adomian Decomposition method.

Different methods are used for the formation of the null basis matrix of a structure followed by calculating the element forces when the force method of structural analysis is utilized. Singular value decomposition (SVD) method is one of the algebraic methods in force method that uses equilibrium matrix in its computation of finding element forces. By increasing the dimensions of the equilibrium matrix in large scale structures, the time needed for making orthogonal matrices grows. In recent decades many researchers have worked on block-Diagonalization of structural matrices such as stiffness matrix in symmetric structures to reduce the computational time and simplify the equations. Block-Diagonalization of equilibrium matrix can also reduce the computational time in algebraic force methods. In this paper block-Diagonalization of equilibrium matrices of circulant structure is performed using Kronocker product and SVD method is utilized to calculate the block-Diagonalization null basis matrix. Finally the results are compared to those of the method without block-Diagonalization and other algebraic methods.