in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

For random selfadjoint (real symmetric, complex Hermitian, or quaternion self-dual) Toeplitz matrices and real symmetric Hankel matrices, the existence of universal limit distributions for eigenvalues and products of several independent matrices is proved. The joint moments are the integral sums related to certain pair partitions. Our method can apply to random Hankel and Toeplitz band matrices...

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...

In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation. We tabulate these parameters. We also compare the discrete logarithm problem in the group of circulant matrices with the discrete logarithm problem in finite...

Quantum integrable models that possess N = 2 supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some N = 2 supersymmetric boundary integrable models, and the effective boundary Landau-Ginzburg actions are constructed. It is found that N = 2 supersymmetry largely determines the boundary action in terms of the bulk, and in particular, the boundary ...