Abstract It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only the commute. In case non-commuting matrices, best achieved simultaneous block diagonalization. Here we give an efficient algorithm to explicitly compute transfer matrix which realizes diagonalization unitary whose decomposition in irreducible blocks (common invariant subspaces) from elsewh...

In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We...

In this paper, we attempt to answer the three questions about the invariant probability distribution for stochastic matrices: (1) does every stochastic matrix have an invariant probability distribution?; (2) is the invariant probability distribution unique?; and (3) when can we conclude that the power of a stochastic matrix converges? To answer these questions, we present the Perron-Frobenius T...

The interaction of Magnesium hydrate at the phosphate oxygen atom of the pyrimidine nucleotides (CMP,UMP,dTMP) were studied at the Hartree-Fock level Theory. We used LANL2DZ basis set for Mg and 6-31g* basis set for atoms.The basis set superposition error (BSSE) begins to converge for used Method/basis set. The gauge-invariant atomic orbital (GIAO) method and the continuous-set-of-gauge-transfo...

in this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist.

We present a new scale-invariant cost function for non-orthogonal joint-diagonalization of a set of symmetric matrices with application to Independent Component Analysis (ICA). We derive two gradient minimization schemes to minimize this cost function. We also consider their performance in the context of an ICA algorithm based on non-orthogonal joint diagonalization.

The dynamical system (f,R) is introduced and some of its properties are investigated. It is proven that there is an invariant set Λ on which the periodic points of f are dense.