A matrix called Varchenko matrix associated with a hyperplane arrangement was defined by Varchenko in 1991. Matrices that we shall call q-matrices are induced from Varchenko matrices. Many researchers are interested in the invariant factors of these q-matrices. In this paper, we associate this problem with a graph theoretic model. We will discuss some general properties and give some methods fo...

This paper addresses a necessary and sufficient robust stability condition of fractional-order interval linear time invariant systems. The state matrix A is considered as a parametric interval uncertain matrix and fractional commensurate order is considered belonging to 1 ≤ α < 2. Using the existence condition of Hermitian matrix P = P ∗ for a complex Lyapunov inequality, we show that a fractio...

In this thesis we use a semidefinite programming approach to find explicit upper bounds on the size of ternary constant weight codes with prescribed minimum distance d. By constructing a graph Γ = (X,E), on the set, X, of all possible ternary words of weight w letting {x, y} ∈ E ⇔ 0 < dH(x, y) < d, we can view this problem as a special case of the stable set problem. Using symmetry, the constra...

in this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. we then define products of $fs$-matrices andstudy their properties. we finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

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 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...