R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R thereexists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R thereexists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

In this paper, we introduce the new notion of strongly J-clean rings associatedwith polynomial identity g(x) = 0, as a generalization of strongly J-clean rings. We denotestrongly J-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-J-cleanrings. Next, we investigate some properties of strongly g(x)-J-clean.

It is proved that applying sucient regularity conditions to the interval matrix[A jBj;A + jBj], we can create a new unique solvability condition for the absolute valueequation Ax + Bjxj = b, since regularity of interval matrices implies unique solvability oftheir corresponding absolute value equation. This condition is formulated in terms of positivedeniteness of a certain point matrix. Special case B = I is veried too as an application.

The edge detour index polynomials were recently introduced for computing theedge detour indices. In this paper we nd relations among edge detour polynomials for the2-dimensional graph of TUC4C8(S) in a Euclidean plane and TUC4C8(S) nanotorus.

In this paper, a new and ecient approach is applied for numerical approximationof the linear dierential equations with variable coecients based on operational matriceswith respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of theoriginal expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierentialequations to solve a system of linear algebraic equations, thus greatly simplifying the problem.In addition, two experiments are given to demonstrate the validity and applicability of themethod.

In this paper, we present an ecient numerical algorithm for solving fuzzy systemsof linear equations based on homotopy perturbation method. The method is discussed indetail and illustrated by solving some numerical examples.

In this paper, the Method of Fundamental Solutions (MFS) is extended to solvesome special cases of the problem of transient heat conduction in functionally graded mate-rials. First, the problem is transformed to a heat equation with constant coecients usinga suitable new transformation and then the MFS together with the Tikhonov regularizationmethod is used to solve the resulting equation.