it is well known that the matrix exponential function has practical applications in engineering and applied sciences. in this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $x$-form. for instance, $e^{mathbf{a}t}$, $t^{mathbf{a}}$ and $a^{mathbf{a}t}$ will be evaluated by the new formulas in this par...

In this article, a numerical method based on  improvement of block-pulse functions (IBPFs) is discussed for solving the system of linear Volterra and Fredholm integral equations. By using IBPFs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. An efficient error estimation and associated theorems for the proposed method are also ...

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coefficients. Properties of these polynomials and operational matrix of integration are rst presented. Finally, two examples illustra...

A numerical method for solving linear integral equations of the second kind is formulated. Based on a special representation of vector forms of triangular functions and the related operational matrix of integration, the integral equation reduces to a linear system of algebraic equations. Generation of this system needs no integration, so all calculations can easily be implemented. Numerical res...

This paper analyzes an M/M/2 queueing system with two heterogeneous servers. Both servers goes on vacation when there is no customers waiting for service after this server 1 is always available but the other goes on vacation whenever server 2 is idle. The vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. The system is analyzed in the steady st...

this paper proposes a flexible power electronic transformer (fpet) for the application in the micro-grids. the low frequency transformer is usually used at the point of common coupling (pcc) to connect the low voltage grid and utility network to each other. the conventional 50hz transformer results in enhanced low voltage-grid power management system during grid-connected operation. in this pap...

The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN  of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most      relevant information of X. These eigenvectors are called principal components [8]. Ass...

The matrix converter instability can cause a substantial distortion in the input currents and voltages which leads to the malfunction of the converter. This paper deals with the effects of input filter type, grid inductance, voltage fed to the modulation algorithm and the synchronous rotating digital filter time constant on the stability and performance of the matrix converter. The studies are ...