the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

The proposed method was derived from Chen’s Square Matrix Encoding for information hiding. Square Matrix Encoding is modified from Diamond Encoding by changing a diamond matrix to a square matrix. The image distortion is reduced when the secret data were embedded by using the square matrix. In order to further improve the security and reduce image distortion, this paper proposes a mechanism to ...

In this paper, we introduce a new generalized inverse, called MPWG inverse of complex square matrix. We investigate characterizations, representations, and properties for inverse. Then, by using the core-EP decomposition, discuss relationships between other inverses. A variant successive matrix squaring computational iterative scheme is given calculating The Cramer rule solution singular equati...

In this paper operational matrix of Bernstein Polynomials (BPs) is used to solve Bratu equation. This nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. Elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. By using operational matrix of fractional integration...

The Painlev\'e--Kovalevskaya test is applied to find three matrix versions of the Painlev\'e II equation. All these equations are interpreted as group-invariant reductions integrable evolution equations, which makes it possible construct isomonodromic Lax pairs for them.