The fabrication of advanced materials which possess an array desired properties is a significant accomplishment humanity. Composites are described as enhanced they various advantages over conventional materials, why these composite seen viable alternatives in diverse engineering fields such the aerospace, electronics and automobile industries. This work involved metallic with use aluminium (AA1...

The practical scalability of many optimization algorithms for large extensive-form games is often limited by the games' huge payoff matrices. To ameliorate issue, Zhang and Sandholm recently proposed a sparsification technique that factorizes matrix A into sparser object = Â + UVᵀ, where total combined number nonzeros Â, U, V, significantly smaller. Such factorization can be used in place origi...

In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwa...

In this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. To approach this aim the analytical formulas of secant stiffness matrix are presented. The models were validated and used to perform inve...

In this article, we consider the matrix equation $AXB=C$, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explici...

We analyze three-body decays of and . Under the factorization approach, there are tree level diagrams for these decay modes and the transition matrix element of decay is factorized into a form factor multiplied by decay constant and form factor multiplied into weak vertices form factor. The transition matrix element of decay is also factorized into a form factor multiplied into weak vertic...