Given a complex matrix H, we consider the decomposition H = QRP∗, where R is upper triangular and Q and P have orthonormal columns. Special instances of this decomposition include the singular value decomposition (SVD) and the Schur decomposition where R is an upper triangular matrix with the eigenvalues of H on the diagonal. We show that any diagonal for R can be achieved that satisfies Weyl’s...

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...

In this study, it was aimed to investigate the microstructure, hardness and wear behavior of graphene nanoplate (GNP) reinforced composites with Al 99.9 matrix produced by powder metallurgy. Different temperatures times were applied in sintering process. The values increased as temperature time increased. decreased increase GNP reinforcement ratio. losses depending on time. With ratio, reductio...

let r and s be reduced rings with identities whose idempotents are central, and let m be an(r, s)-bimodule such that annr (m)=0. in this paper, we determine first the structure of automorphisms ofthe triangular ring, =sr mt0, and then, for all automorphisms α ,β of t we determine the structureof (α,β)-derivations of t.

in this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (fdm). the uniform temperature change is utilized to study thermal effect. the surface energy effects are taken into account using the gurtin-murdoch’s theory. using the principle of virtual work, the...