This study was undertaken to investigate the effects of Cu and solution heat treatment on the microstructure and hardness of cast Al-Al4Sr metal matrix composite. Different amounts of Cu (0.3, 0.5, 1, 3 and 5 wt.%) were added to the composite. Specimens were heat treated at 500 °C for 4 hours followed by water quenching. Microstructural studies were assessed by the use of optical microscope, sc...

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of...

A full-rank lattice L in R is a discrete subgroup of R which is the set of all integer linear combinations of n-linearly independent vectors, say b1, · · · ,bn i.e., L = { ∑n i=1 zibi | z1, · · · , zn ∈ Z}. The matrix B = [b1, · · · ,bn] is called the basis of the lattice and the matrix Q = B′B is called a Gram matrix of the lattice. A lattice is integral if its Gram matrix has only integer ent...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

In this paper we develop a theory of t-cycle D−Z representations for s-dimensional lattice rules of prime-power order. Of particular interest are canonical forms which, by definition, have a D-matrix consisting of the nontrivial invariants. Among these is a family of triangular forms, which, besides being canonical, have the defining property that their Z-matrix is a column permuted version of ...

The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of 1-forms is a free module over the algebra of matrices. The concept of a generalised algebra is defined and it is shown that this is required in order for the sp...

Through the matrix rank method, this paper gives necessary and sufficient conditions for a partitioned matrix to have generalized inverses with Banachiewicz-Schur forms. In addition, this paper investigates the idempotency of generalized Schur complements in a partitioned idempotent matrix.

Through the matrix rank method, this paper gives necessary and sufficient conditions for a partitioned matrix to have generalized inverses with Banachiewicz-Schur forms. In addition, this paper investigates the idempotency of generalized Schur complements in a partitioned idempotent matrix.