The cluster representation matrices have already been successfully used to enumerate close-packed vacancy clusters in all single-lattice crystals [I, 2]. Point defect clusters in double-lattice crystals may have identical geometry but are distinct due to unique atomic postions enclosing them. The method of representation matrices is extended to make it applicable to represent and enumerate ...

Siffness matrices for axial and bending deformations of a beam having a rectangular cross sectional area of constant width and linearly varying thickness are developed. A consistant load vector for a uniformly distributed lateral load is also calculated, using the principal of potential energy. The matrices are used to obtain numerical results for a variety of beams with non-uniform thickness t...

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

‎in this paper‎, ‎the type-{rm ii} matrices on (negative) latin square graphs are considered and it is proved that‎, ‎under‎ ‎certain conditions‎, ‎the nomura algebras of such type-{rm ii} matrices are trivial‎. ‎in addition‎, ‎we construct type-{rm ii} matrices‎ ‎on doubly regular tournaments and show that the nomura algebras of such matrices are also trivial‎.

let $cr_n(f_p)$ denote the algebra of $n times n$ circulant‎ ‎matrices over $f_p$‎, ‎the finite field of order $p$ a prime‎. ‎the‎ ‎order of the unit groups $mathcal{u}(cr_3(f_p))$‎, ‎$mathcal{u}(cr_4(f_p))$ and $mathcal{u}(cr_5(f_p))$ of algebras of‎ ‎circulant matrices over $f_p$ are computed‎.

In this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. We then define products of $fs$-matrices andstudy their properties. We finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

in this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional euclidean space, which are the einstein and möbius gyrovector spaces. we introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and see its interest...

 In this paper we characterize all $2times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2times 2$ matrix  over a UFD is nil-clean.