Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

A comparison in the context of sparse matrices is made between the Product Form of the Inverse PFI (a form of Gauss-Jordan elimination) and the Elimination Form of the Inverse EFI (a form of Gaussian elimination). The precise relation of the elements of these two forms of the inverse is given in terms of the nontrivial elements of the three matrices L, U, U~l associated with the triangular fact...

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

Abstract We introduce and study model-theoretic connected components of rings as an analogue definable groups. develop their basic theory use them to describe both the classical Bohr compactifications rings. then explicitly calculate some matrix groups, such discrete Heisenberg group ${\mathrm {UT}}_3({\mathbb {Z}})$ , continuous {R}})$ and, more generally, groups upper unitriangular invertible...

A comparison in the context of sparse matrices is made between the Product Form of the Inverse PFI (a form of Gauss-Jordan elimination) and the Elimination Form of the Inverse EFI (a form of Gaussian elimination). The precise relation of the elements of these two forms of the inverse is given in terms of the nontrivial elements of the three matrices L, U, U~l associated with the triangular fact...

<p>This paper addresses the convergence analysis of triangular-based power flow (PF) method in alternating current radial distribution networks. The PF formulation is made via upper-triangular matrices, which enables finding a general iterative formula that does not require admittance matrix calculations. this carried out by applying Banach fixed-point theorem (BFPT), allows demonstrating...

The paper continues the study of recently introduced class SDD1 matrices. general matrices and its three subclasses are considered. In particular, it is shown that nonsingular ℌ-matrices. Also parameter-free upper bounds for l∞-norm inverses to derived. block triangular form which any matrix can be brought by a symmetric permutation rows columns described.