the star-mesh transformation allows the reduction of nodes in an electrical circuit. the gauss elimination method allows the reduction of unknowns in a system of linear equations . triangular decomposition can be used to find the inverse of a matrix. in this paper the coherence between these methods are discussed. it is shown that the gauss elimination method gives the same formula for star-mes...

In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.

Let U be a (B, A)-bimodule, A and B rings, formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using left global dimensions B, estimate dimension T-module.

Let R be a left and right Noetherian ring and n, k any non-negative integers. R is said to satisfy the Auslander-type condition Gn(k) if the right flat dimension of the (i+1)-st term in a minimal injective resolution of RR is at most i+ k for any 0 ≤ i ≤ n− 1. In this paper, we prove that R is Gn(k) if and only if so is a lower triangular matrix ring of any degree t over R.

Ž . For a ring R with identity, define Unip R to be the group of upper-triangular n matrices over R all of whose diagonal entries are 1. For i 1, 2, . . . , n 1, let Si denote the matrix whose only nonzero off-diagonal entry is a 1 in the ith row and Ž . Ž . i 1 st column. Then for any integer m including m 0 , it is easy to see that Ž . the S generate Unip Z mZ . Reiner gave relations among th...

this paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (tfs) in combination with the collocation method. the method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. finally, the error analysis and some numerical examples are provided...

Let $\Delta =\left(\begin{smallmatrix} A & {_AN_B}\\ {_BM_A} B \\\end{smallmatrix}\right)$ be a Morita ring with $M\otimes_{A}N=0=N\otimes_{B}M$.We first study how to construct (complete) duality pairs of $\Delta$-modules using $A$-modules and $B$-modules, generalizing the result Mao (Comm. Algebra, 2020, 12: 5296--5310) about over triangular matrix ring. Moreover, we Gorenstein projective modu...

‎Triangular matrix rings are examples of trivial extensions‎. ‎In this article we determine the structure of derivations and biderivations of the trivial extensions‎, ‎and thereby we describe the derivations and biderivations of the upper triangular matrix rings‎. ‎Some related results are also obtained‎.

An involutory upper triangular Pascal matrix Un is investigated. Eigenvectors of Un and of UT n are considered. A characterization of Un is obtained, and it is shown how the results can be extended to matrices over a commutative ring with unity. © 2004 Elsevier Inc. All rights reserved.