In this article, a new numerical method based on triangular functions for solving  nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and eff...

The classes of clean and nil-clean rings are closed with respect standard constructions as direct products and (triangular) matrix rings, cf. [12] resp. [4], while the classes of weakly (nil-)clean rings are not closed under these constructions. Moreover, while all matrix rings over fields are clean, [12] when we consider nil-clean rings there are strongly restrictions: if a matrix ring over a ...

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.

For little q-Jacobi polynomials, q-Hahn polynomials and big q-Jacobi 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 decompositions into a lower triangular matrix times upper triangular matrix. We develop a general theory of such decompositions rela...

We prove a lower bound of 52n 2 3n for the rank of n n–matrix multiplication over an arbitrary field. Similar bounds hold for the rank of the multiplication in noncommutative division algebras and for the multiplication of upper triangular matrices.

In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, ba...

Nakajima conjectured in [N] that the transition matrix between certain PBW-basis constructed in [LXZ] and the affine canonical basis is upper triangular with the diagonal entries equal to one and the upper diagonal entries in vZ[v]. In this paper, we show that the transition matrix between the PBW-basis in [LXZ] and the canonical basis is upper triangular with the diagonal entries equal to one ...

Given a matrix M over a ring K, a target rank r and a bound k, we want to decide whether the rank of M can be brought down to below r by changing at most k entries of M . This is a decision version of the well-studied notion of matrix rigidity. We examine the complexity of the following related problems and obtain completeness results for small (counting logspace or smaller) classes: (a) comput...