We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic or non-deterministic, has the same power to the square tile assembly system in computation, which is Turing universal. By providing counter-examples, we show that the triangu...

The convergence analysis of the power flow methodologies for direct current (dc) electrical networks is addressed in this paper. Banach fixed-point theorem employed to prove and uniqueness solution two different alternatives based on graph theory named successive approximations triangular-based flow. approximation method works with radial mesh grids, including multiple voltage-controlled source...

We show that every logmodular subalgebra of Mn(C) is unitary equivalent to an algebra of block upper triangular matrices, which was conjectured in [5]. In particular, this shows that every unital contractive representation of a logmodular subalgebra of Mn(C) is automatically completely contractive.

We study two random walks on a group of upper triangular matrices. In each case, we give upper bound on the mixing time by using a stopping time technique.

In this paper, we define the first topological (σ, τ)-cohomology group and examine vanishing of the first (σ, τ)-cohomology groups of certain triangular Banach algebras. We apply our results to study the (σ, τ)-weak amenability and (σ, τ)-amenability of triangular Banach algebras.

Let K be a field and let UTn(K) and Tn(K) denote the groups of all unitriangular and triangular matrices over field K, respectively. In the paper, the lattices of verbal subgroups of these groups are characterized. Consequently the equalities between certain verbal subgroups and their verbal width are determined. The considerations bring a series of verbal subgroups with exactly known finite wi...

We prove some new equivalences of Anderson’s paving conjectures. Among these are a paving conjecture for positive matrices and for strictly upper triangular matrices.