Let G be a finite group generated by reflections. It is shown that the elements of G can be arranged in a cycle (a "Gray. code") such that each element is obtained from the previous one by applying one of the generators. The case G = d[ ' yields a conventional binary Gray code. These generalized Gray codes provide an efficient wa), to run through the elements of any finite reflection group.

In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pu...

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...

A CMOS circuit for low voltage Pulse Duration Modulation (PDM) is proposed. This circuit is intended for portable low voltage VLSI system-on-a-chip applications like Hearing aids. The chip operates on a 3V supply and has a power consumption of 0.7mW. The chip occupies an are a of 0.0375mm on a 0.6υm standard CMOS technology. The triangle wave generation is carried out using micro power CMOS com...

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...