We study the large scale geometry of the upper triangular subgroup of PSL2(Z[ 1 n ]), which arises naturally in a geometric context. We prove a quasi-isometry classification theorem and show that these groups are quasi-isometrically rigid with infinite dimensional quasi-isometry group. We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogue...

Article history: Received 12 September 2015 Accepted 21 December 2015 Available online xxxx Submitted by R. Brualdi MSC: primary 05E15 secondary 15A21

In this paper, we investigate the recently defined notion of inverse along an element in the context of matrices over a ring. Precisely, we study the inverse of a matrix along a lower triangular matrix, under some conditions.

For the all-ones lower triangular matrices, the upper and lower bounds on rigidity are known to match [13]. In this short note, we apply these techniques to the allones extended lower triangular matrices, to obtain upper and lower bounds with a small gap between the two; we show that the rigidity is θ( 2 r ).

In this paper, a new algorithm of approximating rational triangular B-B surfaces using polynomial triangular B-B surfaces is presented. This algorithm has a simple expression and insured convergence. The core idea of the algorithm is to yield a polynomial triangular B-B surface, which has the same degree and new control vertices of the degree-elevated rational triangular B-B surface, to approxi...