We investigate the resonance varieties, lower central series ranks, and Chen ranks of the pure virtual braid groups and their upper-triangular subgroups. As an application, we give a complete answer to the 1-formality question for this class of groups. In the process, we explore various connections between the Alexander-type invariants of a finitely generated group and several of the graded Lie...

In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite fields can be built using the proposed groups and a set of automorphisms of these groups. We also show that the security of this proposed MOR cryptosystem is equi...

Everyone knows that the waterfall life cycle model suffers from a number of problems but in spite of this, it continues to be the most widely used life cycle model. This paper argues that many of these problems stem from project management best practices that are inappropriately applied in the waterfall model. A different life cycle approach is proposed that emphasise the product life cycle rat...

Triangular B-splines are a new tool for modeling a broad class of objects defined over arbitrary, nonrectangular domains. They provide an elegant and unified representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additi...

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...

Triangular B-splines are a new tool for modeling a broad class of objects deened over arbitrary, non-rectangular domains. They provide an elegant and uniied representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additio...

Triangular B-splines are a new tool for modeling a broad class of objects de ned over arbitrary, non-rectangular domains. They provide an elegant and uni ed representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additio...