This paper presents the basic results for using the parallel coordinate representation as a high dimensional data analysis tool. Several alternatives are reviewed. The basic algorithm for parallel coordinates is laid out and a discussion of its properties as a projective transformation are shown. The several of the duality results are discussed along with their interpretations as data analysis ...

‎In this paper we study the dynamics of the 2D-motion of a particle of monolayer‎. First we consider the usual physical time component and the plan manifold R2, having the polar coordinates. Then a geometric approach to nonholonomic constrained mechanical systems is applied to a problem from the two dimensional geometric dynamics of the Langmuir-Blodgett monolayer‎. We consider a constraint sub...

safety and failure in gas pipelines are very important in gas and petroleum industry. for this reason, it is important to study the effect of different parameters in order to reach the maximum safety in design and application. in this paper, a three dimensional finite element analysis is carried out to study the effect of crack length, crack depth, crack position, internal pressure and pipe thi...

We consider rational surface patches s(u, v) in the four– dimensional Minkowski space IR, which describe parts of the medial surface (or medial axis) transform of spatial domains. The corresponding segments of the domain boundary are then obtained as the envelopes of the associated two–parameter family of spheres. If the Plücker coordinates of the line at infinity of the (two–dimensional) tange...

Safety and failure in gas pipelines are very important in gas and petroleum industry. For this reason, it is important to study the effect of different parameters in order to reach the maximum safety in design and application. In this paper, a three dimensional finite element analysis is carried out to study the effect of crack length, crack depth, crack position, internal pressure and pipe thi...

The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of (n−d) curvilinear coordinates parametrizing the manifold of configurations satisfying the constraints, and to compute the Lagrangian generating the unconstrained dynamics in these (n−d) configuration coordinates. Starting from this...