Non-commutativity in polar coordinates

Betweenness in Polar Coordinates

betweenness, geometry, lines, polar coordinates, trilinear coordinates We consider straight line drawings. From a graph theoretic point of view these are plane graphs with a set of preferred paths. This graph is expressed in geometric terms through the consideration of the betweenness of the points of intersection along each of the lines. If we fix a reference system for polar coordinates, we c...

Non–commutativity in Teleportation

We show, using the no–disentanglement theorem, that to teleport (exactly) any set of non–commuting states (i.e., a set containing at least two non–commuting states), it is necessary to have an entangled channel. We further show that to teleport any set of commuting states it is sufficient to have a classically correlated channel. Using this result we provide a simple proof of the fact that any ...

Commutativity in non-Abelian Groups

Let P2(G) be defined as the probability that any two elements selected at random from the group G, commute with one another. If G is an Abelian group, P2(G) = 1, so our interest lies in the properties of the commutativity of nonAbelian groups. Particular results include that the maximum commutativity of a non-Abelian group is 5/8, and this degree of commutativity only occurs when the order of t...

GENERAL SOLUTION OF ELASTICITY PROBLEMS IN TWO DIMENSIONAL POLAR COORDINATES USING MELLIN TRANSFORM

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic  ...

The Laplacian in Spherical Polar Coordinates