Homogeneous Contact Transformations

Rotation Matrices and Homogeneous Transformations

A coordinate frame in an n-dimensional space is defined by n mutually orthogonal unit vectors. In particular, for a two-dimensional (2D) space, i.e., n = 2, a coordinate frame is defined by an X axis and a Y axis with these two axes being orthogonal to each other. The intersection between the X axis and the Y axis is the origin of the coordinate frame. For a three-dimensional (3D) space, i.e., ...

Complex Contact and Lift Transformations

We study mappings from sets of real variables into complex variables, which extend features of lift and contact transformations between real variables that we explored in a previous paper. In particular the relationship between lifts in R and the CauchyRiemann equations for functions of n complex variables is discussed. Explicit examples are given to illustrate the anatomy of such transformatio...

Anisotropic Contact Processes on Homogeneous Trees

Sufficient conditions for the existence of a weak survival phase are given for an anisotropic contact process on a homogeneous tree. These require that the contact process be homogeneous, that is, for any two vertices x, y of the tree there is an automorphism mapping x to y leaving the infection rates invariant; and that the contact process be weakly symmetric, that is, for each vertex there sh...

Anisotropic Contact Process on Homogeneous Trees

The existence of a weak survival region is established for the anisotropic symmetric contact process on a homogeneous tree T2d of degree 2d ≥ 4 : For parameter values in a certain connected region of positive Lebesgue measure, the population survives forever with positive probability but ultimately vacates every finite subset of the tree with probability one. In this phase, infection trails mus...

A Note on Homogeneous Complex Contact Manifolds