We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration ...

The morphological skeleton and morphological shape decomposition (MSD) are the two popular approaches for morphological shape representation. Each method represents an object as the union of a number of components, where each component is given by a locus of points dilated by a speciied structuring element homothetic. Anecdotal evidence suggests that for many objects, an MSD-based representatio...

Metric symmetries have always played a large role in the development of exact solutions to the Einstein field equations. Often a choice of metric symmetry is made based on an assumed symmetry of the matter distribution, i.e., spherical symmetry for astrophysical objects or cylindrical symmetry for a simple string. A homothetic motion ~homothety! describes the symmetry of scale transformations, ...

H is the upper half plane, a complex manifold. It will be helpful to interpret H in multiple ways. A lattice Λ ⊂ C is a free abelian group of rank 2, for which the map Λ ⊗Z R → C is an isomorphism. In other words, Λ is a subgroup of C of the form Zα⊕Zβ, where {α, β} is basis for C/R. Two lattices Λ and Λ′ are homothetic if Λ′ = θΛ for some θ ∈ C∗. This is an equivalence relation, and the equiva...

We study pricing by multiproduct firms in the context of unregulated monopoly, regulated monopoly and Cournot oligopoly. Using the concept of consumer surplus as a function of quantities (rather than prices), we present simple formulas for optimal prices and show that Cournot equilibrium exists and corresponds to a Ramsey optimum. We then present a tractable class of demand systems that involve...