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...

In this study, notion of pluriharmonic map applied onto conformal bi-slant Riemannian maps from a Kaehler manifold to examine its geometric properties. Such that, relations between map, horizontally homothetic and totally geodesic were obtained.

We prove a sharp stability result concerning how close homothetic sets attaining near-equality in the Brunn–Minkowski inequality are to being convex. In particular, resolving conjecture of Figalli and Jerison, we show there universal constants $\\smash{C_n,d_n>0}$ such that for $\\smash{A \\subset \\mathbb{R}^n}$ positive measure, if $\\smash{|\\frac{A+A}{2}\\setminus A| \\le d_n |A|}$, then $\...