• Input homotheticity is equivalent with output under the α -returns to scale technology. Hicks neutrality neutral technical change α-returns The Malmquist and Hicks-Moorsteen productivity indexes can coincide if technology either input homothetic or homothetic. neutral. We analyze two popular notions in production theory: notion of Both these are characterized by radial expansions contractions...

We prove that for any finite point set P in the plane, a triangle T , and a positive integer k, there exists a coloring of P with k colors such that any homothetic copy of T containing at least 144k8 points of P contains at least one of each color. This is the first polynomial bound for range spaces induced by homothetic polygons. The only previously known bound for this problem applies to the ...

We characterize three classes of demand systems, all of which are defined non-parametrically: homothetic demand systems with a single aggregator (HSA), those with direct implicit additivity (HDIA), and those with indirect implicit additivity (HIIA). In HSA, all the cross-price effects are captured by one price aggregator, while in HDIA and in HIIA, they are captured by two price aggregators. Ea...

We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in particular as homothetic time-dependent solutions to Newton’s equations of motion and as stationary states in the One Component Plasma model. Concentrating mainly o...

We prove that for any polygon S with at least four sides, and any k > 0, there is a k-fold covering of the plane with homothetic copies of S that can not be decomposed into two coverings.

We study boundary properties of one class periodic functions as $\varepsilon \rightarrow 0$, where $\varepsilon$ is a period periodically perforated domain. show that their weak limit the homothetic mean value such functions.