The formalism developed by Fayos and Sopuerta for isometries in vacuum spacetimes is generalised in three ways: to include the case of homotheties, to allow for a tetrad not aligned to the symmetry structure and to allow for a non-normalised tetrad. The new formalism is used to recover results by McIntosh and also applied to the particular cases of Robinson-Trautman and Kundt type N. AMS Classi...

We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on S for n = 4, 8, 12, 14, 16, 20, 23, and 24, and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming.

In this paper we prove that there are no domains E ⊂ R2, other than the ellipses, such that the Lebesgue measure of the intersection of E and its homothetic image εE translated to a boundary point q ∈ ∂E is independent of q, provided that E is ”centered” at a certain interior point O ∈ E (the center of homothety). Similar problems arise in various fields of mathematics, including, for example, ...

We reconsider the CES production functions, focusing on their additive separability properties and the constraints these impose on dual elasticites of gross substitution and complementarity. In particular, we offer some alternative characterizations of the (standard) homogeneous cases that seem to have gone unnoticed, as far as we know. We also start exploring the cases of the (additively separ...

A new two-stage approach for nonlinear brain image registration is proposed. In the first stage, an active contour algorithm is used to establish a homothetic one-to-one map between a set of region boundaries in two images to be registered. This mapping is used in the second step: a two-dimensional transformation which is based on an elastic body deformation. This method is tested by registerin...

The volumes of the surfaces of 3-dimensional Euclidean Space which are traced by a fixed point as a trajectory surface during 3-parametric motions are given by H. R. Müller [3], [4], [5] and W. Blaschke [1]. In this paper, the volumes of the trajectory surfaces of fixed points under 3-parametric homothetic motions are computed. Also, using a certain pseudo-Euclidean metric we generalized the we...

A new two-stage approach for nonlinear brain image registration is proposed. In the first stage, an active contour algorithm is used to establish a homothetic one-to-one map between a set of region boundaries in two images to be registered. This mapping is used in the second step: a two-dimensional transformation which is based on an elastic body deformation. This method is tested by registerin...

This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant S-curvature. As its application, we present explici...