In the context of mathematical cosmology, study necessary and sufficient conditions for a semi-Riemannian manifold to be (generalized) Robertson-Walker space-time is important. particular, it requirement development initial data reproduce or approximate standard cosmological model. Usually these involve Einstein field equations, which change if one considers alternative theories gravity couplin...

Optical texture patterns contain three quasi-independent cues to planar surface orientation: perspective scaling, projective foreshortening and density. The purpose of this work was to estimate the perceptual weights assigned to these texture cues for discriminating surface orientation and to measure the visual system's reliance on an isotropy assumption in interpreting foreshortening informati...

This article presents a new performance measure, the actuation e ciency, which describes isotropy in acceleration capability for non-redundant manipulators. It measures the imbalance between the end-e ector accelerations achievable in di erent directions. Prior to this, no measure of this characteristic was adequate for a six degree-of-freedom manipulator, because its ende ector motions are ref...

A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution structure’ consisting of equivariant iterated fibrations of the boundary faces. T...

This article presents a new performance meamre, the actuation eficiency, which describes isotropy in acceleration capability for non-redundant manipulators. It measures the imbalance between the end-effector accelerations achievable in different directions. Prior to this, no measurre of this characteriStic was adequate for a six dem-of-freedom manipulator, because its endeffector motions are re...