On conditions under which local isometries are motions

Conditions under which stereopsis and motion perception are blind.

We describe modified random-dot stereograms in which the corresponding elements differ from non-corresponding elements in colour, size, and luminance. Despite these visible differences between the elements, depth perception collapses when the spatially integrated luminous flux is similar for the corresponding and non-corresponding elements. Our results suggest that a low-pass spatial filter pre...

A Theorem on Local Isometries

A mapping 0 of a G-space R (Busemann [l ]) on itself is a locally isometric mapping if for each x£P there is a number r)x>0 such that (x), vx). The problem we are concerned with is that of determining conditions on a G-space R under which every locally isometric mapping of R on itself is an isometry. Several such conditions have ...

Geometric Models for Quasicrystals II. Local Rules Under Isometries

The atomic structures of quasicrystalline materials exhibit long range order under translations. It is believed that such materials have atomic structures which approximately obey local rules restricting the location of nearby atoms. These local constraints are typically invariant under rotations, and it is of interest to establish conditions under which such local rules can nevertheless enforc...

On the Conditions under which Audit Risk Increases with Information

It has been reported in the literature on strategic auditing that audit risk (the probability of audit failure) may increase when the auditor obtains information, whereas conditions for such cases have not been identified as yet. This paper provides simple models to analyze the general tendencies of exogenous parameters for such cases. The analysis shows that audit risk increases with more info...

On the Physical Conditions under Which Coal Was Formed.