Limitation of the Press-Schechter Formalism

The Press-Schechter(PS) formalism for the mass function of the collapsed objects are reanalyzed. The factor of two in the Press-Schechter formalism is argued to be correct in the sharp $k$-space filter even when we use the another approach proposed by Jedamzik(1994) in the cloud-in-cloud problem, which is different from the previous approach by Peacock & Heavens(1990) and Bond et al.(1991). The spatial correlation of the density fluctuations, however, had been neglected in the cloud-in-cloud problem. The effects of this spatial correlation is analyzed by using the Jedamzik formalism and it is found that this effect alter the PS mass function especially on larger mass scales. Furthermore the exact formula of deriving mass function is shown. We also find that the probability of the overlap of the collapsed objects can be neglected on very small mass scales while it might not be neglected on other mass scales.Comment: 23 pages, uuencoded compressed Postscrip

On the Cartan Model of the Canonical Vector Bundles over Grassmannians

We give a representation of canonical vector bundles over Grassmannian manifolds as non-compact affine symmetric spaces as well as their Cartan model in the group of the Euclidean motions.Comment: 6 page

Detection of individual sub-pixel features in Edge-Illumination X-Ray Phase Contrast Imaging by means of the dark-field channel

We report on a direct comparison in the detectability of individual sub-pixel-size features between the three complementary contrast channels provided by edge-illumination x-ray phase contrast imaging at constant exposure time and spatial sampling pitch. The dark-field (or ultra-small-angle x-ray scattering) image is known to provide information on sample micro-structure at length scales that are smaller than the system's spatial resolution, averaged over its length. By using a custom-built groove sample, we show how this can also be exploited to detect individual, isolated features. While these are highlighted in the dark-field image, they remain invisible to the phase and attenuation contrast channels. Finally, we show images of a memory SD card as an indication towards potential applications