Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.

Polymeric grafting of acrylic acid onto poly(3-hydroxybutyrate-co-3-hydroxyvalerate): Surface functionalization for tissue engineering applications

Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) melt processed disks and solvent cast films were modified by graft co-polyinerization with acrylic acid (AAc) in methanol solution at ambient temperature using gamma irradiation (dose rate of 4.5 kGy/h). To assess the presence of carboxylic acid groups on the surface, reaction with pentafluorophenol was performed prior to X-ray photoelectron spectroscopy analysis. The grafting yield for all samples increased with monomer concentration (2-15%), and for the solvent cast films, it also increased with dose (2-9 kGy). However, the grafting yield of the melt processed disks was largely independent of the radiation dose (2-8 kGy). Toluidine blue was used to stain the modified materials facilitating, visual information about the extent of carboxylic acid functionalization and depth penetration of the grafted copolymer. Covalent linking of glucosamine to the functionalized surface was achieved using carbodimide chemistry verifying that the modified substrates are suitable for biomolecule attachment.

A multiresolution terrain model for efficient visualization query processing

Multiresolution Triangular Mesh (MTM) models are widely used to improve the performance of large terrain visualization by replacing the original model with a simplified one. MTM models, which consist of both original and simplified data, are commonly stored in spatial database systems due to their size. The relatively slow access speed of disks makes data retrieval the bottleneck of such terrain visualization systems. Existing spatial access methods proposed to address this problem rely on main-memory MTM models, which leads to significant overhead during query processing. In this paper, we approach the problem from a new perspective and propose a novel MTM called direct mesh that is designed specifically for secondary storage. It supports available indexing methods natively and requires no modification to MTM structure. Experiment results, which are based on two real-world data sets, show an average performance improvement of 5-10 times over the existing methods.