Acrylamide was grafted in low density polyethylene during melt processing in the presence of a free radical initiator using a torque rheometer in a closed system. Effects of processing time, acrylamide and benzoyl peroxide concentrations were studied. FTIR studies revealed that the degree of grafting increased by an increase in acrylamide concentration. Maximum grafting was obtained at 7 mi...

We report a very low density ( approximately 0.5 g/cm(3)) structure of solid ozone. It is produced by irradiation of solid oxygen with 100 keV protons at 20 K followed by heating to sublime unconverted oxygen. Upon heating to 47 K the porous ozone compacts to a density of approximately 1.6 g/cm(3) and crystallizes. We use a detailed analysis of the main infrared absorption band of the porous oz...

The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of suuciently low density. Both methods rely on basis reduction algorithms to nd short non-zero vectors in special lattices. The Lagarias-Odlyzko algorithm would solve almost all subset sum prob...

We define a novel, basic, unsupervised learning problem learning the lowest density homogeneous hyperplane separator of an unknown probability distribution. This task is relevant to several problems in machine learning, such as semi-supervised learning and clustering stability. We investigate the question of existence of a universally consistent algorithm for this problem. We propose two natura...

We study density-based clustering under low-noise conditions. Our framework allows for sharply defined clusters such as clusters on lower dimensional manifolds. We show that accurate clustering is possible even in high dimensions. We propose two data-based methods for choosing the bandwidth and we study the stability properties of density clusters. We show that a simple graph-based algorithm kn...