Small gaps between products of two primes

Let $q_n$ denote the $n^{th}$ number that is a product of exactly two distinct primes. We prove that $$\liminf_{n\to \infty} (q_{n+1}-q_n) \le 6.$$ This sharpens an earlier result of the authors (arXivMath NT/0506067), which had 26 in place of 6. More generally, we prove that if $\nu$ is any positive integer, then $$\liminf_{n\to \infty} (q_{n+\nu}-q_n) \le C(\nu) = \nu e^{\nu-\gamma} (1+o(1)).$$ We also prove several other results on the representation of numbers with exactly two prime factors by linear forms.Comment: 11N25 (primary) 11N36 (secondary

Tunable adsorption on carbon nanotubes

We investigated the adsorption of a single atom, hydrogen and aluminum, on single wall carbon nanotubes from first-principles. The adsorption is exothermic, and the associated binding energy varies inversely as the radius of the zigzag tube. We found that the adsorption of a single atom and related properties can be modified continuously and reversibly by the external radial deformation. The binding energy on the high curvature site of the deformed tube increases with increasing radial deformation. The effects of curvature and radial deformation depend on the chirality of the tube.Comment: To be appear in Physical Review Letter

Misalignment factors to affect the fatigue of welded load-carrying joints

To assess the effects of misalignment on the weld fatigue, we present experimental fatigue test results of load- carrying cruciform joints which are subjected to axial variable amplitude loading. The welds were produced from steel AH36 grade and fatigue strength improved by high-frequently mechanical impact treatment. We identify several misalignment factors affecting the fatigue by considering the real and reference welded joint geometries. Our methodology includes proposals for the empirical calibration functions and local stress analyses by using the Structural Hot Spot Stress, Effective Notch Stress and Peak Stress Method. Additionally, we apply our methodology to other sixteen data sets which are extracted from the literature for load-carrying cruciform and butt welded joints subjected to constant amplitude loading. Finally, we present the resultant calibration functions with respect to corresponding fatigue test data