A scaling limit for the length of the longest cycle in a sparse random digraph

We discuss the length of the longest directed cycle in the sparse random digraph , constant. We show that for large there exists a function such that a.s. The function where is a polynomial in . We are only able to explicitly give the values , although we could in principle compute any .     

Small Scale Models Subjected to Buried Blast Loading Part I: Floorboard Accelerations and Related Passenger Injury Metrics with Protective Hulls

Small scale models representing key vehicle structural elements, including both floorboards and bottom-mounted, downward V-shape hulls in various configurations, have been manufactured and subjected to a range of buried blast loading conditions. By varying surface stand-off distance and depth of burial for several hull and structure configurations, the input-scaled response of aluminum full-scale vehicle floorboards has been quantified using high speed stereo-vision. Specifically, the maximum vertical acceleration on the floorboard and the corresponding Head Injury Criterion (HIC₁₅) are quantified as metrics to assess the severity of the blast event. Results show standard V-shaped hulls provide essential blast mitigation, with reductions in floorboard measurements up to 47X in maximum acceleration and HIC₁₅. Though variations in protective hull geometry provide modest reductions in the severity of a floorboard blast event, results also show that personnel on typical floorboard structures during blast loading events will incur unacceptable shock loading conditions, resulting in either serious or fatal injury. A more appropriate design scenario would be to consider situations that employ frame-mounted passenger seating to reduce the potential for injury. A second set of experiments will be presented in Part II that focuses on frame motions and accelerations when steel frames and steel structures are employed with various frame connections and coatings for frame blast mitigation.     

Synthesis and biological evaluation of 3-aryltyramines as fragments binding to BACE-1 and BACE-2

3-Aryltyramines were prepared in one single step from tyramine and various arenediazonium salts by radical arylation. Binding as well as enzyme inhibition data of the 14 compounds do not prove true interaction with BACE-1. In contrast, with BACE-2 inhibition and binding could be confirmed indicating that 3-aryltyramines are potential starting points for a drug discovery effort.     

Separation of isomeric disaccharides by traveling wave ion mobility mass spectrometry using CO2 as drift gas

The use of CO₂ as a massive and polarizable drift gas is shown to greatly improve peak‐to‐peak resolution (R_p‐p), as compared with N₂, for the separation of disaccharides in a Synapt G2 traveling wave ion mobility cell. Near or baseline R_p‐p was achieved for three pairs of sodiated molecules of disaccharide isomers, that is, cellobiose and sucrose (R_p‐p = 0.76), maltose and sucrose (R_p‐p = 1.04), and maltose and lactose (R_p‐p = 0.74). Ion mobility mass spectrometry using CO₂ as the drift gas offers therefore an attractive alternative for fast and efficient separation of isomeric disaccharides. Copyright © 2012 John Wiley & Sons, Ltd.     

Erratum to “Unique continuation results for Ricci curvature and applications” [J. Geom. Phys. 58 (2008) 179–207]

Corrections are given to some of the proofs of the paper mentioned in the title.     

Spectrally selective coatings of gold nanorods on architectural glass

Infrared-blocking coatings on window glass can be produced by dispersing gold nanorods into a polymer coating. The spectral selectivity of the coating is controlled by the shape and aspect ratio of the nanoparticles, which are in turn determined by the conditions applied during their synthesis. Coatings of nanorods in polyvinyl alcohol were deposited onto glass and characterized in both laboratory and sun-lit conditions. Selective attenuation of the near-infrared was demonstrated with the test panels transmitting approximately one-third of the incident solar radiation and absorbing nearly two-thirds. The high absorptive cross sections of the gold nanorods suggest that they can be applied in efficacious coatings at relatively low volume fractions.