Sums and Products with Smooth Numbers

We estimate the sizes of the sumset A + A and the productset A $\cdot$ A in the special case that A = S (x, y), the set of positive integers n less than or equal to x, free of prime factors exceeding y.Comment: 12 page

Hygroscopic growth of sub-micrometer and one-micrometer aerosol particles measured during ACE-Asia

International audienceHygroscopic properties of aerosol particles in the sub-micrometer and one-micrometer size ranges were measured during the ACE-Asia study (Aerosol Characterization Experiment-Asia) in spring 2001. The measurements took place off the coasts of Japan, Korea, and China. All instruments contributing to this study were deployed in a container on the forward deck of the NOAA Research Vessel Ronald H. Brown. Air masses with primarily marine influence and air masses from the Asian continent affected by both anthropogenic sources and by the transport of desert dust aerosol were encountered during the cruise. Results showed very different hygroscopic behavior in the sub-micrometer size range compared to the one-micrometer size range. In general, for all continentally influenced air masses, the one-micrometer particle population was characterized by two different particle groups ? a nearly hydrophobic fraction with growth factors around 1.0 representative of dust particles and a sea salt fraction with hygroscopic growth factors around 2.0. The number fraction of dust particles was generally about 60% independent of long-range air mass origin. For sub-micrometer particles, a dominant, more hygroscopic particle fraction with growth factors between 1.5 and 1.9 (depending on dry particle size) consistent with ammonium sulfate or non-neutralized sulfates as major component was always found. In marine air masses and for larger sizes within the sub-micrometer range (Dp=250 and 350 nm), a sea salt fraction with growth factors between 2.0 and 2.1 was also observed. For all other air masses, the more hygroscopic particle fraction in the sub-micrometer size range was mostly accompanied by a less hygroscopic particle fraction with growth factors between 1.20 and 1.55 depending on both the continental sources and the dry particle size. Number fractions of this particle group varied between 4 and 39% depending on dry particle size and air mass type. Nearly hydrophobic particles indicating dust particles in the sub-micrometer size regime were only found for particles with Dp=250 and 350 nm during a time period when the aerosol was influenced by transport from Asian desert regions

Liquid rhizobial inoculants for lentil and field pea

Non-Peer ReviewedThe traditional peat legume inoculants are viewed by western Canadian farmers as being difficult to apply. Accordingly, more "user-friendly" inoculants are being developed to ensure more wide-spread inoculation of legumes. A liquid inoculant developed by LiphaTech was evaluated as a carrier for Rhizobium leguminosarum strains 99A1 for lentil and 128C56G for pea. These two strains survived at titres exceeding log 8.0 per mL for ten months at 5°C and there was no loss of viability during shipping and handling. The Prairie Agricultural Machine Institute (PAMI) determined that the liquid inoculant gave a very flowable and uniform coverage of the seeds when applied through a grain auger and various types of seeding equipment. Liquid inoculant for pea and lentil resulted in yields equal or better than those observed for the traditional peat-based inoculant

Influence of particle size and chemistry on the cloud nucleating properties of aerosols

International audienceThe ability of an aerosol particle to act as a cloud condensation nuclei (CCN) is a function of the size of the particle, its composition and mixing state, and the supersaturation of the cloud. In-situ data from field studies provide a means to assess the relative importance of these parameters. During the 2006 Texas Air Quality ? Gulf of Mexico Atmospheric Composition and Climate Study (TexAQS-GoMACCS), the NOAA RV Ronald~H.~Brown encountered a wide variety of aerosol types ranging from marine near the Florida panhandle to urban and industrial in the Houston-Galveston area. These varied sources provided an opportunity to investigate the role of aerosol sources, chemistry, and size in the activation of particles to form cloud droplets. Measurements were made of CCN concentrations, aerosol chemical composition in the size range relevant for particle activation, and aerosol size distributions. Variability in aerosol composition was parameterized by the mass fraction of Hydrocarbon-like Organic Aerosol (HOA) for particle diameters less than 200 nm (vacuum aerodynamic). The HOA mass fraction in this size range was lowest for marine aerosol and highest for aerosol sampled close to anthropogenic sources. Combining all data from the experiment reveals that composition (defined by HOA mass fraction) explains 40% of the variance in the critical diameter for particle activation at 0.44% supersaturation (S). Correlations between HOA mass fraction and aerosol mean diameter show that these two parameters are essentially independent of one another for this data set. We conclude that, based on the variability of the HOA mass fraction observed during TexAQS-GoMACCS, composition played a significant role in determining the fraction of particles that could activate to form cloud droplets. In addition, we estimate the error that results in calculated CCN concentrations if the HOA mass fraction is neglected (i.e., a fully soluble composition of (NH4)2SO4 is assumed) for the range of mass fractions and mean diameters observed during the experiment. This error is then related to the source of the aerosol. At 0.22 and 0.44% S, the error is considerable (>50%) for anthropogenic aerosol sampled near the source region as this aerosol had, on average, a high HOA mass fraction in the sub-200 nm diameter size range (vacuum aerodynamic). The error is lower for aerosol distant from anthropogenic source regions as it had a lower HOA mass fraction. Hence, the percent error in calculated CCN concentration is larger for organic-rich aerosol sampled near the source and smaller for aerosol sampled away from sources of anthropogenic particulate organic matter (POM)