On an Asymptotic Series of Ramanujan

An asymptotic series in Ramanujan's second notebook (Entry 10, Chapter 3) is concerned with the behavior of the expected value of $\phi(X)$ for large $\lambda$ where $X$ is a Poisson random variable with mean $\lambda$ and $\phi$ is a function satisfying certain growth conditions. We generalize this by studying the asymptotics of the expected value of $\phi(X)$ when the distribution of $X$ belongs to a suitable family indexed by a convolution parameter. Examples include the problem of inverse moments for distribution families such as the binomial or the negative binomial.Comment: To appear, Ramanujan

Residents\u27 Perceptions of Community and Environmental Impacts From Development of Natural Gas in the Marcellus Shale: A Comparison of Pennsylvania and New York Cases

Communities experiencing rapid growth due to energy development (‘boomtowns’) have reported positive and negative impacts on community and individual well-being. The perceptions of impacts vary according to stage of energy development as well as experience with extractive industries. Development of the Marcellus Shale provides an opportunity to examine these impacts over time and across geographic and historical contexts. This paper describes case study research in Pennsylvania and New York to document preliminary impacts of development occurring there. Cases vary by level of development and previous extractive history. The study finds that, in areas with low population density, higher levels of development lead to a broader awareness of natural gas impacts, both positive and negative. Participants draw from the regional history of extraction to express environmental concern despite direct, local experience. Our findings suggest the need to track these perceptions during development, and as individuals and communities react and adapt to the impacts

Thermal Excitation Energy Distribution of 475 MeV and 2 GeV Proton and 3He Induced Reactions in Heavy Nuclei

The 4pi neutron detector ORION was installed at SATURNE laboratory to perform experiments with high energy light- and heavy- ion beams. The first preliminary results are now available. The thermal excitation energy distribution of nuclei produced in high energy proton induced reactions was measured using almost direct approach. Comparison of the experimental results and predictions of the intranuclear cascade (INC) model is presented. The experimentally observed distributions are in fair agreement with the results of the INC model.</p

Search for CP Violation in the Decay Z -> b (b bar) g

About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between the two quarks and the gluon in three-jet events and by measuring the differential two-jet rate. No signal of CP violation is found. For the combinations of anomalous CP violating couplings, ${\hat{h}}_b = {\hat{h}}_{Ab}g_{Vb}-{\hat{h}}_{Vb}g_{Ab}$ and $h^{\ast}_b = \sqrt{\hat{h}_{Vb}^{2}+\hat{h}_{Ab}^{2}}$, limits of \hat{h}_b < 0.59$and$h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st

The extent and variability of storm-induced temperature changes in lakes measured with long-term and high-frequency data

The intensity and frequency of storms are projected to increase in many regions of the world because of climate change. Storms can alter environmental conditions in many ecosystems. In lakes and reservoirs, storms can reduce epilimnetic temperatures from wind-induced mixing with colder hypolimnetic waters, direct precipitation to the lake's surface, and watershed runoff. We analyzed 18 long-term and high-frequency lake datasets from 11 countries to assess the magnitude of wind- vs. rainstorm-induced changes in epilimnetic temperature. We found small day-to-day epilimnetic temperature decreases in response to strong wind and heavy rain during stratified conditions. Day-to-day epilimnetic temperature decreased, on average, by 0.28 degrees C during the strongest windstorms (storm mean daily wind speed among lakes: 6.7 +/- 2.7 m s(-1), 1 SD) and by 0.15 degrees C after the heaviest rainstorms (storm mean daily rainfall: 21.3 +/- 9.0 mm). The largest decreases in epilimnetic temperature were observed >= 2 d after sustained strong wind or heavy rain (top 5(th) percentile of wind and rain events for each lake) in shallow and medium-depth lakes. The smallest decreases occurred in deep lakes. Epilimnetic temperature change from windstorms, but not rainstorms, was negatively correlated with maximum lake depth. However, even the largest storm-induced mean epilimnetic temperature decreases were typicallyPeer reviewe

Limit on Bs0B^0_s oscillation using a jet charge method

A lower limit is set on the B_{s}^{0} meson oscillation parameter \Delta m_{s} using data collected from 1991 to 1994 by the ALEPH detector. Events with a high transverse momentum lepton and a reconstructed secondary vertex are used. The high transverse momentum leptons are produced mainly by b hadron decays, and the sign of the lepton indicates the particle/antiparticle final state in decays of neutral B mesons. The initial state is determined by a jet charge technique using both sides of the event. A maximum likelihood method is used to set a lower limit of \, \Delta m_{s}. The 95\% confidence level lower limit on \Delta m_s ranges between 5.2 and 6.5(\hbar/c^{2})~ps^{-1} when the fraction of b quarks from Z^0 decays that form B_{s}^{0} mesons is varied from 8\% to 16\%. Assuming that the B_{s}^{0} fraction is 12\%, the lower limit would be \Delta m_{s} 6.1(\hbar/c^{2})~ps^{-1} at 95\% confidence level. For x_s = \Delta m_s \, \tau_{B_s}, this limit also gives x_s 8.8 using the B_{s}^{0} lifetime of \tau_{B_s} = 1.55 \pm 0.11~ps and shifting the central value of \tau_{B_s} down by 1\sigma

Measurement of the Bs0^0_s lifetime and production rate with Ds−l+^-_s l^+ combinations in Z decays

The lifetime of the \bs meson is measured in approximately 3 million hadronic Z decays accumulated using the ALEPH detector at LEP from 1991 to 1994. Seven different \ds decay modes were reconstructed and combined with an opposite sign lepton as evidence of semileptonic \bs decays. Two hundred and eight \dsl candidates satisfy selection criteria designed to ensure precise proper time reconstruction and yield a measured \bs lifetime of \mbox{\result .} Using a larger, less constrained sample of events, the product branching ratio is measured to be \mbox{\pbrresult