On sums of three squares

Let $r_3(n)$ be the number of representations of a positive integer $n$ as a sum of three squares of integers. We give two distinct proofs of a conjecture of Wagon concerning the asymptotic value of the mean square of $r_3(n)$.Comment: 11 pages, minor revisions made; to appear in Internat. J. Number Theor

Fractionation of Hydrogen Isotopes by Sulfate- and Nitrate-Reducing Bacteria.

Hydrogen atoms from water and food are incorporated into biomass during cellular metabolism and biosynthesis, fractionating the isotopes of hydrogen-protium and deuterium-that are recorded in biomolecules. While these fractionations are often relatively constant in plants, large variations in the magnitude of fractionation are observed for many heterotrophic microbes utilizing different central metabolic pathways. The correlation between metabolism and lipid δ(2)H provides a potential basis for reconstructing environmental and ecological parameters, but the calibration dataset has thus far been limited mainly to aerobes. Here we report on the hydrogen isotopic fractionations of lipids produced by nitrate-respiring and sulfate-reducing bacteria. We observe only small differences in fractionation between oxygen- and nitrate-respiring growth conditions, with a typical pattern of variation between substrates that is broadly consistent with previously described trends. In contrast, fractionation by sulfate-reducing bacteria does not vary significantly between different substrates, even when autotrophic and heterotrophic growth conditions are compared. This result is in marked contrast to previously published observations and has significant implications for the interpretation of environmental hydrogen isotope data. We evaluate these trends in light of metabolic gene content of each strain, growth rate, and potential flux and reservoir-size effects of cellular hydrogen, but find no single variable that can account for the differences between nitrate- and sulfate-respiring bacteria. The emerging picture of bacterial hydrogen isotope fractionation is therefore more complex than the simple correspondence between δ(2)H and metabolic pathway previously understood from aerobes. Despite the complexity, the large signals and rich variability of observed lipid δ(2)H suggest much potential as an environmental recorder of metabolism

On two 10th order mock theta identities

We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan Journa

Lorenz gauge gravitational self-force calculations of eccentric binaries using a frequency domain procedure

We present an algorithm for calculating the metric perturbations and gravitational self-force for extreme-mass-ratio inspirals (EMRIs) with eccentric orbits. The massive black hole is taken to be Schwarzschild and metric perturbations are computed in Lorenz gauge. The perturbation equations are solved as coupled systems of ordinary differential equations in the frequency domain. Accurate local behavior of the metric is attained through use of the method of extended homogeneous solutions and mode-sum regularization is used to find the self-force. We focus on calculating the self-force with sufficient accuracy to ensure its error contributions to the phase in a long term orbital evolution will be $\delta\Phi \lesssim 10^{-2}$ radians. This requires the orbit-averaged force to have fractional errors $\lesssim 10^{-8}$ and the oscillatory part of the self-force to have errors $\lesssim 10^{-3}$ (a level frequently easily exceeded). Our code meets this error requirement in the oscillatory part, extending the reach to EMRIs with eccentricities of $e \lesssim 0.8$, if augmented by use of fluxes for the orbit-averaged force, or to eccentricities of $e \lesssim 0.5$ when used as a stand-alone code. Further, we demonstrate accurate calculations up to orbital separations of $a \simeq 100 M$, beyond that required for EMRI models and useful for comparison with post-Newtonian theory. Our principal developments include (1) use of fully constrained field equations, (2) discovery of analytic solutions for even-parity static modes, (3) finding a pre-conditioning technique for outer homogeneous solutions, (4) adaptive use of quad-precision and (5) jump conditions to handle near-static modes, and (6) a hybrid scheme for high eccentricities

Evaluating the role of bacterial diversity in supporting soil ecosystem functions under anthropogenic stress

Ecosystem functions and services are under threat from anthropogenic global change at a planetary scale. Microorganisms are the dominant drivers of nearly all ecosystem functions and therefore ecosystem-scale responses are dependent on responses of resident microbial communities. However, the specific characteristics of microbial communities that contribute to ecosystem stability under anthropogenic stress are unknown. We evaluated bacterial drivers of ecosystem stability by generating wide experimental gradients of bacterial diversity in soils, applying stress to the soils, and measuring responses of several microbial-mediated ecosystem processes, including C and N cycling rates and soil enzyme activities. Some processes (e.g., C mineralization) exhibited positive correlations with bacterial diversity and losses of diversity resulted in reduced stability of nearly all processes. However, comprehensive evaluation of all potential bacterial drivers of the processes revealed that bacterial α diversity per se was never among the most important predictors of ecosystem functions. Instead, key predictors included total microbial biomass, 16S gene abundance, bacterial ASV membership, and abundances of specific prokaryotic taxa and functional groups (e.g., nitrifying taxa). These results suggest that bacterial α diversity may be a useful indicator of soil ecosystem function and stability, but that other characteristics of bacterial communities are stronger statistical predictors of ecosystem function and better reflect the biological mechanisms by which microbial communities influence ecosystems. Overall, our results provide insight into the role of microorganisms in supporting ecosystem function and stability by identifying specific characteristics of bacterial communities that are critical for understanding and predicting ecosystem responses to global change

Wage differentials and their determinants in US tourism and tourism-associated industries

This paper examines variations in wages for tourism related industries in the US for the period 2004-2009. It critically assesses the extent to which tourism related activities conform to their low wage stereotype and finds this to be true in general but not universally. It then considers the possibility that wages in US tourism related industries can be explained by observable characteristics of these industries. Recent research has suggested that the use of wage data at the level of highly detailed occupations is an effective alternative to other ways of capturing underlying skill differences. In line with this literature data from the US Occupational Employment Statistics (OES) were used to provide this detail. The results strongly support the importance of difference between occupations in wages in understanding differences between industries. They also support the importance of a number of industry characteristics including profitability, multi-factor productivity and demand growth. The paper also considers the relevance of an industry wage premium or discount for tourism related activities in the US over the same period. To assess this it estimates an industry wage model separately for five individual occupations across all industries which employ the occupation concerned. Within the small number of occupations covered the analysis find that workers in the two more highly paid occupations exhibit evidence of a tourism related discount but that workers in the three more lowly paid occupations exhibit a tourism related wage premium

Control design for the ACTEX flight experiment using the robust, fixed-structure toolbox

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76647/1/AIAA-1999-3952-918.pd

Analysis of social, fiscal, and structural factors affecting integrated pest management programs in Missouri and implications for future programs to protect water quality

Integrated Pest Management (IPM) has experienced a resurgence of interest due in part to continuing reports of drinking water contamination by agricultural pesticides. In response to the decertification of certain pesticides used for soil insect control on corn, in the early 1970s federal programs established Cooperative Extension Service sponsored IPM programs in several midwestern States to promote insect scouting on corn and cotton. This report documents the various factors which facilitated the growth and decline of these programs in Missouri and the ongoing transformation of such services into the private sector and other agencies. The objective of this report is to provide policy prescriptions to enhance the future adoption of IPM in Missouri and other areas that will facilitate the protection of water resources. Research in Missouri regarding pesticide use practices and water quality issues indicates that there is a considerably higher incidence of IPM use in counties that historically had, or still currently have, Extension sponsored programs. Interviews were conducted with University personnel responsible for implementing these programs, county Extension agents responsible for overseeing the programs, private sector businesspeople who are currently offering IPM services, and farm opeators who previously used, and/or now participate in, IPM Extension programs or private services. Interviewees were asked what factors contributed to the success, failure, and/or transformation of the county programs. Results indicate that these factors include quality and turnover of the scouts, committment of the Extension agent, economic and climatological variables, institutional support, and packaging IPM programs with other programs such as irrigation.Project # G-2029-04 Agreement # 14-08-0001-G-2029-0