Spectral asymptotics of periodic elliptic operators

We demonstrate that the structure of complex second-order strongly elliptic operators $H$ on ${\bf R}^d$ with coefficients invariant under translation by ${\bf Z}^d$ can be analyzed through decomposition in terms of versions $H_z$, $z\in{\bf T}^d$, of $H$ with $z$-periodic boundary conditions acting on $L_2({\bf I}^d)$ where ${\bf I}=[0,1>$. If the semigroup $S$ generated by $H$ has a H\"older continuous integral kernel satisfying Gaussian bounds then the semigroups $S^z$ generated by the $H_z$ have kernels with similar properties and $z\mapsto S^z$ extends to a function on ${\bf C}^d\setminus\{0\}$ which is analytic with respect to the trace norm. The sequence of semigroups $S^{(m),z}$ obtained by rescaling the coefficients of $H_z$ by $c(x)\to c(mx)$ converges in trace norm to the semigroup $\hat{S}^z$ generated by the homogenization $\hat{H}_z$ of $H_z$. These convergence properties allow asymptotic analysis of the spectrum of $H$.Comment: 27 pages, LaTeX article styl

Diode laser 87Rb optical pumping in an evacuated wall-coated cell

The evacuated wall coated sealed cell coupled with diode laser optical pumping offers a number of attractive potential advantages for use in Rb or Cs atomic frequency standards. An investigation of systematic effects is required to explore possible limitations of the technique. The use of diode laser optical pumping of 87 Rb in an evacuated wall coated sealed cell is presented. Experimental results/discussion to be presented include the signal strength and line broadening of the 0 - 0 hyperfine resonance as a function of light intensity for the D1 optical transitions (F - F prime) - (2 1 prime) and (2 - 2 prime), shift of the 0 - 0 hyperfine frequency as a function of laser intensity and de-tuning from optical resonance, and diode laser frequency stabilization techniques

Molecular evidence for sediment nitrogen fixation in a temperate New England estuary

Primary production in coastal waters is generally nitrogen (N) limited with denitrification outpacing nitrogen fixation (N2-fixation). However, recent work suggests that we have potentially underestimated the importance of heterotrophic sediment N2-fixation in marine ecosystems. We used clone libraries to examine transcript diversity of nifH (a gene associated with N2-fixation) in sediments at three sites in a temperate New England estuary (Waquoit Bay, Massachusetts, USA) and compared our results to net sediment N2 fluxes previously measured at these sites. We observed nifH expression at all sites, including a site heavily impacted by anthropogenic N. At this N impacted site, we also observed mean net sediment N2-fixation, linking the geochemical rate measurement with nifH expression. This same site also had the lowest diversity (non-parametric Shannon = 2.75). At the two other sites, we also detected nifH transcripts, however, the mean N2 flux indicated net denitrification. These results suggest that N2-fixation and denitrification co-occur in these sediments. Of the unique sequences in this study, 67% were most closely related to uncultured bacteria from various marine environments, 17% to Cluster III, 15% to Cluster I, and only 1% to Cluster II. These data add to the growing body of literature that sediment heterotrophic N2-fixation, even under high inorganic nitrogen concentrations, may be an important yet overlooked source of N in coastal systems

Asymptotic enumeration of correlation-immune boolean functions

A boolean function of $n$ boolean variables is {correlation-immune} of order $k$ if the function value is uncorrelated with the values of any $k$ of the arguments. Such functions are of considerable interest due to their cryptographic properties, and are also related to the orthogonal arrays of statistics and the balanced hypercube colourings of combinatorics. The {weight} of a boolean function is the number of argument values that produce a function value of 1. If this is exactly half the argument values, that is, $2^{n-1}$ values, a correlation-immune function is called {resilient}. An asymptotic estimate of the number $N(n,k)$ of $n$-variable correlation-immune boolean functions of order $k$ was obtained in 1992 by Denisov for constant $k$. Denisov repudiated that estimate in 2000, but we will show that the repudiation was a mistake. The main contribution of this paper is an asymptotic estimate of $N(n,k)$ which holds if $k$ increases with $n$ within generous limits and specialises to functions with a given weight, including the resilient functions. In the case of $k=1$, our estimates are valid for all weights.Comment: 18 page

On the controversy concerning the definition of quark and gluon angular momentum

A major controversy has arisen in QCD as to how to split the total angular momentum into separate quark and gluon contributions, and as to whether the gluon angular momentum can itself be split, in a gauge invariant way, into a spin and orbital part. Several authors have proposed various answers to these questions and offered a variety of different expressions for the relevant operators. I argue that none of these is acceptable and suggest that the canonical expression for the momentum and angular momentum operators is the correct and physically meaningful one. It is then an inescapable fact that the gluon angular momentum operator cannot, in general, be split in a gauge invariant way into a spin and orbital part. However, the projection of the gluon spin onto its direction of motion i.e. its helicity is gauge invariant and is measured in deep inelastic scattering on nucleons. The Ji sum rule, relating the quark angular momentum to generalized parton distributions, though not based on the canonical operators, is shown to be correct, if interpreted with due care. I also draw attention to several interesting aspects of QED and QCD, which, to the best of my knowledge, are not commented upon in the standard textbooks on Field Theory.Comment: 41 pages; Some incorrect statements have been rectified and a detailed discussion has been added concerning the momentum carried by quarks and the Ji sum rule for the angular momentu

Propulsion Technology Lifecycle Operational Analysis

The paper presents the results of a focused effort performed by the members of the Space Propulsion Synergy Team (SPST) Functional Requirements Sub-team to develop propulsion data to support Advanced Technology Lifecycle Analysis System (ATLAS). This is a spreadsheet application to analyze the impact of technology decisions at a system-of-systems level. Results are summarized in an Excel workbook we call the Technology Tool Box (TTB). The TTB provides data for technology performance, operations, and programmatic parameters in the form of a library of technical information to support analysis tools and/or models. The lifecycle of technologies can be analyzed from this data and particularly useful for system operations involving long running missions. The propulsion technologies in this paper are listed against Chemical Rocket Engines in a Work Breakdown Structure (WBS) format. The overall effort involved establishing four elements: (1) A general purpose Functional System Breakdown Structure (FSBS). (2) Operational Requirements for Rocket Engines. (3) Technology Metric Values associated with Operating Systems (4) Work Breakdown Structure (WBS) of Chemical Rocket Engines The list of Chemical Rocket Engines identified in the WBS is by no means complete. It is planned to update the TTB with a more complete list of available Chemical Rocket Engines for United States (US) engines and add the Foreign rocket engines to the WBS which are available to NASA and the Aerospace Industry. The Operational Technology Metric Values were derived by the SPST Sub-team in the form of the TTB and establishes a database for users to help evaluate and establish the technology level of each Chemical Rocket Engine in the database. The Technology Metric Values will serve as a guide to help determine which rocket engine to invest technology money in for future development

Using blubber explants to investigate adipose function in grey seals:glycolytic, lipolytic and gene expression responses to glucose and hydrocortisone

Adipose tissue is fundamental to energy balance, which underpins fitness and survival. Knowledge of adipose regulation in animals that undergo rapid fat deposition and mobilisation aids understanding of their energetic responses to rapid environmental change. Tissue explants can be used to investigate adipose regulation in wildlife species with large fat reserves, when opportunities for organismal experimental work are limited. We investigated glucose removal, lactate, glycerol and NEFA accumulation in media, and metabolic gene expression in blubber explants from wild grey seals. Glycolysis was higher in explants incubated in 25 mM glucose (HG) for 24 h compared to controls (C: 5.5 mM glucose). Adipose-derived lactate likely contributes to high endogenous glucose production in seals. Lipolysis was not stimulated by HG or high hydrocortisone (HC: 500 nM hydrocortisone) and was lower in heavier animals. HC caused NEFA accumulation in media to decrease by ~30% relative to C in females, indicative of increased lipogenesis. Lipolysis was higher in males than females in C and HG conditions. Lower relative abundance of 11-β-hydroxysteroid dehydrogenase 1 mRNA in HG explants suggests glucose involvement in blubber cortisol sensitivity. Our findings can help predict energy balance responses to stress and nutritional state in seals, and highlight the use of explants to study fat tissue function in wildlife