New bounds for Gauss sums derived from kk-th powers, and for Heilbronn's exponential sum

We show that ∑pn=1exp(2πiank/p) ≪ min(k5/8p5/8, k3/8p3/4) and ∑pn=1exp(2πianp/p2) ≪ p7/8 when p \(crossed)a. The proof uses a modification of Stepanov's method

Firm Performance, Worker Commitment and Loyalty

Using matched employer-employee level data drawn from the UK Workplace and Employee Relations Survey, we explore the influence of worker commitment and loyalty on firm level labour productivity and financial performance. Our empirical findings suggest that worker commitment and loyalty enhance both labour productivity and financial performance at the firm level thereby highlighting a hitherto neglected conduit for improved firm performance. Using employee level data, we also explore the determinants of worker commitment and loyalty in order to ascertain how such attachments to the firm may be engendered. In general, our employee level analysis suggests that it is firm level characteristics (such as appraisal schemes, supervision, suspensions and redundancies) that influence attachments to the firm. Such findings suggest that firms may be able to exert some influence over the loyalty and commitment of its workforce, which, in turn, may affect firm performance

Higher Descent Data as a Homotopy Limit

We define the 2-groupoid of descent data assigned to a cosimplicial 2-groupoid and present it as the homotopy limit of the cosimplicial space gotten after applying the 2-nerve in each cosimplicial degree. This can be applied also to the case of $n$-groupoids thus providing an analogous presentation of "descent data" in higher dimensions.Comment: Appeared in JHR

Hamiltonians for a general dilaton gravity theory on a spacetime with a non-orthogonal, timelike or spacelike outer boundary

A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d+1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.Comment: 17 pages, 3 figures. Typos correcte

Circumferential pressure distributions in a model labyrinth seal

A research program to isolate and study leakage flow through labyrinth glands was initiated. Circumferential pressure distributions were measured in the labyrinth glands with geometry appropriate to the high pressure labyrinths in large steam turbines. Knowledge of this pressure distribution is essential as it is this unequal pressure field that results in the destabilizing force. Parameters that are likely to affect the pressure distributions are incorporated into the test rig. Some preliminary pressure profiles are presented

Action and Energy of the Gravitational Field

We present a detailed examination of the variational principle for metric general relativity as applied to a ``quasilocal'' spacetime region \M (that is, a region that is both spatially and temporally bounded). Our analysis relies on the Hamiltonian formulation of general relativity, and thereby assumes a foliation of \M into spacelike hypersurfaces $\Sigma$. We allow for near complete generality in the choice of foliation. Using a field--theoretic generalization of Hamilton--Jacobi theory, we define the quasilocal stress-energy-momentum of the gravitational field by varying the action with respect to the metric on the boundary \partial\M. The gravitational stress-energy-momentum is defined for a two--surface $B$ spanned by a spacelike hypersurface in spacetime. We examine the behavior of the gravitational stress-energy-momentum under boosts of the spanning hypersurface. The boost relations are derived from the geometrical and invariance properties of the gravitational action and Hamiltonian. Finally, we present several new examples of quasilocal energy--momentum, including a novel discussion of quasilocal energy--momentum in the large-sphere limit towards spatial infinity.Comment: To be published in Annals of Physics. This final version includes two new sections, one giving examples of quasilocal energy and the other containing a discussion of energy at spatial infinity. References have been added to papers by Bose and Dadhich, Anco and Tun

Temporal and Spatial Turbulent Spectra of MHD Plasma and an Observation of Variance Anisotropy

The nature of MHD turbulence is analyzed through both temporal and spatial magnetic fluctuation spectra. A magnetically turbulent plasma is produced in the MHD wind-tunnel configuration of the Swarthmore Spheromak Experiment (SSX). The power of magnetic fluctuations is projected into directions perpendicular and parallel to a local mean field; the ratio of these quantities shows the presence of variance anisotropy which varies as a function of frequency. Comparison amongst magnetic, velocity, and density spectra are also made, demonstrating that the energy of the turbulence observed is primarily seeded by magnetic fields created during plasma production. Direct spatial spectra are constructed using multi-channel diagnostics and are used to compare to frequency spectra converted to spatial scales using the Taylor Hypothesis. Evidence for the observation of dissipation due to ion inertial length scale physics is also discussed as well as the role laboratory experiment can play in understanding turbulence typically studied in space settings such as the solar wind. Finally, all turbulence results are shown to compare fairly well to a Hall-MHD simulation of the experiment.Comment: 17 pages, 17 figures, Submitted to Astrophysical Journa