169,608 research outputs found
New bounds for Gauss sums derived from -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 -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 . 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 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
Lightcone reference for total gravitational energy
We give an explicit expression for gravitational energy, written solely in
terms of physical spacetime geometry, which in suitable limits agrees with the
total Arnowitt-Deser-Misner and Trautman-Bondi-Sachs energies for
asymptotically flat spacetimes and with the Abbot-Deser energy for
asymptotically anti-de Sitter spacetimes. Our expression is a boundary value of
the standard gravitational Hamiltonian. Moreover, although it stands alone as
such, we derive the expression by picking the zero-point of energy via a
``lightcone reference.''Comment: latex, 7 pages, no figures. Uses an amstex symbo
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