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Assessing time knowledge in children aged 10 to 11 years
The acquisition of time knowledge involves learning how to read clocks, estimate time, read dates and learn about temporal sequences. Evidence suggests that many of these competencies are acquired by 10 years of age although not all children may follow this developmental path. The main purpose of this study was to collect normative data for a screening tool that assesses time knowledge. These data identify the prevalence and pattern of difficulties with time knowledge among a UK sample of Year 6 pupils (aged 10 to 11 years). The Time Screening Assessment tool (Doran, Dutt & Pembery, 2015), designed to assess time knowledge, was administered individually to a sample of 79 children. Findings revealed a median overall score of 32 out of a maximum score of 36. 25% of children performed at or close to ceiling, however seven children scored more than -1.5 standard deviations below the mean. The value of these findings to practitioners working with children in schools is discussed
Quadratic Lagrangians and Topology in Gauge Theory Gravity
We consider topological contributions to the action integral in a gauge
theory formulation of gravity. Two topological invariants are found and are
shown to arise from the scalar and pseudoscalar parts of a single integral.
Neither of these action integrals contribute to the classical field equations.
An identity is found for the invariants that is valid for non-symmetric Riemann
tensors, generalizing the usual GR expression for the topological invariants.
The link with Yang-Mills instantons in Euclidean gravity is also explored. Ten
independent quadratic terms are constructed from the Riemann tensor, and the
topological invariants reduce these to eight possible independent terms for a
quadratic Lagrangian. The resulting field equations for the parity
non-violating terms are presented. Our derivations of these results are
considerably simpler that those found in the literature
A new form of the Kerr solution
A new form of the Kerr solution is presented. The solution involves a time
coordinate which represents the local proper time for free-falling observers on
a set of simple trajectories. Many physical phenomena are particularly clear
when related to this time coordinate. The chosen coordinates also ensure that
the solution is well behaved at the horizon. The solution is well suited to the
tetrad formalism and a convenient null tetrad is presented. The Dirac
Hamiltonian in a Kerr background is also given and, for one choice of tetrad,
it takes on a simple, Hermitian form.Comment: 8 pages, LaTeX, no figures. Corrected and improved version. To appear
in Phys. Rev.
Fermion absorption cross section of a Schwarzschild black hole
We study the absorption of massive spin-half particles by a small
Schwarzschild black hole by numerically solving the single-particle Dirac
equation in Painleve-Gullstrand coordinates. We calculate the absorption cross
section for a range of gravitational couplings Mm/m_P^2 and incident particle
energies E. At high couplings, where the Schwarzschild radius R_S is much
greater than the wavelength lambda, we find that the cross section approaches
the classical result for a point particle. At intermediate couplings we find
oscillations around the classical limit whose precise form depends on the
particle mass. These oscillations give quantum violations of the equivalence
principle. At high energies the cross section converges on the geometric-optics
value of 27 \pi R_S^2/4, and at low energies we find agreement with an
approximation derived by Unruh. When the hole is much smaller than the particle
wavelength we confirm that the minimum possible cross section approaches \pi
R_S^2/2.Comment: 11 pages, 3 figure
New Techniques for Analysing Axisymmetric Gravitational Systems. 1. Vacuum Fields
A new framework for analysing the gravitational fields in a stationary,
axisymmetric configuration is introduced. The method is used to construct a
complete set of field equations for the vacuum region outside a rotating
source. These equations are under-determined. Restricting the Weyl tensor to
type D produces a set of equations which can be solved, and a range of new
techniques are introduced to simplify the problem. Imposing the further
condition that the solution is asymptotically flat yields the Kerr solution
uniquely. The implications of this result for the no-hair theorem are
discussed. The techniques developed here have many other applications, which
are described in the conclusions.Comment: 30 pages, no figure
Imposing Observation-Varying Equality Constraints Using Generalised Restricted Least Squares
Linear equality restrictions derived from economic theory are frequently observation-varying. Except in special cases, Restricted Least Squares (RLS) cannot be used to impose such restrictions without either underconstraining or overconstraining the parameter space. We solve the problem by developing a new estimator that collapses to RLS in cases where the restrictions are observation-invariant. We derive some theoretical properties of our so-called Generalised Restricted Least Squares (GRLS) estimator, and conduct a simulation experiment involving the estimation of a constant returns to scale production function. We find that GRLS significantly outperforms RLS in both small and large samples
The Impact of Zero-Dispersion Wavelength Fluctuations in > 110 nm Fiber Optical Raman+Parametric Amplification
In this paper numerical results supported by experimental results, demonstrate that zero-dispersion wavelength fluctuations are found to be the main reason for the gain bandwidth limitation even in fiber optical parametric amplifiers employing ultra-short (25 m) gain fibres
Varying Alpha Monopoles
We study static magnetic monopoles in the context of varying alpha theories
and show that there is a group of models for which the t'Hooft-Polyakov
solution is still valid. Nevertheless, in general static magnetic monopole
solutions in varying alpha theories depart from the classical t'Hooft-Polyakov
solution with the electromagnetic energy concentrated inside the core seeding
spatial variations of the fine structure constant. We show that Equivalence
Principle constraints impose tight limits on the allowed variations of alpha
induced by magnetic monopoles which confirms the difficulty to generate
significant large-scale spatial variation of the fine structure constant found
in previous works. This is true even in the most favorable case where magnetic
monopoles are the source for these variations.Comment: 8 pages, 10 figures; Version to be published in Phys. Rev.
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