15,504 research outputs found
Do wavelets really detect non-Gaussianity in the 4-year COBE data?
We investigate the detection of non-Gaussianity in the 4-year COBE data
reported by Pando, Valls-Gabaud & Fang (1998), using a technique based on the
discrete wavelet transform. Their analysis was performed on the two DMR faces
centred on the North and South Galactic poles respectively, using the
Daubechies 4 wavelet basis. We show that these results depend critically on the
orientation of the data, and so should be treated with caution. For two
distinct orientations of the data, we calculate unbiased estimates of the
skewness, kurtosis and scale-scale correlation of the corresponding wavelet
coefficients in all of the available scale domains of the transform. We obtain
several detections of non-Gaussianity in the DMR-DSMB map at greater than the
99 per cent confidence level, but most of these occur on pixel-pixel scales and
are therefore not cosmological in origin. Indeed, after removing all multipoles
beyond from the COBE maps, only one robust detection remains.
Moreover, using Monte-Carlo simulations, we find that the probability of
obtaining such a detection by chance is 0.59. We repeat the analysis for the
53+90 GHz coadded COBE map. In this case, after removing
multipoles, two non-Gaussian detections at the 99 per cent level remain.
Nevertheless, again using Monte-Carlo simulations, we find that the probability
of obtaining two such detections by chance is 0.28. Thus, we conclude the
wavelet technique does {\em not} yield strong evidence for non-Gaussianity of
cosmological origin in the 4-year COBE data.Comment: 7 pages, 5 figures. Revised version including discussion of
orientation sensitivity of the wavelet decomposition. MNRAS submitte
Analytical approach to the transition to thermal hopping in the thin- and thick-wall approximations
The nature of the transition from the quantum tunneling regime at low
temperatures to the thermal hopping regime at high temperatures is investigated
analytically in scalar field theory. An analytical bounce solution is
presented, which reproduces the action in the thin-wall as well as thick-wall
limits. The transition is first order for the case of a thin wall while for the
thick wall case it is second order.Comment: Latex file, 22 pages, 4 Postscript figure
Quadrupole Vibrations and the Electric Quadrupole Moment of Some Closed Shell Plus (or Minus) a Single Nucleon Nuclei
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