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The random point fields which describe the position distributions of the systems of ideal boson gas in states of Bose Einstein condensations are obtained through the thermodynamic limits.
This involved sampling successive shrubs from the first shrub (closest to the random point), with each successive shrub being the closest shrub to the previous in the forward-facing 180 degrees (Wyoming Game and Fish Department 1982).
Since the non-drain polygons cover much larger areas of land compared to the area covered by linear drain features, there was a strong bias towards non-drain polygons in the random point data.
It is shown in the present paper that the requirement does apply providing that the random point process representing the system natural frequencies is at least locally stationary (which is a much weaker condition than local stationarity of the frequency response function), and a number of the implications of this result are explored.
We performed this procedure one thousand times and calculated for each of the one thousand realizations the proportional availability of landcover types by intersecting the random point locations with the GIS landcover types.
The target genes in TE tagged lines can be cloned based on the TE tag sequences, a major advantage over the random point mutagenesis approaches (e.g. EMS and UV mediated mutation).
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The random points on the reference skull and face are shown in Figure5c,d.
We add the transient noise segments to the random points of time of the speech signals.
Most of the random points fell outside these buffered areas, in the not-drain areas.
Then, all random points with coordinates |ρ i –r 1| ≤ D were removed from the initial set of the random points.
Osada et al. [21] defined five shape functions which basically calculate Euclidean distances between the random points.
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