78 research outputs found
Average Emissivity Curve of BATSE Gamma-Ray Bursts with Different Intensities
Six intensity groups with ~150 BATSE gamma-ray bursts each are compared using
average emissivity curves. Time-stretch factors for each of the dimmer groups
are estimated with respect to the brightest group, which serves as the
reference, taking into account the systematics of counts-produced noise effects
and choice statistics. A stretching/intensity anti-correlation is found with
good statistical significance during the average back slopes of bursts. A
stretch factor ~2 is found between the 150 dimmest bursts, with peak flux
4.1 ph
cm^{-2} s^{-1}. On the other hand, while a trend of increasing stretching
factor may exist for rise fronts for burst with decreasing peak flux from >4.1
ph cm^{-2} s^{-1} down to 0.7 ph cm^{-2} s^{-1}, the magnitude of the
stretching factor is less than ~ 1.4 and is therefore inconsistent with
stretching factor of back slope.Comment: 21 pages, 3 figures. Accepted to Ap
On cogrowth function of algebras and its logarithmical gap
Let be an associative algebra. A finite word over alphabet is -reducible if its image in is a -linear combination of length-lexicographically lesser words. An obstruction is a subword-minimal -reducible word. If the number of obstructions is finite then has a finite Gröbner basis, and the word problem for the algebra is decidable. A cogrowth function is the number of obstructions of length . We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth
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