1,563 research outputs found
Imbeddings into topological groups preserving dimensions
AbstractWe give a negative answer to the following question of Bel'nov: Can every Tychonoff space X be imbedded as a subspace of a topological group G so that dim G ⩽ dim X? We show that if n ≠ 0, 1, 3, 7, then the n-dimensional sphere Sn cannot be imbedded into an n-dimensional topological group G (no matter which dimension function, ind, Ind or dim, is considered). However, in case dim X = 0 the answer to Bel'nov's question is “yes”. We prove that, for every Tychonoff space X, dim X =0 implies (in fact, equivalent to) dim F∗(X) = 0 and dim A∗(X) = 0, where F∗(X) (A∗(X)) is the free precompact (Abelian) group of X. As a corollary we obtain that every precompact group G is a quotient group of a precompact group H such that dim H = 0 and w(H) = w(G). A complete metric space X1 and a pseudocompact Tychonoff space X2 are constructed such that ind Xi = 0, while ind F∗(Xi) ≠ 0 and ind A∗(Xi) ≠ 0 (i = 1, 2). The equivalence of ind G = 0 and dim G = 0 for a precompact group G is established. We prove that dim H ⩽ dim G whenever H is a precompact subgroup of a topological group G. We also show that for every Tychonoff topology T on a set X with ind(X, T) = 0 one can find a precompact Hausdorff group topology T̃ on the free (Abelian) group G(X) of X such that w(G(X), T̃) = w(X, T), T̃ |x = T and dim(G(X), T̃) = 0
An Off-line Scan of the BATSE Daily Records and a Large Uniform Sample of Gamma-Ray Bursts
During a scan of the archival BATSE daily records covering the entire 9.1
years (TJD 8369-11690) of the BATSE operation, 3906 gamma-ray bursts (GRBs)
have been detected. 2068 of these GRBs are previously known BATSE triggers
while 1838 of them are new non-triggered bursts. It is important that all
events were detected in the same type of data and were processed with the same
procedure. Therefore these 3906 GRBs constitute a uniform sample. We have
created a publically available electronic data base containing this sample. We
describe the procedures of the data reduction, the selection of the GRB
candidates, and the statistical tests for possible non-GRB contaminations. We
also describe a novel test burst method used to measure the scan efficiency and
the information obtained using the test bursts. Our scan decreases the BATSE
detection threshold to ~0.1 photons/sec/cm2. As a first result, we show that
the differential log N - log P distribution corrected for the detection
efficiency extends to low brightnesses without any indication of a turn-over.
Any reasonable extrapolation of the new log N - log P to lower brightnesses
imply a rate of several thousands of GRBs in the Universe per year.Comment: 14 pages; 23 figures; revised version accepted to ApJ; electronic
version of Table 2 is available at
ftp://ftp.astro.su.se/pub/head/grb/catalogs/etable2.txt The GRB archive is
available at http://www.astro.su.se/groups/head/grb_archive.htm
The applicability of Raman spectroscopy for estimation of interfaces thickness in the AlN/GaN superlattices
AbstractPolar optical phonons in quaternary nitride-based superlattices have been investigated in the framework of the dielectric continuum model. In the considered systems, the superlattice period consisted of two main GaN and AlN layers and two interstitial Al0.5Ga0.5N layers. Such a structure simulates binary superlattices with diffuse interfaces. The presence of the finite thickness interface layers was shown to give rise to appearance of several low-intensity additional phonon modes active in Raman scattering; frequency splitting of such modes is sensitive to relative thickness of intermediate layers. The fundamental Raman-intense polar phonon modes were also stated to be independent on the interface thickness, and these modes were very sensitive to the main layer thicknesses
Landauer Conductance of Luttinger Liquids with Leads
We show that the dc conductance of a quantum wire containing a Luttinger
liquid and attached to non-interacting leads is given by per spin
orientation, regardless of the interactions in the wire. This explains the
recent observations of the absence of conductance renormalization in long
high-mobility wires by Tarucha, Honda and Saku (Solid State
Communications {\bf 94}, 413 (1995)).Comment: 4 two-column pages, RevTeX + 1 uuencoded figure
Stability of slow magnetoacoustic and entropy waves in the solar coronal plasma with thermal misbalance
The back-reaction of the perturbed thermal equilibrium in the solar corona on
compressive perturbations, also known as the effect of wave-induced thermal
misbalance, is known to result in thermal instabilities chiefly responsible for
the formation of fine thermal structuring of the corona. We study the role of
the magnetic field and field-aligned thermal conduction in triggering
instabilities of slow magnetoacoustic and entropy waves in quiescent and hot
active region loops, caused by thermal misbalance. Effects of the magnetic
field are accounted for by including it in the parametrisation of a guessed
coronal heating function, and the finite plasma parameter , in terms of
the first-order thin flux tube approximation. Thermal conduction tends to
stabilise both slow and entropy modes, broadening the interval of plausible
coronal heating functions allowing for the existence of a thermodynamically
stable corona. This effect is most pronounced for hot loops. In contrast to
entropy waves, the stability of which is found to be insensitive to the
possible dependence of the coronal heating function on the magnetic field, slow
waves remain stable only for certain functional forms of this dependence,
opening up perspectives for its seismological diagnostics in future.Comment: Accepted for publication in the Physics journa
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