2,573 research outputs found
Skew -Derivations on Semiprime Rings
For a ring with an automorphism , an -additive mapping
is called a skew
-derivation with respect to if it is always a -derivation
of for each argument. Namely, it is always a -derivation of for
the argument being left once arguments are fixed by elements in
. In this short note, starting from Bre\v{s}ar Theorems, we prove that a
skew -derivation () on a semiprime ring must map into the
center of .Comment: 8 page
Compact Routing on Internet-Like Graphs
The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing
scheme delivering a nearly optimal local memory upper bound. Using both direct
analysis and simulation, we calculate the stretch distribution of this routing
scheme on random graphs with power-law node degree distributions, . We find that the average stretch is very low and virtually
independent of . In particular, for the Internet interdomain graph,
, the average stretch is around 1.1, with up to 70% of paths
being shortest. As the network grows, the average stretch slowly decreases. The
routing table is very small, too. It is well below its upper bounds, and its
size is around 50 records for -node networks. Furthermore, we find that
both the average shortest path length (i.e. distance) and width of
the distance distribution observed in the real Internet inter-AS graph
have values that are very close to the minimums of the average stretch in the
- and -directions. This leads us to the discovery of a unique
critical quasi-stationary point of the average TZ stretch as a function of
and . The Internet distance distribution is located in a
close neighborhood of this point. This observation suggests the analytical
structure of the average stretch function may be an indirect indicator of some
hidden optimization criteria influencing the Internet's interdomain topology
evolution.Comment: 29 pages, 16 figure
Stellar loci I. Metallicity dependence and intrinsic widths
Stellar loci are widely used for selection of interesting outliers, reddening
determinations, and calibrations. However, hitherto the dependence of stellar
loci on metallicity has not been fully explored and their intrinsic widths are
unclear. In this paper, by combining the spectroscopic and re-calibrated
imaging data of the SDSS Stripe 82, we have built a large, clean sample of
dwarf stars with accurate colors and well determined metallicities to
investigate the metallicity dependence and intrinsic widths of the SDSS stellar
loci. Typically, one dex decrease in metallicity causes 0.20 and 0.02 mag
decrease in colors u-g and g-r, and 0.02 and 0.02 mag increase in colors r-i
and i-z, respectively. The variations are larger for metal-rich stars than for
metal-poor ones, and for F/G/K stars than for A/M ones. Using the sample, we
have performed two dimensional polynomial fitting to the u-g, g-r, r-i, and i-z
colors as a function of color g-i and metallicity [Fe/H]. The residuals, at the
level of 0.029, 0.008, 0.008 and 0.011 mag for the u-g, g-r, r-i, and i-z
colors, respectively can be fully accounted for by the photometric errors and
metallicity uncertainties, suggesting that the intrinsic widths of the loci are
at maximum a few mmag. The residual distributions are asymmetric, revealing
that a significant fraction of stars are binaries. In a companion paper, we
will present an unbiased estimate of the binary fraction for field stars. Other
potential applications of the metallicity dependent stellar loci are briefly
discussed.Comment: 6 pages, 4 figures, 1 table, ApJ in pres
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