4,604 research outputs found
Black Holes with Multiple Charges and the Correspondence Principle
We consider the entropy of near extremal black holes with multiple charges in
the context of the recently proposed correspondence principle of Horowitz and
Polchinski, including black holes with two, three and four Ramond-Ramond
charges. We find that at the matching point the black hole entropy can be
accounted for by massless open strings ending on the D-branes for all cases
except a black hole with four Ramond-Ramond charges, in which case a possible
resolution in terms of brane-antibrane excitations is considered.Comment: 26 pages, harvmac, minor correction
On the relationship between the Hurst exponent, the ratio of the mean square successive difference to the variance, and the number of turning points
The long range dependence of the fractional Brownian motion (fBm), fractional
Gaussian noise (fGn), and differentiated fGn (DfGn) is described by the Hurst
exponent . Considering the realisations of these three processes as time
series, they might be described by their statistical features, such as half of
the ratio of the mean square successive difference to the variance,
, and the number of turning points, . This paper investigates
the relationships between and , and between and . It is
found numerically that the formulae in case of
fBm, and for fGn and DfGn, describe well the
relationship. When is considered, no simple formula is
found, and it is empirically found that among polynomials, the fourth and
second order description applies best. The most relevant finding is that when
plotted in the space of , the three process types form
separate branches. Hence, it is examined whether and may
serve as Hurst exponent indicators. Some real world data (stock market indices,
sunspot numbers, chaotic time series) are analyzed for this purpose, and it is
found that the 's estimated using the relations (expressed
as inverted functions) are consistent with the 's extracted
with the well known wavelet approach. This allows to efficiently estimate the
Hurst exponent based on fast and easy to compute and , given
that the process type: fBm, fGn or DfGn, is correctly classified beforehand.
Finally, it is suggested that the relation for fGn and DfGn
might be an exact (shifted) power-law.Comment: 20 pages in one-column format, 7 figures; matches the version
accepted for publicatio
Regions of linearity, Lusztig cones and canonical basis elements for the quantized enveloping algebra of type A_4
Let U_q be the quantum group associated to a Lie algebra g of rank n. The
negative part U^- of U has a canonical basis B with favourable properties,
introduced by Kashiwara and Lusztig. The approaches of Kashiwara and Lusztig
lead to a set of alternative parametrizations of the canonical basis, one for
each reduced expression for the longest word in the Weyl group of g. We show
that if g is of type A_4 there are close relationships between the Lusztig
cones, canonical basis elements and the regions of linearity of
reparametrization functions arising from the above parametrizations. A graph
can be defined on the set of simplicial regions of linearity with respect to
adjacency, and we further show that this graph is isomorphic to the graph with
vertices given by the reduced expressions of the longest word of the Weyl group
modulo commutation and edges given by long braid relations.
Keywords: Quantum group, Lie algebra, Canonical basis, Tight monomials, Weyl
group, Piecewise-linear functions.Comment: 61 pages, 17 figures, uses picte
Limits of bifractional Brownian noises
Let be a bifractional Brownian motion with
two parameters and . The main result of this paper is
that the increment process generated by the bifractional Brownian motion
converges when to
, where is the
fractional Brownian motion with Hurst index . We also study the behavior of
the noise associated to the bifractional Brownian motion and limit theorems to
- …