28,745 research outputs found
A Functional Approach to FBSDEs and Its Application in Optimal Portfolios
In Liang et al (2009), the current authors demonstrated that BSDEs can be
reformulated as functional differential equations, and as an application, they
solved BSDEs on general filtered probability spaces. In this paper the authors
continue the study of functional differential equations and demonstrate how
such approach can be used to solve FBSDEs. By this approach the equations can
be solved in one direction altogether rather than in a forward and backward
way. The solutions of FBSDEs are then employed to construct the weak solutions
to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a
nonlinear version of Girsanov's transformation. As the solving procedure is
constructive, the authors not only obtain the existence and uniqueness theorem,
but also really work out the solutions to such class of BSDE systems with
quadratic growth. Finally an optimal portfolio problem in incomplete markets is
solved based on the functional differential equation approach and the nonlinear
Girsanov's transformation.Comment: 26 page
The Luminosity - E_p Relation within Gamma--Ray Bursts and Implications for Fireball Models
Using a sample of 2408 time-resolved spectra for 91 BATSE gamma-ray bursts
(GRBs) presented by Preece et al., we show that the relation between the
isotropic-equivalent luminosity (L_iso) and the spectral peak energy (E_p) in
the cosmological rest frame, L_iso \propto E_p^2, not only holds within these
bursts, but also holds among these GRBs, assuming that the burst rate as a
function of redshift is proportional to the star formation rate. The possible
implications of this relation for the emission models of GRBs are discussed. We
suggest that both the kinetic-energy-dominated internal shock model and the
magnetic-dissipation-dominated external shock model can well interpret this
relation. We constrain the parameters for these two models, and find that they
are in a good agreement with the parameters from the fittings to the afterglow
data (abridged).Comment: 3 pages plus 5 figures, emulateapj style, accepted for publication in
ApJ Letter
Constraining and Dark Energy with Gamma-Ray Bursts
An relationship with a small
scatter for current -ray burst (GRB) data was recently reported, where
is the beaming-corrected -ray energy and
is the peak energy in the local observer frame. By considering this
relationship for a sample of 12 GRBs with known redshift, peak energy, and
break time of afterglow light curves, we constrain the mass density of the
universe and the nature of dark energy. We find that the mass density
(at the confident level) for a flat
universe with a cosmological constant, and the parameter of an assumed
static dark-energy equation of state ().
Our results are consistent with those from type Ia supernovae. A larger sample
established by the upcoming {\em Swift} satellite is expected to provide
further constraints.Comment: 8 pages including 4 figures, to appear in ApJ Letters, typos
correcte
The Peak Energy Distribution of the nu F_nu Spectra and the Implications for the Jet Structure Models of Gamma-Ray Bursts
We study the peak energy () distribution of the
spectra of gamma-ray bursts (GRBs) and X-ray flashes (XRFs) with a sample of 57
bursts observed by {\em High Energy Transient Explorer 2} ({\em HETE-2}) French
Gamma Telescope and discuss its implications for the jet structure models.
Combining the observed distribution of {\em HETE--2} GRBs/XRFs
with that of BATSE GRBs, we find that the observed distribution of
GRBs/XRFs is a bimodal one with peaks of keV and
keV. According to the recently-discovered equivalent-isotropic
energy- relationship, such a bimodal distribution implies a
two-component structure of GRB/XRF jets. A simple simulation analysis shows
that this structured jet model does roughly reproduce a bimodal distribution
with peaks of and keV. We argue that future observations
of the peak of keV in the distribution would be evidence
supporting this model. {\em Swift}, which covers an energy band of 0.2--150
keV, is expected to provide a key test for our results.Comment: 4 pages plus 2 figures, emulateapj style, ApJ Letters, 608, in pres
Linear scaling calculation of maximally-localized Wannier functions with atomic basis set
We have developed a linear scaling algorithm for calculating
maximally-localized Wannier functions (MLWFs) using atomic orbital basis. An
O(N) ground state calculation is carried out to get the density matrix (DM).
Through a projection of the DM onto atomic orbitals and a subsequent O(N)
orthogonalization, we obtain initial orthogonal localized orbitals. These
orbitals can be maximally localized in linear scaling by simple Jacobi sweeps.
Our O(N) method is validated by applying it to water molecule and wurtzite ZnO.
The linear scaling behavior of the new method is demonstrated by computing the
MLWFs of boron nitride nanotubes.Comment: J. Chem. Phys. in press (2006
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