53,096 research outputs found
Multiple G-It\^{o} integral in the G-expectation space
In this paper, motivated by mathematic finance we introduce the multiple
G-It\^{o} integral in the G-expectation space, then investigate how to
calculate. We get the the relationship between Hermite polynomials and multiple
G-It\^{o} integrals which is a natural extension of the classical result
obtained by It\^{o} in 1951.Comment: 9 page
Strain Modulated Electronic Properties of Ge Nanowires - A First Principles Study
We used density-functional theory based first principles simulations to study
the effects of uniaxial strain and quantum confinement on the electronic
properties of germanium nanowires along the [110] direction, such as the energy
gap and the effective masses of the electron and hole. The diameters of the
nanowires being studied are up to 50 {\AA}. As shown in our calculations, the
Ge [110] nanowires possess a direct band gap, in contrast to the nature of an
indirect band gap in bulk. We discovered that the band gap and the effective
masses of charge carries can be modulated by applying uniaxial strain to the
nanowires. These strain modulations are size-dependent. For a smaller wire (~
12 {\AA}), the band gap is almost a linear function of strain; compressive
strain increases the gap while tensile strain reduces the gap. For a larger
wire (20 {\AA} - 50 {\AA}), the variation of the band gap with respect to
strain shows nearly parabolic behavior: compressive strain beyond -1% also
reduces the gap. In addition, our studies showed that strain affects effective
masses of the electron and hole very differently. The effective mass of the
hole increases with a tensile strain while the effective mass of the electron
increases with a compressive strain. Our results suggested both strain and size
can be used to tune the band structures of nanowires, which may help in design
of future nano-electronic devices. We also discussed our results by applying
the tight-binding model.Comment: 1 table, 8 figure
Ballistic transport at room temperature in micrometer size multigraphene
The intrinsic values of the carriers mobility and density of the graphene
layers inside graphite, the well known structure built on these layers in the
Bernal stacking configuration, are not well known mainly because most of the
research was done in rather bulk samples where lattice defects hide their
intrinsic values. By measuring the electrical resistance through
microfabricated constrictions in micrometer small graphite flakes of a few tens
of nanometers thickness we studied the ballistic behavior of the carriers. We
found that the carriers' mean free path is micrometer large with a mobility
cm/Vs and a carrier density cm per graphene layer at room temperature. These distinctive
transport and ballistic properties have important implications for
understanding the values obtained in single graphene and in graphite as well as
for implementing this last in nanoelectronic devices.Comment: 6 pages, 6 figure
Detection of Minimum-Ionizing Particles and Nuclear Counter Effect with Pure BGO and BSO Crystals with Photodiode Read-out
Long BGO (Bismuth Germanate) and BSO (Bismuth Silicate) crystals coupled with
silicon photodiodes have been used to detect minimum-ionizing particles(MIP).
With a low noise amplifier customized for this purpose, the crystals can detect
MIPs with an excellent signal-to-noise ratio. The NCE(Nuclear Counter Effect}
is also clearly observed and measured. Effect of full and partial wrapping of a
reflector around the crystal on light collection is also studied.Comment: 18 pages, including 5 figures; LaTeX and EP
Probing High Redshift Radiation Fields with Gamma-Ray Absorption
The next generation of gamma-ray telescopes may be able to observe gamma-ray
blazars at high redshift, possibly out to the epoch of reionization. The
spectrum of such sources should exhibit an absorption edge due to
pair-production against UV photons along the line of sight. One expects a sharp
drop in the number density of UV photons at the Lyman edge E_{L}. This implies
that the universe becomes transparent after gamma-ray photons redshift below E
(m_{e}c^2)^{2}/E_{L} 18 GeV. Thus, there is only a limited redshift interval
over which GeV photons can pair produce. This implies that any observed
absorption will probe radiation fields in the very early universe, regardless
of the subsequent star formation history of the universe. Furthermore,
measurements of differential absorption between blazars at different redshifts
can cleanly isolate the opacity due to UV emissivity at high redshift. An
observable absorption edge should be present for most reasonable radiation
fields with sufficient energy to reionize the universe. Ly-alpha photons may
provide an important component of the pair-production opacity. Observations of
a number of blazars at different redshifts will thus allow us to probe the rise
in comoving UV emissivity with time.Comment: ApJ accepted version, minor changes. 19 pages, 5 figure
Large-scale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications
In computer vision, many problems such as image segmentation, pixel
labelling, and scene parsing can be formulated as binary quadratic programs
(BQPs). For submodular problems, cuts based methods can be employed to
efficiently solve large-scale problems. However, general nonsubmodular problems
are significantly more challenging to solve. Finding a solution when the
problem is of large size to be of practical interest, however, typically
requires relaxation. Two standard relaxation methods are widely used for
solving general BQPs--spectral methods and semidefinite programming (SDP), each
with their own advantages and disadvantages. Spectral relaxation is simple and
easy to implement, but its bound is loose. Semidefinite relaxation has a
tighter bound, but its computational complexity is high, especially for large
scale problems. In this work, we present a new SDP formulation for BQPs, with
two desirable properties. First, it has a similar relaxation bound to
conventional SDP formulations. Second, compared with conventional SDP methods,
the new SDP formulation leads to a significantly more efficient and scalable
dual optimization approach, which has the same degree of complexity as spectral
methods. We then propose two solvers, namely, quasi-Newton and smoothing Newton
methods, for the dual problem. Both of them are significantly more efficiently
than standard interior-point methods. In practice, the smoothing Newton solver
is faster than the quasi-Newton solver for dense or medium-sized problems,
while the quasi-Newton solver is preferable for large sparse/structured
problems. Our experiments on a few computer vision applications including
clustering, image segmentation, co-segmentation and registration show the
potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern
Analysis and Machine Intelligenc
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