28,700 research outputs found
Dispersive estimates for four dimensional Schr\"{o}dinger and wave equations with obstructions at zero energy
We investigate dispersive
estimates for the Schr\"odinger operator when there are
obstructions, a resonance or an eigenvalue, at zero energy. In particular, we
show that if there is a resonance or an eigenvalue at zero energy then there is
a time dependent, finite rank operator satisfying for such that
We also show that the operator if there is an eigenvalue but no
resonance at zero energy. We then develop analogous dispersive estimates for
the solution operator to the four dimensional wave equation with potential.Comment: 32 page
Attenuation of the Ganglion Cell Layer in a Premature Infant Revealed with Handheld Spectral Domain Optical Coherence Tomography
Purpose: To report on subclinical retinal abnormalities shown through handheld spectral domain optical coherence tomography on a premature infant.
Methods: Case report.
Results: The initial and follow-up exams on a premature infant revealed severely attenuated ganglion cell and nerve fiber layers. There was cystoid macular edema in both eyes at the initial visits, which resolved by the 1-year follow-up.
Discussion: Optical coherence tomography can reveal significant retinal abnormalities in premature infants which are not detectable through funduscopic exam. Documenting such findings may be useful for the comprehensive management of vision problems in children with a history of premature birth
L^p boundedness of the wave operator for the one dimensional Schroedinger operator
Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we
consider the associated wave operators W_+, W_- defined as the strong L^2
limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the
wave operators are bounded operators on L^p for all 1<p<\infty, provided
(1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a
resonance. For p=\infty we obtain an estimate in terms of the Hilbert
transform. Some applications to dispersive estimates for equations with
variable rough coefficients are given.Comment: 26 page
Recommended from our members
Upgrade to the SHARP EUV mask microscope
The Sharp High-NA Actinic Reticle review Project (SHARP) is a synchrotron-based, extreme ultraviolet (EUV) microscope dedicated to photomask research. A potential upgrade to the SHARP microscope is presented. The upgrade includes changing the light path in the instrument from its current off-Axis configuration to an on-Axis configuration. This change allows for an increased working distance of 2.5 mm or more. A central obscuration, added to the zoneplate aperture, blocks stray light from reaching the central part of the image, thus improving the image contrast. The imaging performance of the two configurations is evaluated by means of ray tracing
On the boundedness of wave operators for two-dimensional Schr\"odinger operators with threshold obstructions
Let be a Schr\"odinger operator on with
real-valued potential , and let . If has sufficient
pointwise decay, the wave operators are known to be bounded on for all if zero is not an eigenvalue or resonance. We show that if there is an
s-wave resonance or an eigenvalue only at zero, then the wave operators are
bounded on for . This result stands in
contrast to results in higher dimensions, where the presence of zero energy
obstructions is known to shrink the range of valid exponents .Comment: Revised according to referee's comments. 22 pages, to appear in J.
Funct. Ana
Lunar contour mapping system /lucom/ final report, 5 aug. 1964 - 18 mar. 1965
Radar sensor system for acquisition of lunar surface data - Lunar contour mapping syste
Anisotropic Hubble expansion of large scale structures
We investigate the dynamics of an homogenous distribution of galaxies moving
under the cosmological expansion through Euler-Poisson equations system. The
solutions are interpreted with the aim of understanding the cosmic velocity
fields in the Local Super Cluster, and in particular the presence of a bulk
flow. Among several solutions, we shows a planar kinematics with constant
(eternal) and rotational distortion, the velocity field is not potential
Microlensing and the Search for Extraterrestrial Life
Are microlensing searches likely to discover planets that harbor life? Given
our present state of knowledge, this is a difficult question to answer. We
therefore begin by asking a more narrowly focused question: are conditions on
planets discovered via microlensing likely to be similar to those we experience
on Earth? In this paper I link the microlensing observations to the well-known
"Goldilocks Problem" (conditions on the Earth-like planets need to be "just
right"), to find that Earth-like planets discovered via microlensing are likely
to be orbiting stars more luminous than the sun. This means that light from the
planetary system's central star may contribute a significant fraction of the
baseline flux relative to the star that is lensed. Such blending of light from
the lens with light from the lensed source can, in principle, limit our ability
to detect these events. This turns out not to be a significant problem,
however. A second consequence of blending is the opportunity to determine the
spectral type of the lensed spectral type of the lensed star. This
circumstance, plus the possibility that finite-source-size effects are
important, implies that some meaningful follow-up observations are likely to be
possible for a subset Earth-like planets discovered via microlensing. In
addition, calculations indicate that reasonable requirements on the planet's
density and surface gravity imply that the mass of Earth-like planets is likely
to be within a factor of of an Earth mass.Comment: 15 pages, 2 figures. To be published in the Astrophysical Journa
General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry
The Hamiltonian formulation of general relativity on a null surface is
established in the teleparallel geometry. No particular gauge conditons on the
tetrads are imposed, such as the time gauge condition. By means of a 3+1
decomposition the resulting Hamiltonian arises as a completely constrained
system. However, it is structurally different from the the standard
Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the
basic field quantities are tetrads that transform under the global SO(3,1) and
the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra
Cosmology from String Theory
We explore the cosmological content of Salam-Sezgin six dimensional
supergravity, and find a solution to the field equations in qualitative
agreement with observation of distant supernovae, primordial nucleosynthesis
abundances, and recent measurements of the cosmic microwave background. The
carrier of the acceleration in the present de Sitter epoch is a quintessence
field slowly rolling down its exponential potential. Intrinsic to this model is
a second modulus which is automatically stabilized and acts as a source of cold
dark matter with a mass proportional to an exponential function of the
quintessence field (hence realizing VAMP models within a String context).
However, any attempt to saturate the present cold dark matter component in this
manner leads to unacceptable deviations from cosmological data -- a numerical
study reveals that this source can account for up to about 7% of the total cold
dark matter budget. We also show that (1) the model will support a de Sitter
energy in agreement with observation at the expense of a miniscule breaking of
supersymmetry in the compact space; (2) variations in the fine structure
constant are controlled by the stabilized modulus and are negligible; (3)
``fifth''forces are carried by the stabilized modulus and are short range; (4)
the long time behavior of the model in four dimensions is that of a
Robertson-Walker universe with a constant expansion rate (w = -1/3). Finally,
we present a String theory background by lifting our six dimensional
cosmological solution to ten dimensions.Comment: Version to be published in Physical Review
- …