6,514 research outputs found
Numerical solution of Fredholm integral equation of the first kind
Numerical solution of first kind Fredholm integral equatio
An optimal statistical testing policy for software reliability demonstration of safety-critical systems
When software reliability demonstration of safety-critical systems by statistical testing is treated as a Test, Analyse and Fix (TAAF) process, an optimal testing policy can be found, which maximises the probability of success of the whole process, over a pre-determined period of time. The optimisation problem is formulated, solved by stochastic dynamic programming, and demonstrated by two numerical examples
The origin of the core-level binding energy shifts in nanoclusters
We investigate the shifts of the core-level binding energies in small gold
nanoclusters by using {\it ab initio} density functional theory calculations.
The shift of the 4 states is calculated for magic number nanoclusters in a
wide range of sizes and morphologies. We find a non-monotonous behavior of the
core-level shift in nanoclusters depending on the size. We demonstrate that
there are three main contributions to the Au 4 shifts, which depend
sensitively on the interatomic distances, coordination and quantum confinement.
They are identified and explained by the change of the on-site electrostatic
potential.Comment: 7 pages, 9 figure
Pinpointing the massive black hole in the Galactic Center with gravitationally lensed stars
A new statistical method for pinpointing the massive black hole (BH) in the
Galactic Center on the IR grid is presented and applied to astrometric IR
observations of stars close to the BH. This is of interest for measuring the IR
emission from the BH, in order to constrain accretion models; for solving the
orbits of stars near the BH, in order to measure the BH mass and to search for
general relativistic effects; and for detecting the fluctuations of the BH away
from the dynamical center of the stellar cluster, in order to study the stellar
potential. The BH lies on the line connecting the two images of any background
source it gravitationally lenses, and so the intersection of these lines fixes
its position. A combined search for a lensing signal and for the BH shows that
the most likely point of intersection coincides with the center of acceleration
of stars orbiting the BH. This statistical detection of lensing by the BH has a
random probability of ~0.01. It can be verified by deep IR stellar
spectroscopy, which will determine whether the most likely lensed image pair
candidates (listed here) have identical spectra.Comment: 4 pages, 2 figures, submitted to ApJ
Immunizing Conic Quadratic Optimization Problems Against Implementation Errors
We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchiās robust approach, and in the adjustable robust counterpart.Conic Quadratic Program;hidden convexity;implementation error;robust optimization;simultaneous diagonalizability;S-lemma
Exciton-polariton emission from organic semiconductor optical waveguides
We photo-excite slab polymer waveguides doped with J-aggregating dye
molecules and measure the leaky emission from strongly coupled waveguide
exciton polariton modes at room temperature. We show that the momentum of the
waveguide exciton polaritons can be controlled by modifying the thickness of
the excitonic waveguide. Non-resonantly pumped excitons in the slab excitonic
waveguide decay into transverse electric and transverse magnetic strongly
coupled exciton waveguide modes with radial symmetry. These leak to cones of
light with radial and azimuthal polarizations
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