9,458 research outputs found
Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes
A derivation operator and a divergence operator are defined on the algebra of
bounded operators on the symmetric Fock space over the complexification of a
real Hilbert space \eufrak{h} and it is shown that they satisfy similar
properties as the derivation and divergence operator on the Wiener space over
\eufrak{h}. The derivation operator is then used to give sufficient
conditions for the existence of smooth Wigner densities for pairs of operators
satisfying the canonical commutation relations. For
\eufrak{h}=L^2(\mathbb{R}_+), the divergence operator is shown to coincide
with the Hudson-Parthasarathy quantum stochastic integral for adapted
integrable processes and with the non-causal quantum stochastic integrals
defined by Lindsay and Belavkin for integrable processes.Comment: 28 pages, amsart styl
Quicksort with unreliable comparisons: a probabilistic analysis
We provide a probabilistic analysis of the output of Quicksort when
comparisons can err.Comment: 29 pages, 3 figure
Performance Comparison of Hyperspectral Target Detection Algorithms in Altitude Varying Scenes
Many different hyperspectral target detection algorithms have been developed and tested under various assumptions, methods, and data sets. This work examines the spectral angle mapper (SAM), adaptive coherence estimator (ACE), and constrained energy maximization (CEM) algorithms. Algorithm performance is examined over multiple images, targets, and backgrounds. Methods to examine algorithm performance are plentiful and several different metrics are used here. Quantitative metrics are used to make direct comparisons between algorithms. Further analysis using visual performance metrics is made to examine interesting trends in the data. Results show an increase in detection algorithm performance as image altitude increases and spatial information decreases. Theories to explain this phenomenon are introduced
Absence of a consistent classical equation of motion for a mass-renormalized point charge
The restrictions of analyticity, relativistic (Born) rigidity, and negligible
O(a) terms involved in the evaluation of the self electromagnetic force on an
extended charged sphere of radius "a" are explicitly revealed and taken into
account in order to obtain a classical equation of motion of the extended
charge that is both causal and conserves momentum-energy. Because the
power-series expansion used in the evaluation of the self force becomes invalid
during transition time intervals immediately following the application and
termination of an otherwise analytic externally applied force, transition
forces must be included during these transition time intervals to remove the
noncausal pre-acceleration and pre-deceleration from the solutions to the
equation of motion without the transition forces. For the extended charged
sphere, the transition forces can be chosen to maintain conservation of
momentum-energy in the causal solutions to the equation of motion within the
restrictions of relativistic rigidity and negligible O(a) terms under which the
equation of motion is derived. However, it is shown that renormalization of the
electrostatic mass to a finite value as the radius of the charge approaches
zero introduces a violation of momentum-energy conservation into the causal
solutions to the equation of motion of the point charge if the magnitude of the
external force becomes too large. That is, the causal classical equation of
motion of a point charge with renormalized mass experiences a high acceleration
catastrophe.Comment: 13 pages, No figure
Self-forces on extended bodies in electrodynamics
In this paper, we study the bulk motion of a classical extended charge in
flat spacetime. A formalism developed by W. G. Dixon is used to determine how
the details of such a particle's internal structure influence its equations of
motion. We place essentially no restrictions (other than boundedness) on the
shape of the charge, and allow for inhomogeneity, internal currents,
elasticity, and spin. Even if the angular momentum remains small, many such
systems are found to be affected by large self-interaction effects beyond the
standard Lorentz-Dirac force. These are particularly significant if the
particle's charge density fails to be much greater than its 3-current density
(or vice versa) in the center-of-mass frame. Additional terms also arise in the
equations of motion if the dipole moment is too large, and when the
`center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly
speaking). These conditions are often quite restrictive. General equations of
motion were also derived under the assumption that the particle can only
interact with the radiative component of its self-field. These are much simpler
than the equations derived using the full retarded self-field; as are the
conditions required to recover the Lorentz-Dirac equation.Comment: 30 pages; significantly improved presentation; accepted for
publication in Phys. Rev.
A Combinatorial Interpretation of Lommel Polynomials and Their Derivatives
In this paper we present interpretations of Lommel polynomials and their derivatives. A combinatorial interpretation uses matchings in graphs. This gives an interpretation for the derivatives as well. Then Lommel polynomials are considered from the point of view of operator calculus. A step-3 nilpotent Lie algebra and finite-difference operators arise in the analysis
Incorporation of Polarization Into the DIRSIG Synthetic Image Generation Model
The Digital Imaging and Remote Sensing Synthetic Image Generation (DIRSIG) model uses a quantitative first principles approach to generate synthetic hyperspectral imagery. This paper presents the methods used to add modeling of polarization phenomenology. The radiative transfer equations were modified to use Stokes vectors for the radiance values and Mueller matrices for the energy-matter interactions. The use of Stokes vectors enables a full polarimetric characterization of the illumination and sensor reaching radiances. The bi-directional reflectance distribution function (BRDF) module was rewritten and modularized to accommodate a variety of polarized and unpolarized BRDF models. Two new BRDF models based on Torrance- Sparrow and Beard-Maxwell were added to provide polarized BRDF estimations. The sensor polarization characteristics are modeled using Mueller matrix transformations on a per pixel basis. All polarized radiative transfer calculations are performed spectrally to preserve the hyperspectral capabilities of DIRSIG. Integration over sensor bandpasses is handled by the sensor module
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