10,296 research outputs found
Hand-printed input for on-line systems
Recognition program for handwritten information in real time computer operatio
Berezinians, Exterior Powers and Recurrent Sequences
We study power expansions of the characteristic function of a linear operator
in a -dimensional superspace . We show that traces of exterior
powers of satisfy universal recurrence relations of period .
`Underlying' recurrence relations hold in the Grothendieck ring of
representations of \GL(V). They are expressed by vanishing of certain Hankel
determinants of order in this ring, which generalizes the vanishing of
sufficiently high exterior powers of an ordinary vector space. In particular,
this allows to explicitly express the Berezinian of an operator as a rational
function of traces. We analyze the Cayley--Hamilton identity in a superspace.
Using the geometric meaning of the Berezinian we also give a simple formulation
of the analog of Cramer's rule.Comment: 35 pages. LaTeX 2e. New version: paper substantially reworked and
expanded, new results include
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Development Of Third Harmonic Generation As A Short Pulse Probe Of Shock Heated Material
We are studying high-pressure laser produced shock waves in silicon (100). To examine the material dynamics, we are performing pump-probe style experiments utilizing 600 ps and 40 fs laser pulses from a Ti:sapphire laser. Two-dimensional interferometry reveals information about the shock breakout, while third harmonic light generated at the rear surface is used to infer the crystalline state of the material as a function of time. Sustained third harmonic generation (THG) during a similar to 100 kbar shock breakout indicate that the rear surface remains crystalline for at least 3 ns. However, a decrease in THG during a similar to 300 kbar shock breakout suggests a different behavior, which could include a change in crystalline structure.Mechanical Engineerin
Orthosymplectically invariant functions in superspace
The notion of spherically symmetric superfunctions as functions invariant
under the orthosymplectic group is introduced. This leads to dimensional
reduction theorems for differentiation and integration in superspace. These
spherically symmetric functions can be used to solve orthosymplectically
invariant Schroedinger equations in superspace, such as the (an)harmonic
oscillator or the Kepler problem. Finally the obtained machinery is used to
prove the Funk-Hecke theorem and Bochner's relations in superspace.Comment: J. Math. Phy
Quantum rainbow scattering at tunable velocities
Elastic scattering cross sections are measured for lithium atoms colliding
with rare gas atoms and SF6 molecules at tunable relative velocities down to
~50 m/s. Our scattering apparatus combines a velocity-tunable molecular beam
with a magneto-optic trap that provides an ultracold cloud of lithium atoms as
a scattering target. Comparison with theory reveals the quantum nature of the
collision dynamics in the studied regime, including both rainbows as well as
orbiting resonances
Infusion of Non-HLA Matched, Off-the-Shelf Ex Vivo Expanded Cord Blood Progenitor Cells in Patients Undergoing Myeloablative Cord Blood Transplantation Is Safe and Decreases the Time to Neutrophil Recovery
Spherically symmetric space-time with the regular de Sitter center
The requirements are formulated which lead to the existence of the class of
globally regular solutions to the minimally coupled GR equations which are
asymptotically de Sitter at the center. The brief review of the resulting
geometry is presented. The source term, invariant under radial boots, is
classified as spherically symmetric vacuum with variable density and pressure,
associated with an r-dependent cosmological term, whose asymptotic in the
origin, dictated by the weak energy condition, is the Einstein cosmological
term. For this class of metrics the ADM mass is related to both de Sitter
vacuum trapped in the origin and to breaking of space-time symmetry. In the
case of the flat asymptotic, space-time symmetry changes smoothly from the de
Sitter group at the center to the Lorentz group at infinity. Dependently on
mass, de Sitter-Schwarzschild geometry describes a vacuum nonsingular black
hole, or G-lump - a vacuum selfgravitating particlelike structure without
horizons. In the case of de Sitter asymptotic at infinity, geometry is
asymptotically de Sitter at both origin and infinity and describes, dependently
on parameters and choice of coordinates, a vacuum nonsingular cosmological
black hole, selfgravitating particlelike structure at the de Sitter background
and regular cosmological models with smoothly evolving vacuum energy density.Comment: Latex, 10 figures, extended version of the plenary talk at V
Friedmann Intern. Conf. on Gravitation and Cosmology, Brazil 2002, to appear
in Int.J.Mod.Phys.
Splines and Wavelets on Geophysically Relevant Manifolds
Analysis on the unit sphere found many applications in
seismology, weather prediction, astrophysics, signal analysis, crystallography,
computer vision, computerized tomography, neuroscience, and statistics.
In the last two decades, the importance of these and other applications
triggered the development of various tools such as splines and wavelet bases
suitable for the unit spheres , and the
rotation group . Present paper is a summary of some of results of the
author and his collaborators on generalized (average) variational splines and
localized frames (wavelets) on compact Riemannian manifolds. The results are
illustrated by applications to Radon-type transforms on and
.Comment: The final publication is available at http://www.springerlink.co
On the reduction of the multidimensional Schroedinger equation to a first order equation and its relation to the pseudoanalytic function theory
Given a particular solution of a one-dimensional stationary Schroedinger
equation (SE) this equation of second order can be reduced to a first order
linear differential equation. This is done with the aid of an auxiliary Riccati
equation. We show that a similar fact is true in a multidimensional situation
also. We consider the case of two or three independent variables. One
particular solution of (SE) allows us to reduce this second order equation to a
linear first order quaternionic differential equation. As in one-dimensional
case this is done with the aid of an auxiliary Riccati equation. The resulting
first order quaternionic equation is equivalent to the static Maxwell system.
In the case of two independent variables it is the Vekua equation from theory
of generalized analytic functions. We show that even in this case it is
necessary to consider not complex valued functions only, solutions of the Vekua
equation but complete quaternionic functions. Then the first order quaternionic
equation represents two separate Vekua equations, one of which gives us
solutions of (SE) and the other can be considered as an auxiliary equation of a
simpler structure. For the auxiliary equation we always have the corresponding
Bers generating pair, the base of the Bers theory of pseudoanalytic functions,
and what is very important, the Bers derivatives of solutions of the auxiliary
equation give us solutions of the main Vekua equation and as a consequence of
(SE). We obtain an analogue of the Cauchy integral theorem for solutions of
(SE). For an ample class of potentials (which includes for instance all radial
potentials), this new approach gives us a simple procedure allowing to obtain
an infinite sequence of solutions of (SE) from one known particular solution
Shapes and Shears, Stars and Smears: Optimal Measurements for Weak Lensing
We present the theoretical and analytical bases of optimal techniques to
measure weak gravitational shear from images of galaxies. We first characterize
the geometric space of shears and ellipticity, then use this geometric
interpretation to analyse images. The steps of this analysis include:
measurement of object shapes on images, combining measurements of a given
galaxy on different images, estimating the underlying shear from an ensemble of
galaxy shapes, and compensating for the systematic effects of image distortion,
bias from PSF asymmetries, and `"dilution" of the signal by the seeing. These
methods minimize the ellipticity measurement noise, provide calculable shear
uncertainty estimates, and allow removal of systematic contamination by PSF
effects to arbitrary precision. Galaxy images and PSFs are decomposed into a
family of orthogonal 2d Gaussian-based functions, making the PSF correction and
shape measurement relatively straightforward and computationally efficient. We
also discuss sources of noise-induced bias in weak lensing measurements and
provide a solution for these and previously identified biases.Comment: Version accepted to AJ. Minor fixes, plus a simpler method of shape
weighting. Version with full vector figures available via
http://www.astro.lsa.umich.edu/users/garyb/PUBLICATIONS
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