803 research outputs found
Inverse spectral problems for Dirac operators with summable matrix-valued potentials
We consider the direct and inverse spectral problems for Dirac operators on
with matrix-valued potentials whose entries belong to ,
. We give a complete description of the spectral data
(eigenvalues and suitably introduced norming matrices) for the operators under
consideration and suggest a method for reconstructing the potential from the
corresponding spectral data.Comment: 32 page
Analyticity and uniform stability in the inverse spectral problem for Dirac operators
We prove that the inverse spectral mapping reconstructing the square
integrable potentials on [0,1] of Dirac operators in the AKNS form from their
spectral data (two spectra or one spectrum and the corresponding norming
constants) is analytic and uniformly stable in a certain sense.Comment: 19 page
Non-characteristic Half-lives in Radioactive Decay
Half-lives of radionuclides span more than 50 orders of magnitude. We
characterize the probability distribution of this broad-range data set at the
same time that explore a method for fitting power-laws and testing
goodness-of-fit. It is found that the procedure proposed recently by Clauset et
al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the
power-law hypothesis even for power-law synthetic data. In contrast, we
establish the existence of a power-law exponent with a value around 1.1 for the
half-life density, which can be explained by the sharp relationship between
decay rate and released energy, for different disintegration types. For the
case of alpha emission, this relationship constitutes an original mechanism of
power-law generation
Boundary relations and generalized resolvents of symmetric operators
The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint
exit space extensions of a, not necessarily densely defined, symmetric
operator, in terms of maximal dissipative (in \dC_+) holomorphic linear
relations on the parameter space (the so-called Nevanlinna families). The new
notion of a boundary relation makes it possible to interpret these parameter
families as Weyl families of boundary relations and to establish a simple
coupling method to construct the generalized resolvents from the given
parameter family. The general version of the coupling method is introduced and
the role of boundary relations and their Weyl families for the
Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page
Jets Produced in π^-, π^+, and Proton Interactions at 200 GeV on Hydrogen and Aluminum Targets
This paper presents results from an experiment on the production of jets (groups of particles) with high p_⊥ produced in 200-GeV/c interactions. Results are presented on the comparison of jet cross sections on aluminum and hydrogen targets. The jet fragmentation distributions are also examined. Both the cross section and the jet structure are found to depend strongly on the beam and target types
Measurement of Forward Jets Produced in High-Transverse-Momentum Hadron-Proton Collisions
A measurement of charged-particle production is reported for the forward region in events triggered by high-transverse-momentum (p⊥) jets and single particles. The momentum distributions of forward-going particles are observed to scale in a simple p⊥-dependent longitudinal variable. Forward-going (beam) jets are observed to be tilted away from the original direction by an amount which agrees with muon-pair data when interpreted in a parton (quantum-chromodynamics) model
Observation of the Production of Jets of Particles at High Transverse Momentum and Comparison with Inclusive Single-Particle Reactions
Data are presented on production by 200-GeV/c hadrons incident on beryllium of both single particles and jets (groups of particles) with high p_T (transverse momentum). The experiment was performed in a wide-aperture multiparticle spectrometer at Fermilab. The jet and single-particle cross sections have a similar shape from p_T=3 to 5 GeV/c but the jet cross section is over two orders of magnitude larger. The distributions of charged-particle momenta show striking similarities to those observed in lepton-induced processes
Experimental Tests of Quantum Chromodynamics in High-p_⊥ Jet Production in 200-GeV/c Hadron-Proton Collisions
Data on inclusive jet production in the transverse-momentum (p_⊥) range 0-8 GeV/c for 200-GeV/c p, π^-, π^+, K^-, K^+, and p incident on a hydrogen target are presented. The jet cross section is fully corrected for losses and biases, and compared with the predictions of a model based on quantum chromodynamics. Both the absolute cross section and the inclusive charged-particle distributions inside and outside the jet are in qualitative agreement with the model
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