10,382 research outputs found
Atomic data from the Iron Project.XLIV. Transition probabilities and line ratios for Fe VI with fluorescent excitation in planetary nebulae
Relativistic atomic structure calculations for electric dipole E1, electric
quadrupole E2 and magnetic dipole M1 transition probabilities among the first
80 fine-structure levels of Fe VI, dominated by configurations 3d^3, 3d^24s,
and 3d^24p, are carried out using the Breit-Pauli version of the code
Superstructure. Experimental energies are used to improve the accuracy of these
transition probabilities. Employing the 80-level collision-radiative (CR) model
with these dipole and forbidden transition probabilities, and Iron Project
R-matrix collisional data, we present a number of [Fe VI] line ratios
applicable to spectral diagnostics of photoionized H II regions. It is shown
that continuum fluorescent excitation needs to be considered in CR models in
order to interpret the observed line ratios of optical [Fe VI] lines in
planetary nebulae NGC 6741, IC 351, and NGC 7662. The analysis leads to
parametrization of line ratios as function of, and as constraints on, the
electron density and temperature, as well as the effective radiation
temperature of the central source and a geometrical dilution factor. The
spectral diagnostics may also help ascertain observational uncertainties. The
method may be generally applicable to other objects with intensive background
radiation fields, such as novae and active galactic nuclei. The extensive new
Iron Project radiative and collisional calculations enable a consistent
analysis of many line ratios for the complex iron ions.Comment: 25 pages, 8 figures, submitted to Astron.Astrophys. Suppl.Se
Martingale Problem under Nonlinear Expectations
We formulate and solve the martingale problem in a nonlinear expectation
space. Unlike the classical work of Stroock and Varadhan (1969) where the
linear operator in the associated PDE is naturally defined from the
corresponding diffusion process, the main difficulty in the nonlinear setting
is to identify an appropriate class of nonlinear operators for the associated
fully nonlinear PDEs.
Based on the analysis of the martingale problem, we introduce the notion of
weak solution for stochastic differential equations under nonlinear
expectations and obtain an existence theorem under the H\"older continuity
condition of the coefficients. The approach to establish the existence of weak
solutions generalizes the classical Girsanov transformation method in that it
no longer requires the two (probability) measures to be absolutely continuous.Comment: The new version simplifies some proofs for the main theorems and
generalizes some result
Nearly Optimal Stochastic Approximation for Online Principal Subspace Estimation
Processing streaming data as they arrive is often necessary for high
dimensional data analysis. In this paper, we analyse the convergence of a
subspace online PCA iteration, as a followup of the recent work of Li, Wang,
Liu, and Zhang [Math. Program., Ser. B, DOI 10.1007/s10107-017-1182-z] who
considered the case for the most significant principal component only, i.e., a
single vector. Under the sub-Gaussian assumption, we obtain a finite-sample
error bound that closely matches the minimax information lower bound of Vu and
Lei [Ann. Statist. 41:6 (2013), 2905-2947].Comment: 37 page
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