The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions

Necessary and sufficient conditions are given for a maximum likelihood estimate of a subset of mixture proportions. From these conditions, likelihood equations are derived satisfied by the maximum-likelihood estimate and a successive-approximations procedure is discussed as suggested by equations for numerically evaluating the maximum-likelihood estimate. It is shown that, with probability one for large samples, this procedure converges locally to the maximum-likelihood estimate whenever a certain step-size lies between zero and two. Furthermore, optimal rates of local convergence are obtained for a step-size which is bounded below by a number between one and two

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

A general iterative procedure is given for determining the consistent maximum likelihood estimates of normal distributions. In addition, a local maximum of the log-likelihood function, Newtons's method, a method of scoring, and modifications of these procedures are discussed

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence

The relative abundance of neon and magnesium in the solar corona

A technique is proposed for specifically determining the relative solar coronal abundance of neon and magnesium. The relative abundance is calculated directly from the relative intensity of the resonance lines of Ne X (12.134A) and Mg XI (9.169A) without the need for the development of a detailed model of the thermal structure of the corona. Moderate resolution Bragg crystal spectrometer results from the OVI-10 satellite were used to determine a coronal neon to magnesium relative abundance of 1.47 + or - 0.38. The application of this technique to a recent higher resolution rocket observation gave an abundance ratio of approximately 0.93 + or - 0.15

Methodology of measuring internal contamination in spacecraft hardware Final report

Methodology of measuring internal contamination in spacecraft hardwar

Contribution to the extragalactic X-ray background from clusters of galaxies

The contribution to the extragalactic background from clusters of galaxies in the 2-6 keV band was computed. Two different cluster luminosity functions and two different models for cluster evolution were considered and a cluster X-ray luminosity-temperature relationship of the type L alpha T sup alpha +1/2 was assumed. It is found that the overall contribution of clusters to the background is approximately 10% of the total observed X-ray extragalactic approximately 150 eV is superimposed on the observed background. This result is quite insensitive to the different set of assumptions made in the calculation

Relative coronal abundances derived from X-ray observations 3: The effect of cascades on the relative intensity of Fe (XVII) line fluxes, and a revised iron abundance

Permitted lines in the optically thin coronal X-ray spectrum were analyzed to find the distribution of coronal material, as a function of temperature, without special assumptions concerning coronal conditions. The resonance lines of N, O, Ne, Na, Mg, Al, Si, S, and Ar which dominate the quiet coronal spectrum below 25A were observed. Coronal models were constructed and the relative abundances of these elements were determined. The intensity in the lines of the 2p-3d transitions near 15A was used in conjunction with these coronal models, with the assumption of coronal excitation, to determine the Fe XVII abundance. The relative intensities of the 2p-3d Fe XVII lines observed in the corona agreed with theoretical prediction. Using a more complete theoretical model, and higher resolution observations, a revised calculation of iron abundance relative to hydrogen of 0.000026 was made

X ray imaging microscope for cancer research

The NASA technology employed during the Stanford MSFC LLNL Rocket X Ray Spectroheliograph flight established that doubly reflecting, normal incidence multilayer optics can be designed, fabricated, and used for high resolution x ray imaging of the Sun. Technology developed as part of the MSFC X Ray Microscope program, showed that high quality, high resolution multilayer x ray imaging microscopes are feasible. Using technology developed at Stanford University and at the DOE Lawrence Livermore National Laboratory (LLNL), Troy W. Barbee, Jr. has fabricated multilayer coatings with near theoretical reflectivities and perfect bandpass matching for a new rocket borne solar observatory, the Multi-Spectral Solar Telescope Array (MSSTA). Advanced Flow Polishing has provided multilayer mirror substrates with sub-angstrom (rms) smoothnesss for the astronomical x ray telescopes and x ray microscopes. The combination of these important technological advancements has paved the way for the development of a Water Window Imaging X Ray Microscope for cancer research

An investigation of the structure and composition of the solar atmosphere using X-ray and EUV spectra obtained with the OV1-17 and OSO-4 and OSO-5 satellites

Studies of the structure and composition of the solar corona were undertaken, using a number of satellite observations of the coronal X-ray spectrum. A systematic technique was developed to carry out the required analysis, and the analytical techniques available to calculate the coronal spectrum have been developed and improved. A review of other analyses of solar coronal structure is also included

The ultra high resolution XUV spectroheliograph: An attached payload for the Space Station Freedom

The principle goal of the ultra high resolution XUV spectroheliograph (UHRXS) is to improve the ability to identify and understand the fundamental physical processes that shape the structure and dynamics of the solar chromosphere and corona. The ability of the UHRXS imaging telescope and spectrographs to resolve fine scale structures over a broad wavelength (and hence temperature) range is critical to this mission. The scientific objectives and instrumental capabilities of the UHRXS investigation are reviewed before proceeding to a discussion of the expected performance of the UHRXS observatory