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NASA NTRS1984

'Microquasars' and the X-ray background

The recent discovery of small active nuclei (via emission lines) in normal spiral galaxies greatly expands the range of the quasar phenomenon. By using the relationship between Lx and L(H-alpha) found in more luminous Seyfert galaxies and assuming that it holds for smaller active nuclei, a bivariate X-ray luminosity function can be calculated. This luminosity function fits naturally onto the higher luminosity X-ray luminosity function derived from the HEAO-1/A2 survey. The contribution to the X-ray background from small active nuclei hiding in large spiral galaxies is greater than 15 percent.

Elvis, M.↗

NASA NTRS1984

Development of dynamic simulation of TF34-GE-100 turbofan engine with post-stall capability

This paper describes the development of a hybrid computer simulation of a TF34-GE-100 turbofan engine with post-stall capability. The simulation operates in real-time and will be used to test and evaluate stall recovery control modes for this engine. The simulation calculations are performed by an analog computer with a peripheral multivariable function generation unit used for computing bivariate functions. Tabular listings of simulation variables are obtained by interfacing to a digital computer and using a custom software package for data collection and display.

Krosel, S. M.↗

NASA NTRS1983

Atmospheric attenuation for correlated satellite communication ground sites

Link margin estimates are calculated for 30/20 GHz satellite communication systems employing closely-spaced (4 to 100 km) 'dual diversity' switched ground sites. The link margin estimates are based on a new analysis in which the bivariate rain attenuation density function for two correlated ground sites is modelled by an exponential density function. The results of the exponential density function analysis enable derivation of a direct relation between rain margin estimates and probability of exceedance (link availability). Margins typically in the range 2 to 12 dB are calculated for various ground site separations and summarized for seven city locations and five satellite orbit positions over the U.S. The results can be easily extended to other EHF satellite frequencies and other locations.

Christopher, P.↗

NASA NTRS1984

Floating-point function generation routines for 16-bit microcomputers

Several computer subroutines have been developed that interpolate three types of nonanalytic functions: univariate, bivariate, and map. The routines use data in floating-point form. However, because they are written for use on a 16-bit Intel 8086 system with an 8087 mathematical coprocessor, they execute as fast as routines using data in scaled integer form. Although all of the routines are written in assembly language, they have been implemented in a modular fashion so as to facilitate their use with high-level languages.

Mackin, M. A.↗

NASA NTRS1984

Multivariate spline methods in surface fitting

The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.

Guseman, L. F., Jr.↗

NASA NTRS1985

An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures.

Derose, T. D.↗

NASA NTRS1986

The analysis of ensembles of moderately saturated interstellar lines

It is shown that the combined equivalent widths for a large population of Gaussian-like interstellar line components, each with different central optical depths tau(0) and velocity dispersions b, exhibit a curve of growth (COG) which closely mimics that of a single, pure Gaussian distribution in velocity. Two parametric distributions functions for the line populations are considered: a bivariate Gaussian for tau(0) and b and a power law distribution for tau(0) combined with a Gaussian dispersion for b. First, COGs for populations having an extremely large number of nonoverlapping components are derived, and the implications are shown by focusing on the doublet-ratio analysis for a pair of lines whose f-values differ by a factor of two. The consequences of having, instead of an almost infinite number of lines, a relatively small collection of components added together for each member of a doublet are examined. The theory of how the equivalent widths grow for populations of overlapping Gaussian profiles is developed. Examples of the composite COG analysis applied to existing collections of high-resolution interstellar line data are presented.

Jenkins, E. B.↗

NASA NTRS1986

X-ray properties of optically selected QSOs

The dependence of the X-ray-to-optical luminosity ratio on optical luminosity and redshift for optically selected QSOs is studied, largely on the basis of two, complete, magnitude-limited samples (Bright Quasar Survey /1983/ and Braccesi Faint /1984/) which were observed with the Einstein Observatory. Heterogeneous samples are established as adequate for the study of that dependence. Optimal choices for increasing the size of the data set for such a study are pointed out. The previous results of Avni and Tananbaum for alpha sub 0, x(z, L sub opt) are confirmed and strengthened, and the numerical sensitivity to changes in the values of q sub 0 and of the optical spectral index is evaluated. It is shown that the large majority, probably all, of optically selected QSOs are X-ray loud; no more than a few percent can be X-ray quiet. Thus X-ray emission appears to be a universal property of QSOs. It is shown that comparisons of optically selected QSOs with X-ray selected QSOs are numerically sensitive to the details of the input ingredients. A residual discrepancy of about a factor of 2 between calculated and observed X-ray number counts is found. Directions for further research that are important for understanding the full bivariate optical-X-ray evolution and luminosity function for QSOs are discussed.

Avni, Y.↗

NASA NTRS1986

Statistical methods for astronomical data with upper limits. II - Correlation and regression

Statistical methods for calculating correlations and regressions in bivariate censored data where the dependent variable can have upper or lower limits are presented. Cox's regression and the generalization of Kendall's rank correlation coefficient provide significant levels of correlations, and the EM algorithm, under the assumption of normally distributed errors, and its nonparametric analog using the Kaplan-Meier estimator, give estimates for the slope of a regression line. Monte Carlo simulations demonstrate that survival analysis is reliable in determining correlations between luminosities at different bands. Survival analysis is applied to CO emission in infrared galaxies, X-ray emission in radio galaxies, H-alpha emission in cooling cluster cores, and radio emission in Seyfert galaxies.

Isobe, T.↗

NASA NTRS1987

Global petrologic variations of the Moon: A ternary-diagram approach

A ternary-diagram approach is used to show on a single map as much detailed geochemical information concerning petrologic variations within the lunar crust as is possible. The classification map shows the global spatial distributions of end-member compositions, the transitional spatial relations between end-member compositions, and quantitative estimates of relative proportions of each end member at each pixel location within the orbital groundtracks. The use of elemental ratios in this analysis, instead of the commonly used elemental bivariate diagrams, shows geologic information that is otherwise hidden in individual elemental databases.

Davis, Philip A.↗

NASA NTRS1986

Information extraction from multivariate images

An overview of several multivariate image processing techniques is presented, with emphasis on techniques based upon the principal component transformation (PCT). Multiimages in various formats have a multivariate pixel value, associated with each pixel location, which has been scaled and quantized into a gray level vector, and the bivariate of the extent to which two images are correlated. The PCT of a multiimage decorrelates the multiimage to reduce its dimensionality and reveal its intercomponent dependencies if some off-diagonal elements are not small, and for the purposes of display the principal component images must be postprocessed into multiimage format. The principal component analysis of a multiimage is a statistical analysis based upon the PCT whose primary application is to determine the intrinsic component dimensionality of the multiimage. Computational considerations are also discussed.

Park, S. K.↗

NASA NTRS1988

Ascent structural wind loads for the National Space Transportation System (NSTS)

An aerospace vehicle must withstand the design ascent structural load or be within any flight constraint to safely reach orbit. For the NSTS an assessment for flight readiness is made for each mission. This assessment for ascent loads and performance parameters is stated in terms of launch probability derived from samples of Jimsphere wind profiles. For the day of launch operations an allowance is made for the ascent load variability due to the wind profile variability over a 3.5-hour period. This is the current time period required to obtain a Jimsphere measurement and perform a complete load simulation prior to launch time. The load variability is derived from a sample of 3.5-hour Jimsphere wind profile pairs. It is applied as a conditional percentile value given the wind load at 3.5 hours prior to launch time. Probability models are used for these analyses. Application of the univariate, bivariate and conditional forms of the extreme value (Gumbel) probability distribution to the analysis of extreme wind speeds, wind shears and vehicle loads is described.

Smith, O. E.↗

NASA NTRS1988

Winds aloft statistical analysis in support of day of launch Shuttle systems evaluation

In connection with the development of the Meteorological Interactive Data Display System (MIDDS) for utilization by the Launch Systems Evaluation Advisory Team (LSEAT), requirements have been established to expand the pre-launch analysis of winds aloft for the Space Shuttle. Statistical analyses developed for the system include: comparison of pre-launch wind component profiles to wind component extremes at each altitude calculated from launch site historical data; conditional probability ellipses for wind vectors at a future time given the wind vector at an initial time; comparison of observed extreme wind shear and associated wind speed with launch site historical data utilizing the bivariate extreme value (Gumbel) distribution; estimation of extremes of wind speed or wind shear at a future time given the extremes of either variable at an initial time, utilizing the conditional extreme value distribution; power spectrum analysis for tracking wind perturbation energy in sequential pre-launch Jimsphere wind profiles.

Adelfang, S. I.↗

NASA NTRS1988

A prediction for the size of sunspot cycle 22

Based on 'annual' averages, a bivariate analysis of the maximum amplitude of the sunspot cycle against its minimum amplitude and the minimum value of the aa geomagnetic index (in the vicinity of sunspot cycle minimum) results in a fit that closely matches the observable record. The bilinear fit has a high coefficient of correlation (r = 0.982) and a small standard deviation (s = 9.5), suggesting that it may be useful for predicting the size of a sunspot cycle 3 to 4 years before maximum amplitude occurrence. Applying the fit to cycle 22, the annual average of maximum amplitude is found to be 92 + or - 19 (equivalent to 96 + or - 20 in terms of the 13-month running mean or smoothed sunspot number).

Wilson, Robert M.↗

NASA NTRS1988

FFT applications to plane-polar near-field antenna measurements

The four-point bivariate Lagrange interpolation algorithm was applied to near-field antenna data measured in a plane-polar facility. The results were sufficiently accurate to permit the use of the FFT (fast Fourier transform) algorithm to calculate the far-field patterns of the antenna. Good agreement was obtained between the far-field patterns as calculated by the Jacobi-Bessel and the FFT algorithms. The significant advantage in using the FFT is in the calculation of the principal plane cuts, which may be made very quickly. Also, the application of the FFT algorithm directly to the near-field data was used to perform surface holographic diagnosis of a reflector antenna. The effects due to the focusing of the emergent beam from the reflector, as well as the effects of the information in the wide-angle regions, are shown. The use of the plane-polar near-field antenna test range has therfore been expanded to include these useful FFT applications.

Gatti, Mark S.↗

NASA NTRS1988

Focal region fields of distorted reflectors

The problem of the focal region fields scattered by an arbitrary surface reflector under uniform plane wave illumination is solved. The physical optics (PO) approximation is used to calculate the current induced on the reflector. The surface of the reflector is described by a number of triangular domain-wise 5th degree bivariate polynomials. A 2-dimensional Gaussian quadrature is employed to numerically evaluate the integral expressions of the scattered fields. No Freshnel or Fraunhofer zone approximations are made. The relation of the focal fields problem to surface compensation techniques and other applications are mentioned. Several examples of distorted parabolic reflectors are presented. The computer code developed is included, together with instructions on its usage.

Buris, N. E.↗

NASA NTRS1989

Statistical study of the correlation of hard X-ray and type 3 radio bursts in solar flares

A large number of hard X-ray events which were recorded by the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM) during the maximum of the 21st solar cycle (circa 1980) are analyzed in order to study their statistical correlation with type 3 bursts. The earlier finding by Kane (1981) are confirmed qualitatively that flares with stronger hard X-ray emission, especially those with harder spectra, are more likely to produce a type 3 burst. The observed distribution of hard X-ray and type 3 events and their correlations are shown to be satisfactorily described by a bivariate distribution consistent with the assumption of statistical linear dependence of X-ray and radio burst intensities. From this analysis it was determined that the distribution of the ratio of X-ray intensity (in counts/s) to type 3 intensity (in solar flux units) which has a wide range and a typical value for this ratio of about 10. The implications of the results for impulsive phase models are discussed.

Hamilton, Russell J.↗

NASA NTRS1989

Wind models for the NSTS ascent trajectory biasing for wind load alleviation

New concepts are presented for aerospace vehicle ascent wind profile biasing. The purpose for wind biasing the ascent trajectory is to provide ascent wind loads relief and thus decrease the probability for launch delays due to wind loads exceeding critical limits. Wind biasing trajectories to the profile of monthly mean winds have been widely used for this purpose. The wind profile models presented give additional alternatives for wind biased trajectories. They are derived from the properties of the bivariate normal probability function using the available wind statistical parameters for the launch site. The analytical expressions are presented to permit generalizations. Specific examples are given to illustrate the procedures. The wind profile models can be used to establish the ascent trajectory steering commands to guide the vehicle through the first stage. For the National Space Transportation System (NSTS) program these steering commands are called I-loads.

Smith, O. E.↗