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Correlations between X-ray and type 3 radio emission of solar bursts are described through a bivariate distribution function. Procedures for determining the form of this distribution are described. A model is constructed to explain the correlation between the X-ray spectral index and the ratio of X-ray to radio intensities. Implications of the model are discussed. Previously announced in STAR as N82-32243
Wind gust data were analyzed by statistical and mathematical procedures, developed for the bivariate gamma distribution. The results of the analysis are summarized.
The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.
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 a simulation variables are obtained by interfacing to a digital computer and using a custom software package for data collection and display.
For the period considered, December 1977 through February 1978, bivariate Gaussian discriminant function cloud identification revealed that more than 93 percent of the 8-km resolution GOES infrared pixels were cloud contaminated. Cloud-free in-situ calibration points were distributed in nonrandom groups; this resulted in systematic errors when using least squares techniques. Surfaces and regression lines were least squares fitted between satellite and in-situ data; use was also made of differences and ratios. The best results were achieved with a regression in the form of the infrared radiative transfer equation; but this was no better than + or - 0.9 K. Because of extensive cloudiness, the linear regressions were seldom useful, and temperature ratios with + or - 1.3 K experimental errors best represent the applicability of GEOS data to sea surface temperatures.
The relationship between the ocean's normalized radar cross section (NRCS) at 14.6 GHz and the surface wind vector is derived using the 3 months of Seasat microwave scatterometer (SASS) measurements. The derivation is based on the statistics of the SASS observations, and no in situ measurements are required, other than a mean global wind speed, which comes from climatology. The frequency distribution of the global wind vectors observed by SASS is assumed to be a bivariate normal probability function. A NRCS model function is found that maps the assumed wind vector statistics into the observed SASS NRCS statistics. This function is compared with a NRCS model coming from the Joint Air Sea Interaction Experiment (JASIN) and with aircraft scatterometer measurements. The results indicate that the statistically derived NRCS model is an improvement over the JASIN model, which was based on a limited number of in situ anemometer measurements.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.