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At least 145 records · Page 8
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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.↗
NASA NTRS1990

Interpolation And FFT Of Near-Field Antenna Measurements

Bivariate Lagrange interpolation applied to plane-polar measurement scans. Report discusses recent advances in application of fast-Fourier-transform (FFT) techniques to measurements of near radiation fields of antennas on plane-polar grid. Attention focused mainly on use of such measurements to calculate far radiation fields. Also discussion of use of FFT's in holographic diagnosis of distortions of antenna reflectors. Advantage of scheme, it speeds calculations because it requires fewer data and manipulations of data than other schemes used for this purpose.

Gatti, Mark S.↗
NASA NTRS1989

Scattering of light by stochastically rough particles

The single particle phase function and the linear polarization for large stochastically deformed spheres have been calculated by Monte Carlo simulation using the geometrical optics approximation. The radius vector of a particle is assumed to obey a bivariate lognormal distribution with three free parameters: mean radius, its standard deviation and the coherence length of the autocorrelation function. All reflections/refractions which include sufficient energy have been included. Real and imaginary parts of the refractive index can be varied without any restrictions. Results and comparisons with some earlier less general theories are presented. Applications of this theory to the photometric properties of atmosphereless bodies and interplanetary dust are discussed.

Peltoniemi, Jouni I.↗
NASA NTRS1990

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 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.↗
NASA NTRS1989

Neural network implementations of data association algorithms for sensor fusion

The paper is concerned with locating a time varying set of entities in a fixed field when the entities are sensed at discrete time instances. At a given time instant a collection of bivariate Gaussian sensor reports is produced, and these reports estimate the location of a subset of the entities present in the field. A database of reports is maintained, which ideally should contain one report for each entity sensed. Whenever a collection of sensor reports is received, the database must be updated to reflect the new information. This updating requires association processing between the database reports and the new sensor reports to determine which pairs of sensor and database reports correspond to the same entity. Algorithms for performing this association processing are presented. Neural network implementation of the algorithms, along with simulation results comparing the approaches are provided.

Brown, Donald E.↗
NASA NTRS1990

Elliptic grid generation with orthogonality and spacing control on an arbitrary number of boundaries

A procedure for the generation of two and quasi-three-dimensional grids with control of orthogonality and spacing with respect to any and/or all boundaries of the domain is described. The elliptic grid generation equations of Thompson are solved implicitly. Control of the grid behavior is achieved through the introduction of forcing functions terms in the manner of Steger and Sorenson or in a modification of the method of Hilgenstock. The forcing function terms are constructed on the boundaries and propagated into the domain using transfinite Lagrangian bivariate interpolation. An anisotropic transfinite stencil is introduced and is shown to produce excellent grid behavior particularly in the vicinity of corner singularities. Emphasis is placed on the generation of viscous grids and the method is shown to be suited for use in the generation of grids for internal as well as external flow geometries. A FORTRAN program named PISCES has been written to implement the algorithm. Examples of grids for internal and external flows are given that highlight the characteristics and behavior of the algorithm.

White, J. A.↗