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Tabulation of high accuracy gamma function values for some rational arguments, noting applications to Gaussian quadrature formulas, fractional Bessel functions and Airy functions
The computer executive functional system design concepts derived from study of the Space Station/Base are presented. Information Management System hardware configuration as directly influencing the executive design is reviewed. The hardware configuration and generic executive design requirements are considered in detail in a previous report (System Configuration and Executive Requirements Specifications for Reusable Shuttle and Space Station/Base, 9/25/70). This report defines basic system primitives and delineates processes and process control. Supervisor states are considered for describing basic multiprogramming and multiprocessing systems. A high-level computer executive including control of scheduling, allocation of resources, system interactions, and real-time supervisory functions is defined. The description is oriented to provide a baseline for a functional simulation of the computer executive system.
Cross-spectral functions for the vertical and longitudinal components of turbulence of a two-dimensional gust field are derived from the point correlation function for turbulence due to von Karman. Closed form solutions in terms of Bessel functions of order 5/6 and 11/6 are found. An asymptotic expression for large values of the frequency argument, and series results for small values of frequency, are also given. These results now form the base for studying the effect of spanwise variations in turbulence for a turbulence environment which is characterized by the von Karman isotropic spectral relations. Previous studies were based mainly on the Dryden-type spectral representation.
A multiple-impulse function is represented as a sequence of single-impulse functions. The single-impulse transfer which yields the velocity change required to transfer from a specified initial orbit to a partially specified final orbit is developed. Analytic derivatives of the function are obtained for use in optimization techniques. A four-impulse transfer is outlined. The analytic derivatives may allow more efficient optimization than numerical derivatives do.
Electron work functions, surface potentials, and electron number density distributions and electric fields in the surface region of 26 metals were calculated from first principles within the free electron model. Calculation proceeded from an expression of the total energy as a functional of the electron number density, including exchange and correlation energies, as well as a first inhomogeneity term. The self-consistent solution was obtained via a variational procedure. Surface barriers were due principally to many-body effects; dipole barriers were small only for some alkali metals, becoming quite large for the transition metals. Surface energies were inadequately described by this model, which neglects atomistic effects. Reasonable results were obtained for electron work functions and surface potential characteristics, maximum electron densities varying by a factor of over 60.
Systems engineering is examined in terms of functional activities that are performed in the conduct of a system definition/design, and system development is described in a parametric analysis that combines functions, performance, and design variables. Emphasis is placed on identification of activities performed by design organizations, design specialty groups, as well as a central systems engineering organizational element. Identification of specific roles and responsibilities for doing functions, and monitoring and controlling activities within the system development operation are also emphasized.
A computer program was developed that selects, from a list of candidate functions, the approximating functions and associated coefficients which result in the best curve fit of a given set of numerical data. The advantages of the approach used here are: (1) Multivariable approximations can be performed. (2) Flexibility with respect to the type of approximations used is available. (3) The program is designed to choose the best terms to be used in the approximation from an arbitrary list of possible terms so that little knowledge of the proper approximating form is required. (4) Recursion relations are used in determining the coefficients of the approximating functions, which reduces the computer execution time of the program.
Two simple methods are outlined for evaluating the effect of transfer-function zeros on the system time response. The pole effects can also be evaluated. These methods are useful for simplified analysis or creating design criteria in terms of desirable regions of pole-zero locations. The type of transfer function studied is limited to those linear systems. Corresponding to ordinary longitudinal or lateral aircraft transfer functions, the denominator polynomial is of fourth order and the numerator of third order at most. With the longitudinal motion of the aircraft as an example, the methods are used in the evaluation of optimal regulator control with respect to a particular performance index structure.
Large interindividual differences among 74 normal subjects in the change in susceptibility to motion sickness with effective lifting of the normal g-load by parabolic flight maneuvers were recorded with high test-retest reliability. Most subjects, who were required to make standardized head movements while seated in a chair rotating at a constant speed, demonstrated either a substantial increase or a decrease in susceptibility, in confirmation of a previous study, while a few appeared to be more or less unaffected by the 1 g to 0 g gravitational change. A similar test procedure conducted with eighteen of the subjects at lunar- and Martian-gravity levels revealed further interindividual differences in susceptiblity as a function of g-level. The subjects with gravity-dependent susceptibility revealed: (1) a progressive change in susceptibility as a function of g-load in either the positive or negative direction that was characteristic of the individual, (2) a susceptibility level that appeared to be maintained at the fractional g-load, and (3) immunity to motion sickness at all g-levels tested below the earth standard. The case history as well as ground-based functional and provocative tests of normal subjects proved to be inadequate in predicting susceptibility to motion sickness under subgravity conditions.
A polycrystalline molybdenum sample was recrystallized and thermally stabilized. Quantitative measurements of the emission from each individual grain were obtained with an electron emission microscope. The effective work function for each grain was then calculated. The crystallographic orientation of each grain was determined by Laue back-reflection techniques. A polar plot of effective work function vs crystallographic orientation for the sample was constructed to provide a correlation between effective work function and crystallographic orientation.
The basis and techniques are presented for generating opacity probability distribution functions for the CN molecule (red and violet systems) and the C2 molecule (Swan, Phillips, Ballik-Ramsay systems), two of the more important diatomic molecules in the spectra of carbon stars, with a view to including these distribution functions in equilibrium model atmosphere calculations. Comparisons to the CO molecule are also shown. T he computation of the monochromatic absorption coefficient uses the most recent molecular data with revision of the oscillator strengths for some of the band systems. The total molecular stellar mass absorption coefficient is established through fifteen equations of molecular dissociation equilibrium to relate the distribution functions to each other on a per gram of stellar material basis.
Review of some of the results of the Mariner 7 ultraviolet spectrometer observations of the south polar cap of Mars. The near ultraviolet polar spectrum shows the predominance of surface reflection over atmospheric scattering. The intensity of the reflected radiation decreased steeply for a change in solar elevation of only about 10 deg. Neither a haze layer nor ground inhomogeneity is considered a likely explanation for this observation. An unusual photometric function of the surface is more probable. An analysis of reflected radiation intensity as a function of incidence and emission angles was made, assuming a photometric function for the surface. The angular inversion revealed a 'smoothness factor' suggestive of an icy or glazed surface. A hypothesis is advanced to explain the observed phenomena and associated polar features.
A study of source-encoding techniques that afford a reduction of data-transmission rates is made with particular emphasis on the compression of transmission bandwidth requirements of band-limited functions. The feasibility of bandwidth compression through analog signal rooting is investigated. It is found that the N-th roots of elements of a certain class of entire functions of exponential type possess contour integrals resembling Fourier transforms, the Cauchy principal values of which are compactly supported on an interval one N-th the size of that of the original function. Exploring this theoretical result, it is found that synthetic roots can be generated, which closely approximate the N-th roots of a certain class of band-limited signals and possess spectra that are essentially confined to a bandwidth one N-th that of the signal subjected to the rooting operation. A source-encoding algorithm based on this principle is developed that allows the compression of data-transmission requirements for a certain class of band-limited signals.
A new method is presented for obtaining network functions in which some, none, or all of the network elements are represented by symbolic parameters (i.e., symbolic network functions). Unlike the topological tree enumeration or signal flow graph methods generally used to derive symbolic network functions, the proposed procedure employs fast, efficient, numerical-type algorithms to determine the contribution of those network branches that are not represented by symbolic parameters. A computer program called NAPPE (for Network Analysis Program using Parameter Extractions) and incorporating all of the concepts discussed has been written. Several examples illustrating the usefulness and efficiency of NAPPE are presented.
This paper considers the design of model-reference adaptive control systems using Liapunov functions. An adaption rule is developed analytically. This adaption rule results from the use of a Liapunov function which contains several positive semidefinite terms not included in previous references. The inclusion of these terms results in an adaption rule which is a function of the error, the plant states and the derivative and integral of these quantities. The adaption rule is applied to a simplified model of the Space Shuttle vehicle. Simulation results show that the maximum response error in the system is reduced by using this adaption rule.
It is shown that the correct lowest-order two-particle correlation function solution to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy is given via a Green's function whose Fourier transform satisfies the analyticity requirements for causality. The Bogoliubov adiabatic approximation is shown to imply a solution which is acausal. Extension to the s-particle correlation function is discussed.
A scheme is presented for realizing any function, combinational or sequential, in a single universal function scheme, termed the universal function object UF. This scheme is addressed to the problem of the proliferation of the number of parts (cards, chips) necessary for conventional implementation in an LSI technology of a computer system. The UF implementation will use about ten times more circuits than a conventional implementation regardless of the size of the design. The UF approach also includes general-purpose spares for failing circuits. The procedure could be used both at manufacture to increase yields, as well as to achieve automatic repair.
The distribution function of ion energy parallel to the magnetic field of a modified Penning discharge has been measured with a retarding potential energy analyzer. These ions escaped through one of the throats of the magnetic mirror geometry. Simultaneous measurements of the ion energy distribution function perpendicular to the magnetic field have been made with a charge exchange neutral detector. The ion energy distribution functions are approximately Maxwellian, and the parallel and perpendicular kinetic temperatures are equal within experimental error. These results suggest that turbulent processes previously observed in this discharge Maxwellianize the velocity distribution along a radius in velocity space and cause an isotropic energy distribution. When the distributions depart from Maxwellian, they are enhanced above the Maxwellian tail.