A hypergeometric mean value.
Hypergeometric mean value, showing expression for mean of order t of series of positive values with positive weights as limiting case
HYPERGEOMETRIC FUNCTION↗
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The mean observed meteorological structure and circulation of the stratosphere and mesosphere
Meteorological soundings of the upper stratosphere and mesosphere, conducted with in situ rocket techniques during all seasons of the year from several sites, ranging in latitude from 8 deg S to 71 deg N, are analyzed. The resulting data are compiled into mean monthly and seasonal profiles of temperature, pressure, density, and wind for each site and are presented in graphical and tabular form. Analyses of these mean values produced time cross sections, quasi-meridional cross sections, and constant level maps which are included.
Theon, J. S.↗
Sky-wave backscatter - A means for observing our environment at great distances.
During the last five years, much progress has been made in the understanding of sky-wave backscatter. An explanation of the various interacting phenomena is presented, as is a review of the current state of knowledge reflecting recent advances in observational methods and analytic techniques. New narrow-beam antennas, coupled with signal modulations that permit fine resolution in time delay, are beginning to yield information concerning the character of the scatterers, which now can be separately discerned. These narrow beams also permit study of polarization fading from small regions, and this shows promise as a means for learning the distant sea state. Doppler shifts of a fraction of a hertz on signals of tens of megahertz are separable, permitting isolation of sea returns from ground returns by virtue of the Doppler effect resulting from sea-wave speed; this also suggests a potential sea-monitoring principle. Despite these advances, there is little practical application of sky-wave backscatter as a means of environmental monitoring. This lack is attributed to the large remaining gaps in our understanding of the echoes and our inability to interpret the forms of data that can be acquired with equipment of reasonable cost.
Croft, T. A.↗
Simplified formula for mean cycle-slip time of phase-locked loops with steady-state phase error.
Previous work shows that the mean time from lock to a slipped cycle of a phase-locked loop is given by a certain double integral. Accurate numerical evaluation of this formula for the second-order loop is extremely vexing because the difference between exponentially large quantities is involved. The presented article demonstrates a method in which a much-reduced precision program can be used to obtain the mean first-cycle slip time for a loop of arbitrary degree tracking at a specified SNR and steady-state phase error. It also presents a simple approximate formula that is asymptotically tight at higher loop SNR.
Tausworthe, R. C.↗
Determination of mean surface position and sea state from the radar return of a short-pulse satellite altimeter
Using the specular point theory of scatter from a very rough surface, the average backscatter cross section per unit area per radar cell width is derived for a cell located at a given height above the mean sea surface. This result is then applied to predict the average radar cross section observed by a short-pulse altimeter as a function of time for two modes of operation: pulse-limited and beam-limited configurations. For a pulse-limited satellite altimeter, a family of curves is calculated showing the distortion of the leading edge of the receiver output signal as a function of sea state (i.e., wind speed). A signal processing scheme is discussed that permits an accurate determination of the mean surface position--even in high seas--and, as a by-product, the estimation of the significant seawave height (or wind speed above the surface). Comparison of these analytical results with experimental data for both pulse-limited and beam-limited operation lends credence to the model. Such a model should aid in the design of short-pulse altimeters for accurate determination of the geoid over the oceans, as well as for the use of such altimeters for orbital sea-state monitoring.
Barrick, D. E.↗
Plate motion and the secular shift of the mean pole
The global plate motion indicates that changes in the products of inertia of the earth due to tectonic plate movement may provide a secular shift of the mean pole. A mathematical procedure for calculating this shift based on the plate theory is presented. Explicit expressions were obtained for the dependence of the secular polar shift on the dimensions and locations of the plate boundaries. Numerical results show that the secular motion of the mean pole is 0.0002 sec/year in the direction of 67 W. Hence, it is deduced that the influence of the plate motion on the secular polar shift may account for 10% of the observed value.
Liu, H.↗
Interplanetary gas. XVIII - Models and the mean free path of protons at 1 astronomical unit.
Velocity distribution functions of solar-wind protons obtained by the Vela 3 satellites have been analyzed to obtain a microscopic determination of the momentum flux along magnetic field lines with respect to a reference frame moving at the bulk speed. The determination from macroscopic parameters allows the calculation of an effective mean free path for protons at 1 AU which averages 0.06 AU and is relatively independent of solar-wind velocity w. For quiet times when w is from 300 to 400 km/sec, the experimental mean free path is 2 to 3 times smaller than the value from plasma theory. For w greater than 400 km/sec, the experimental value is 10 to 100 times smaller than the theoretical value.
Brandt, J. C.↗
A reexamination of the mean H I density along the Hubble sequence.
Using the 21-cm galaxy surveys of both Roberts (1969) and Bottinelli (1971), it is shown that the mean H I space density is at most a weak function of galactic type along the limited Hubble sequence Sb to Irr. On this basis, it is concluded, contrary to previous thought, that the mean H I density is not the large-scale galactic parameter which determines the morphological characteristics of galaxies.
Kellman, S. A.↗
Mean flow and turbulence measurements in a Mach 5 free shear layer
A study of the time-averaged mean flow and the turbulence in a Mach 5 free turbulent shear layer has been performed. When the experimental data were reduced with the assumption of constant static pressure through the shear layer, the mean-velocity profile in similarity coordinates was in good agreement with the low speed velocity profile. The intensities of the velocity fluctuations were about a factor of 2 lower than the low speed measurements but with the maximum velocity fluctuations occurring in the same regions of the supersonic and low speed shear layers. A large density fluctuation was observed in the outer part of the shear layer near the boundary of the shear layer and the potential core.
Wagner, R. D.↗
Algebraically growing waves in ducts with sheared mean flow
Standing or traveling waves which vary algebraically with the axial distance in uniform ducts with sheared mean velocity profiles are investigated. The results show that such waves are not possible for ducts with uniform cross sections and fully developed mean flows.
Nayfeh, A. H.↗
Weather watch studies by means of an optical technique
A series of articles is presented on a passive, optical, cross beam system. The passive, optical, cross beam system was evaluated as a remote sensor of atmospheric conditions. The system employed the light scattered from natural aerosols to sense atmospheric mean and turbulent motion. A space-time correlation of the output of two optical sensors was used to evaluate the mean convective wind speed. In approximately 20% of the tests, signal-to-noise levels were sufficient to allow estimation of convective wind speeds. The feasibility of employing intersecting beams to evaluate the atmospheric turbulent motion was also investigated. The intersecting beams produced maximums in the space-time correlation curves for other than zero delay. The non-zero time delay maximums indicate the cross beam system was detecting aerosol layers in the atmosphere, rather than information from the common intersecting volume.
Turner, R. E.↗
The scattering mean free path in the Uranian atmosphere
New measurements of the equivalent widths of the 4.0 S(0) and S(1) H2 quadrupole lines in the Uranian spectrum have been obtained using high dispersion (4.12 A/mm) image-tube spectrography. The measured equivalent widths are 62 plus or minus 19 mA and 58 plus or minus 13 mA for the S(0) and S(1) lines, respectively. Curve-of-growth analysis in terms of a reflecting layer model yields an H2 column density of 780 (+940 or -330) km amagat and a temperature of 78 (+80 or -24) K. Interpretation using a semiinfinite, homogeneous, isotropically scattering model for line formation yields a scattering mean free path at 6400 A of 550 plus or minus 250 km amagat. Quoted errors for both the H2 column density and the scattering mean free path include the effect of uncertainty in the choice of atmospheric temperature. The results are discussed in terms of current models for the Uranian atmosphere.
Price, M. J.↗
The estimation of 550 km x 550 km mean gravity anomalies
The calculation of 550 km X 550 km mean gravity anomalies from 1 degree X 1 degree mean free-air gravimetry data is discussed. The block estimate procedure developed by Kaula was used, and estimates for 1452 of the 1654 blocks were obtained.
Williamson, M. R.↗
A method of measuring the three-dimensional mean flow and turbulence quantities inside a rotating turbo-machinery passage
A method of measuring the three-dimensional components of mean velocity and turbulence quantities within a rotating turbomachinery passage is developed through the use of hot wire anemometry techniques. Equations are derived which, when solved simultaneously and in conjunction with the data obtained from the hot wire anemometer measurements, will provide values for the radial, axial and tangential components of mean velocity, turbulence intensity and turbulence stress within the rotating turbomachinery passage. A three-bladed rocket pump inducer model, operating in air, was used in the experimentation. The method is very accurate and provides very useful information on the characteristics of the flow inside rotor passages hitherto unexplored.
Gorton, C. A.↗
Mean meridional circulation in the Southern Hemisphere stratosphere based on satellite information
Atmospheric structure derived from satellite multi-channel radiance data is used to calculate zonally-averaged vertical motions in the wintertime stratosphere of both hemispheres using a heat budget approach. The Northern Hemisphere calculations based on the satellite data are shown to compare favorably with a computation carried out with conventional data, and with results of previous studies. The mean Southern Hemisphere pattern for the month of July 1969 indicates a high-latitude cell with the axis of sinking motion at approximately 50 deg S, while the rising motion is centered at 70 deg S. Thus the Antarctic stratospheric jet stream is associated with an indirect cell. Two individual 10-day periods from July 1969 are also examined to compare the mean meridional circulation and eddy heat flux patterns in the Southern Hemisphere during a minor midwinter warming and during a quiet period.
Adler, R. F.↗
Mean colors of Cepheids
Color observations of Cepheids can be interpreted by a color effective temperature relation to give different T sub e values for each kind of mean color. Here, theoretical colors from numerical integrations of Cepheid pulsations are used to determine the proper method of taking the color mean in order to get, by the color T sub e relation, the correct nonpulsating T sub e.
Cox, A. N.↗
A vortex-lattice method for the mean camber shapes of trimmed noncoplanar planforms with minimum vortex drag
A new subsonic method has been developed by which the mean camber surface can be determined for trimmed noncoplanar planforms with minimum vortex drag. This method uses a vortex lattice and overcomes previous difficulties with chord loading specification. A Trefftz plane analysis is utilized to determine the optimum span loading for minimum drag, then solved for the mean camber surface of the wing, which provides the required loading. Sensitivity studies, comparisons with other theories, and applications to configurations which include a tandem wing and a wing winglet combination have been made and are presented.
Lamar, J. E.↗
Evaluation of the 'mean frequency' technique
The 'mean frequency' technique, a simple procedure introduced by Bebb and Gold for the approximate evaluation of sums occurring in high-order perturbation theory, represents a useful approximation method. Its predictions compare favorably to exact results obtained by Gontier and Trahin for multiphoton bound-bound transitions in hydrogen. However, the technique can be in error if the 'mean frequency' lies near certain integers.
Gaddy, E. M.↗