Simplified solutions for two-person percentile games
Specialized zero-sum game solution using expected values for evaluation of marked set assurance probability in two-person percentile games
Kelleher, G. J.↗
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Results for “EXPECTATION VALUE”
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Runaway stars in the Gum Nebula
It is proposed that the two pulsars PSR 0833-45 (the Vela pulsar) and MP 0835 are runaways from a common binary system originally located in the B association around gamma Velorum. Arguments are presented for a simple model of the Gum nebula in which two distinct ionized regions are present. The first consists of the Stromgren spheres of gamma Velorum and zeta Puppis, while the second is a larger, more filamentary region ionized by the supernova explosion associated with PSR 0833-45. Using this model and the available dispersion measures, the distances to the two pulsars were estimated and found to be compatible with a runaway origin. The position angle of the rotation axis of PSR 0833-45 is also compatible with this origin. The masses of the parent stars of the two pulsars can be deduced from the runaway star dynamics and an assumed age for MP 0835. It is concluded that the masses were in excess of 10 solar masses. The dynamically-determined parent star masses are in agreement with the values expected for evolved members of the B association around gamma Velorum.
Got, J. R., III↗
Effect of environmental torques on short-term attitude prediction for a rolling-wheel spacecraft in a sun-synchronous orbit
A numerical evaluation and an analysis of the effects of environmental disturbance torques on the attitude of a hexagonal cylinder rolling wheel spacecraft were performed. The resulting perturbations caused by five such torques were found to be very small and exhibited linearity such that linearized equations of motion yielded accurate results over short periods and the separate perturbations contributed by each torque were additive in the sense of superposition. Linearity of the torque perturbations was not affected by moderate system design changes and persisted for torque-to-angular momentum ratios up to 100 times the nominal expected value. As these conditions include many possible applications, similar linear behavior might be anticipated for other rolling-wheel spacecraft.
Hodge, W. F.↗
Adaptive control of stochastic linear systems with unknown parameters
The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.
Ku, R. T.↗
Acquisition time for sideband modulated phase lock loops.
In this paper a definition for acquisition of a sideband modulated carrier is proposed for the phase lock loop, and the acquisition differential equation solved for a region of the modulation parameter space to determine the expected value of acquisition time. Principally the case of modulation by a single unmodulated subcarrier is considered. The numerical analysis is made for the noiseless case.
Gilbert, A. L.↗
Frequency shifts of ionospheric nfH resonances.
New observational data are analyzed to interpret mechanisms responsible for large positive frequency shifts of Alouette II plasma resonances (corresponding to the first and second electron cyclotron harmonics) relative to frequency values expected from model magnetic field calculations. It is shown that the frequency shifts can be consistently explained by plasma wave dispersion effects combined with sounder transmitter frequency deviation (positive offset of several kilohertz) and a negative offset (several tens of gammas) in the geomagnetic field relative to the model field. Plasma wave dispersion effects are observed on the electron cyclotron second harmonic resonance when it is in the vicinity of the resonance observed near the upper hybrid frequency. The observations suggest that an oblique echo model may be required for interpretation of the electron cyclotron second harmonic resonance.
Benson, R. F.↗
A simple, radially correlated ground state wavefunction for two electron atoms.
A one parameter function is presented as an approximation to the ground state wavefunction of the two electron radial hamiltonian. The parameter may be fixed by a nonvariational criterion. The resulting expectation value of the radial hamiltonian differs from its exact eigenvalue by about 2 parts in 3000 for helium while the 'local energy' never differs by more than 10% from the exact value over the entire r1-r2 plane. The cases Z = 1 and Z = 3 are also investigated.
Altick, P. L.↗
A biased filter for linear discrete dynamic systems.
A recursive estimator, the ridge filter, was developed for the linear discrete dynamic estimation problem. Theorems were established to show that the ridge filter can be, on the average, closer to the expected value of the system state than the Kalman filter. On the other hand, Kalman filter, on the average, is closer to the instantaneous system state than the ridge filter. The ridge filter has been formulated in such a way that the computational features of the Kalman filter are preserved.
Chang, J. W.↗
The use of film actinometry in low intensity ultraviolet irradiation measurement
High resolution film was used to measure solar ultraviolet irradiation at a wavelength of 254 nanometers between energy levels of 3 x 10 to the minus 7 power and 130 x 10 to the minus 7 power joules (3 and 130 ergs). The results imply that the film recorded exposure to energy levels from 2.5 to 13 times the expected values. These high values are being evaluated for the influences of other factors that could affect the recorded values.
Long, R. A.↗
A new criterion for modeling systems
The criterion that is proposed is an expected value of the mean square response error as an alternative to testing a model against new data. Modeling with respect to this new criterion does not change the estimate for a given model format from a maximum likelihood estimate or mean square response error estimate. The new criterion does, however, provide a means of comparing models with different formats and varying complexity. A numerical example is used to illustrate the application of the proposed criteria and the problem of searching for the best model. For all but the most trivial system identification problems, it is shown that a prohibitive number of combinations of terms of the model must be investigated to ensure the final model is best.
Taylor, L. W., Jr.↗
Phased arrays of lasers for power transmission
The phased array is a group of regularly spaced lasers with parallel optical axes. Each laser of the group emits light of the same wavelength and the same phase. Mathematical models of laser transmission systems with regular arrays are presented, taking into account rectangular apertures. It is found that an array of free running lasers has the same normalized expectation value as the single laser, with the actual power a factor of N greater.
Vetter, A. A.↗
The effects of shock wave compaction on the transition temperatures of A15 structure superconductors
Several superconductors with the A15 structure exhibit a positive pressure coefficient, indicating that their transition temperatures increase with applied pressure. Powders of the composition Nb3Al, Nb3Ge, Nb3(Al0.75Ge0.25), and V3Si were compacted by explosive shock waves. The superconducting properties of these materials were measured before and after compaction and it was found that regardless of the sign of the pressure coefficient, the transition temperature is always lowered. The decrease in transition temperature is associated with a decrease in the particle diameter. The shock wave passage through a 3Nb:1Ge powder mixture leads to the formation of at least one compound (probably Nb5Ge3). However, the formation of the A15 compound Nb3Ge is not observed. Elemental niobium powder can be compacted by converging shock waves close to the expected value of the bulk density. Under special circumstances a partial remelting in the center of the sample is observed.
Otto, G. H.↗
Reproducibility of liquid oxygen impact test results
Results for 12,000 impacts on a wide range of materials were studied to determine the reproducibility of the liquid oxygen impact test method. Standard deviations representing the overall variability of results were in close agreement with the expected values for a binomial process. This indicates that the major source of variability is due to the go - no go nature of the test method and that variations due to sampling and testing operations were not significant.
Gayle, J. B.↗
A constructive model potential method for atomic interactions
A model potential method is presented that can be applied to many electron single centre and two centre systems. The development leads to a Hamiltonian with terms arising from core polarization that depend parametrically upon the positions of the valence electrons. Some of the terms have been introduced empirically in previous studies. Their significance is clarified by an analysis of a similar model in classical electrostatics. The explicit forms of the expectation values of operators at large separations of two atoms given by the model potential method are shown to be equivalent to the exact forms when the assumption is made that the energy level differences of one atom are negligible compared to those of the other.
Bottcher, C.↗
The quiet time structure of energetic /35-560 keV/ radiation belt electrons
Detailed Explorer 45 observations of quiet time pitch angle distributions and equatorial radial profiles of energetic radiation belt electrons are presented. The observed pitch angle distributions in the slot region and the outer regions of the plasmasphere are found to agree with the values expected from resonant interactions with the plasmaspheric whistler mode wave band, and Coulomb collisions are found to be the dominant electron loss mechanism in the inner zone. The overall structure of quiet time radial profiles is shown to agree with the equilibrium structure expected to result from a balance between pitch angle scattering losses and radial diffusion from an outer zone source, and this agreement suggests that the dominant quiet time source and loss mechanisms have been correctly identified. Electron fluxes in the inner plasmasphere are found to remain nearly constant during the quiet periods due to their decoupling from magnetic activity variations in the outer plasmasphere.
Lyons, L. R.↗
On the exposure history of the lunar regolith
The observed minimum and mean values of track densities in lunar grains are both found to exceed the values expected from exposure with redistribution by vertical mixing, and the percentage of the smaller grains showing very high track densities is too large by a factor of more than ten. Previous exposure of the material (in space before accretion onto the moon or in regions from which net migration has occurred) may be necessitated.
Gold, T.↗
Numerical procedure for analyzing Langmuir probe data
A numerical procedure is proposed for analyzing Langmuir probe data in the presence of a two-group plasma containing both primary and Maxwellian electrons. The procedure is known as a least-squares differential-correction technique for determining the unknown coefficients of the governing equation. It is shown that for a given set of input data the results of the analysis are unique and independent of the initial estimate of electron temperature, that convergence is fastest when electron temperature is overestimated, that the results are sensitive to the region of the curve used as input and also to the voltage increment, and that plasma properties determined by the proposed numerical procedure are either consistent with those determined graphically or closer to expected values. With a suitable data acquisition system, the Fortran IV program worked out for this procedure could be used to provide real-time plasma diagnostic information for an operating ion thruster.
Beattie, J. R.↗
Application of LSI to signal detection: The deltic DFPCC
The development of the DELTIC DFPCC serial mode signal processor is discussed. The processor is designed to detect in the presence of background noise a signal coded into the zero crossings of the waveform. The unique features of the DELTIC DFPCC include versatility in handling a variety of signals and relative simplicity in implementation. A theoretical performance model is presented which predicts the expected value of the output signal as a function of the input signal to noise ratio. Experimental results obtained with the prototype system, which was breadboarded with LSI, MSI and SSI components, are given. The device was compared with other LSI schemes for signal processing and it was concluded that the DELTIC DFPCC is simpler and in some cases more versatile than other systems. With established LSI technology, low frequency systems applicable to sonar and similar problems are feasible.
Gassaway, J. D.↗