Efficient recursive estimation - application to estimating the parameters of a covariance function.
Estimating parameters of covariance function with modified stochastic approximation
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Estimating parameters of covariance function with modified stochastic approximation
Approximate ground state wave function used in variational principle for second order energy
Perturbation theories for equations of celestial mechanics, obtaining analytical solutions in terms of Chebyshev polynomial series
Approximate ground state wave functions used in calculation of interaction energies by second- order perturbation theory
Study applies the nonequilibrium collision theory of reaction rates to the estimation of rate constants for simple reactions. The complications in the quantum mechanical description of chemical reactions and the care needed in approximating the exact wave function for the collision are shown.
Step function, and application of quadrature formulas to estimation using moments
Approximations to several transcendental functions in universal form of two body problem
H molecule photoionization, using one center wave function with polarized orbital approximation to obtain oscillator strengths in 700 to 300 angstrom range
Rocket sonde measurement of ozone content in the mesosphere and stratosphere is accomplished by an in situ determination of the ozone mixing rates as a function of altitude from approximately 65 km to 20 km. A chemiluminescent detector is used as an ozone sensor.
Numerical method for calculating cumulative distribution of positive random variable
Cumulative probability distribution of positive random variable from moment generating function, exemplifying exponential and Poisson functions
Integrations over solid angle and frequency are performed in the expressions for the radiant heat flux and local energy loss of a line in a region of strong variations of the source function in one direction. Approximations are given for coefficients and kernels in the resulting forms which involve integrals over the physical coordinate.
Integrations over solid angle and frequency are performed in the expressions for the radiant heat flux and local energy loss of a line in a region of strong variations of the source function in one direction. Approximations are given for coefficients and kernels in the resulting forms which involve integrals over the physical coordinate.
A synthesis theory is developed which allows system design to proceed from practical specifications on system command and/or disturbance response to a design which is very nearly optimal in terms of feedback sensor noise effects. The approach taken is to replace the nonlinear element by a mean square error minimizing approximation (dual-input describing function), and then use linear frequency domain synthesis techniques subject to additional constraints imposed by the limit cycle and the approximator. Synthesis techniques are also developed for a similar system using an externally excited oscillating signal with the above approach. The results remove the design of the systems considered from the realm of simulation and experimentation, permitting true synthesis and the optimization that accompanies it.
The following conclusions were reached on passenger responses: (1) Within acceptable limits, the crew/flight attendants do not appear to be able to predict passenger responses. (2) There exists a relationship between passenger and subject overall responses. (3) Finally, a strong relationship exists between a suitably weighted running and overall subjective response. The recommended weighting function W(I) is approximately equal to I to the 0.75 power, indicating that the latter part of a flight is given more importance in a subject's overall comfort evaluation than the beginning of the flight.
Using Lexan and glass detectors, the composition of solar particles with atomic number 2 or greater was determined as a function of energy from approximately 0.2 to 50 MeV/nucleon in four flares of quite different intensity and during a time when the sun was nearly quiet. Fe is nearly completely stripped. The enhancement factor increases with atomic number at a given energy but decreases with energy. Heavy element enhancements are detectable at higher energies in stronger flares. They occurred in ancient as well as in present-day flares. We have observed Li and Be in one flare. Incomplete ionization, preferential leakage of heavy ions, energy loss by ionization, and nuclear reactions appear to be involved in solar particle production.
A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.
Using a multiple-scatter propagation theory, the characteristics of the transionospheric satellite-earth communication links are related to the parameters of the ionosphere. General equations for the frequency correlation functions are derived. Some approximate solutions are obtained and numerical examples are given. Also discussed are the degree of coherence and potential applications of the procedure to characterize the intense fading channel.