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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1974

Stability properties of functional difference equations

Hale and Cruz (1970) have defined the concept of a stable difference operator, and have found that this class of operators is sometimes 'super sensitive' to perturbations. In the present paper, a subclass of general functional difference equations is derived which retain their stability under appropriate perturbations. Also, the results of Hale and Cruz are extended to include difference equations on the Banach space of p-th power integrable functions, and essentially bounded functions.

Melvin, W. R.↗

NASA NTRS1978

Fast algorithm for computing a primitive /2 to power p + 1/p-th root of unity in GF/q squared/

A quick method is described for finding the primitive (2 to power p + 1)p-th root of unity in the Galois field GF(q squared), where q = (2 to power p) - 1 and is known as a Mersenne prime. Determination of this root is necessary to implement complex integer transforms of length (2 to power k) times p over the Galois field, with k varying between 3 and p + 1.

Reed, I. S.↗

NASA NTRS1979

Extreme Mean and Its Applications

Extreme value statistics obtained from normally distributed data are considered. An extreme mean is defined as the mean of p-th probability truncated normal distribution. An unbiased estimate of this extreme mean and its large sample distribution are derived. The distribution of this estimate even for very large samples is found to be nonnormal. Further, as the sample size increases, the variance of the unbiased estimate converges to the Cramer-Rao lower bound. The computer program used to obtain the density and distribution functions of the standardized unbiased estimate, and the confidence intervals of the extreme mean for any data are included for ready application. An example is included to demonstrate the usefulness of extreme mean application.

Swaroop, R.↗