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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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At least 109 records · Page 6

Numerical integration and Riemann-Stieltjes sums.

Numerical integration based on definition of Riemann integral, describing application to nonlinear integral equations of isotropic scattering of radiation in plane parallel atmosphere

RIEMANN INTEGRAL↗

Bounds for the Horner sums.

Chebyshev polynomials maximum property, examining effect of roundoff errors in Horner scheme for floating point arithmetic

Reimer, M.↗

IR pumped third-harmonic generation and sum-frequency generation in diatomic molecules

The potential efficiency of using nonlinear up-conversion techniques for the high efficiency type lasers (CO,CO2, and chemical) is assessed. Results indicate that: the small pump photon energy necessitates the use of molecular media for conversion if resonance enhancement is to be used and that molecular systems present several problems. These difficulties include: their levels are complex; their transition probabilities are often unknown; and the oscillator strengths among vibrational levels in the ground electronic state of a molecule are much smaller than those among electronic states of an atom, thus limiting the magnitude of nonlinear interactions. It is shown that this problem can be eliminated by making use of vibronic transitions which, being primarily electronic transitions have much larger matrix elements and efficient conversion can be achieved with molecular systems.

She, C. Y.↗

IGDS/TRAP Interface Program (ITIP). Software User Manual (SUM)

This specification establishes the requirements, concepts, and preliminary design for a set of software known as the IGDS/TRAP Interface Program (ITIP). This software provides the capability to develop at an Interactive Graphics Design System (IGDS) design station process flow diagrams for use by the NASA Coal Gasification Task Team. In addition, ITIP will use the Data Management and Retrieval System (DMRS) to maintain a data base from which a properly formatted input file to the Time-Line and Resources Analysis Program (TRAP) can be extracted. This set of software will reside on the PDP-11/70 and will become the primary interface between the Coal Gasification Task Team and IGDS, DMRS, and TRAP. The user manual for the computer program is presented.

Jefferys, S.↗

On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

Gottlieb, David↗