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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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Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. Here, the simple explicit result exhibits connections between group theory, combinatorics, and Fourier analysis, especially in the large spin limit. Salient intuitive features of the formula are illustrated and discussed.
MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.
Time-dependent aerodynamic forces with application to a wing deforming harmonically according to a general polynomial equation
Least squares estimation of regression coefficients of balanced polynomials
Digital polynomial and adaptive feedback control system techniques for large launch vehicle guidance, stability, and control
Perturbation theories for equations of celestial mechanics, obtaining analytical solutions in terms of Chebyshev polynomial series
Michailov criterion for exponential polynomials, determining existence of zeros in right half-plane
Computer program ETC improves computation of elastic transfer matrices of Legendre polynomials P/0/ and P/1/. Rather than carrying out a double integration numerically, one of the integrations is accomplished analytically and the numerical integration need only be carried out over one variable.
Hamiltonian for free particle of arbitrary spin and mass formulated in terms of spin matrix polynomials, noting independence of expansion coefficients
Filter properties of least square fitted polynomials
Manual calculations of ionospheric parameters by single polynomial analysis of ionograms
Classification of experimental designs relative to polynomial spline regression functions
Polynomial smoothing formulas and derivative formulas for one or two independent variables
Differential-difference properties of generalized Jacobi polynomials
Single polynomial analysis of ionograms, determining electron density profiles from small number of measured heights
Application of polynomial-smoothing formulas and related derivative-estimating formulas simplifies certain linear least-squares problems. These problems can then be solved by a computer method.
Polynomial method for approximating radiation intensity from plasma light source represented by Abel transforms
Linear physical chains with Sturm-Liouville characteristic polynomials used for natural frequency determination of coupled harmonic oscillators or electrical analog