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Results for “generalized Hermite functions”

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 NTRS1995

Coherent states for the relativistic harmonic oscillator

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

Aldaya, Victor↗
NASA NTRS1993

A highly accurate Voigt function algorithm

A complex Voigt lineshape algorithm is presented whose maximum relative error over the complex plane is less than 1 x 10(exp -8). The algorithm consists of series, rational approximations and Gauss-Hermite integrations which makes it suitable as a general purpose software module for a wide variety of uses, including a Voigt function standard.

Shippony, Z.↗
NASA NTRS1993

A Highly Accurate Voight Function Algorithm

A complex Voight lineshape algorithm is presented whose maximum relative error over the complex plane is less than 1 x 10 super minus 8. The algorithm consists of series, rational approximations and Gauss-Hermite integrations which makes it suitable as a general purpose software module for a wide variety of uses, including a Voight function standard.

Voight lineshape Doppler velocity distribution col↗
NASA NTRS1973

Algorithm for identification of a single class

The class of nonlinear dynamic systems, which is described by the integral Hammerstein operator is discussed. The input and output signals of the system, the nonlinear amplification coefficient, and weighting function are broken down by linear-independent functions in Hermite and Laguerre polynomials. The algorithm for calculating parameter estimates, and the reduction of the estimates are discussed along with generalization in the case of a multidimensional system, and the physical interpretation of the examined class of systems.

Kaminskas, V. A.↗
NASA NTRS1995

Multiresolution Representation Using Biorthogonal Multiwavelets

We generalize Harten's multiresolution representation to biorthogonal multiwavelets. Several variants are considered. For example, a given array of discrete point values is transformed to point values and derivatives or point 'values and cell averages'. Compact Hermite interpolation is used in the decomposition and reconstruction algorithm. The resulting basis functions that are symmetric or skewsymmetric, compact, and smooth with optimal order accuracy. Harten's approach has several advantages: the multiresolution scheme is inherently discrete, non-periodic boundary conditions are easy to implement, and the representation can be extended to unstructured grids in bounded domains. We demonstrate the compression features of the new mutliwavelets by application to variable scale piecewise smooth functions with jump discontinuities typical of numerical solutions of nonlinear hyperbolic conservation laws.

Warming, Robert F.↗