Fast algorithm for the computation of the zero-order Hankel transform

AbstractThis paper endeavors to formulate a stable and fast algorithm for the first time that is quite accurate and fast for numerical evaluation of the Hankel transform using wavelets which are usually difficult to solve analytically so it is required to obtain the approximate solution. So we have proposed an approach depending on separating the integrand $rf(r){J_\nu}(pr)$ into two components, the slowly varying components $rf(r)$ and the rapidly oscillating component ${J_\nu}(pr)$. Then either $rf(r)$ is expanded into wavelet series using wavelets orthonormal basis which are first derived and truncating the series at an optimal level or approximating $rf(r)$ by a quadratic over the subinterval using the Filon quadrature philosophy. A good covenant between the obtained solution and some well-known results has been obtained. The solutions obtained by proposed wavelet method indicate that the approach is easy to implement and computationally very attractive. The novelty of our method is that we give error analysis for wavelet method for the first time in literature.

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Fast computation of zero order Hankel transform

Journal of the Franklin Institute ◽

10.1016/0016-0032(83)90098-4 ◽

1983 ◽

Vol 316 (4) ◽

pp. 317-326 ◽

Cited By ~ 5

Author(s):

K. Gopalan ◽

C.S. Chen

Keyword(s):

Hankel Transform ◽

Zero Order ◽

Fast Computation

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Strain measurement in In0.2Ga0.8As/GaAs quantum wires by convergent beam electron diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100138592 ◽

1995 ◽

Vol 53 ◽

pp. 444-445

Author(s):

S. Hillyard ◽

Y.-P. Chen ◽

J.D. Reed ◽

W.J. Schaff ◽

L.F. Eastman ◽

...

Keyword(s):

Electron Diffraction ◽

Semiconductor Lasers ◽

Quantum Wire ◽

Quantum Wires ◽

Convergent Beam Electron Diffraction ◽

Zero Order ◽

Beam Electron ◽

Local Lattice ◽

Device Applications ◽

Convergent Beam

The positions of high-order Laue zone (HOLZ) lines in the zero order disc of convergent beam electron diffraction (CBED) patterns are extremely sensitive to local lattice parameters. With proper care, these can be measured to a level of one part in 104 in nanometer sized areas. Recent upgrades to the Cornell UHV STEM have made energy filtered CBED possible with a slow scan CCD, and this technique has been applied to the measurement of strain in In0.2Ga0.8 As wires.Semiconductor quantum wire structures have attracted much interest for potential device applications. For example, semiconductor lasers with quantum wires should exhibit an improvement in performance over quantum well counterparts. Strained quantum wires are expected to have even better performance. However, not much is known about the true behavior of strain in actual structures, a parameter critical to their performance.

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