scholarly journals Mellin Transform of an Exponential Fourier Transform Expressed in Terms of the Lerch Function

2021 ◽  
Vol 9 (5) ◽  
pp. 724-735
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Fourier Transform ◽  
Mellin Transform ◽  
Exponential Fourier Transform

Thermoelastic Solutions for Thermal Distributions Moving Over Half Space Surfaces and Application to the Moving Heat Source

1988 ◽  
Vol 55 (1) ◽  
pp. 87-92 ◽  
Author(s):  
M. D. Bryant
Keyword(s):  
Fourier Transform ◽  
Heat Source ◽  
Half Space ◽  
Elastic Half Space ◽  
Temperature Wave ◽  
Exact Results ◽  
Moving Heat Source ◽  
Exponential Fourier Transform

A method is developed for obtaining fundamental thermal and thermoelastic solutions for thermal distributions moving over the surface of an elastic half space. This method uses the concept of a moving temperature wave along with a novel form of an exponential Fourier transform. The technique is developed and then demonstrated on the example of a moving heat source. Exact results are matched with results from Carslaw and Jaeger (1959) and Barber (1984).

THE CLASSICAL LIMIT OF REPRESENTATION THEORY OF THE QUANTUM PLANE

2013 ◽  
Vol 24 (04) ◽  
pp. 1350031 ◽  
Author(s):  
IVAN C. H. IP
Keyword(s):  
Fourier Transform ◽  
Representation Theory ◽  
Unitary Representation ◽  
Classical Limit ◽  
Mellin Transform ◽  
Tensor Products ◽  
Quantum Plane ◽  
The Fourier Transform

We showed that there is a complete analogue of a representation of the quantum plane [Formula: see text] where |q| = 1, with the classical ax+b group. We showed that the Fourier transform of the representation of [Formula: see text] on [Formula: see text] has a limit (in the dual corepresentation) toward the Mellin transform of the unitary representation of the ax+b group, and furthermore the intertwiners of the tensor products representation has a limit toward the intertwiners of the Mellin transform of the classical ax+b representation. We also wrote explicitly the multiplicative unitary defining the quantum ax+b semigroup and showed that it defines the corepresentation that is dual to the representation of [Formula: see text] above, and also correspond precisely to the classical family of unitary representation of the ax+b group.

scholarly journals Spectral biometrical recognition of fingerprints

2011 ◽  
Vol 1 (2) ◽  
Author(s):  
Tibor Csongrády ◽  
Elena Pivarčiová
Keyword(s):  
Fourier Transform ◽  
Image Registration ◽  
Access Control ◽  
Control Systems ◽  
Mellin Transform ◽  
Phase Correlation ◽  
Fingerprint Recognition ◽  
Fingerprint Verification ◽  
The Fourier Transform ◽  
Fourier Mellin Transform

AbstractThe article is aimed at fingerprint recognition or verification, which is used mainly in access control systems. The proposed method of fingerprint verification uses image registration (reconciliation) by applying the Fourier-Mellin transform and consequently compares images by the Fourier transform using modified phase correlation.

scholarly journals On the Fourier transform of the products of M-Wright functions

2014 ◽  
Vol 33 (1) ◽  
pp. 245
Author(s):  
Alireza Ansari
Keyword(s):  
Fourier Transform ◽  
Integral Representation ◽  
Mellin Transform ◽  
Integral Representations ◽  
Wright Function ◽  
The Fourier Transform

In this  note, by applying the Bromwich's integral for the inverse Mellin transform we find a new integral representation for the   M-Wright function  $$ M_\alpha(x)=\sum _{k=0}^{\infty }\frac{(-x)^{k} }{k!\Gamma (-\alpha k+1-\alpha )},\quad  \alpha=\frac{1}{2n+1}, n\in \mathbb{N},$$ and state the Fourier transform of this function. Also, using the new integral representations for the products of the M-Wright functions, we get the Fourier transform of it.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

FR-IR Molecular Microanalysis System

1990 ◽  
Vol 48 (2) ◽  
pp. 270-271
Author(s):  
John A. Reffner ◽  
William T. Wihlborg
Keyword(s):  
Fourier Transform ◽  
Fourier Transform Infrared ◽  
Integrated System ◽  
Morphological Examination ◽  
Fully Integrated ◽  
Ir Microscopy ◽  
Normal Functions ◽  
Infrared Microspectroscopy ◽  
Infrared Spectral ◽  
Ft Ir

The IRμs™ is the first fully integrated system for Fourier transform infrared (FT-IR) microscopy. FT-IR microscopy combines light microscopy for morphological examination with infrared spectroscopy for chemical identification of microscopic samples or domains. Because the IRμs system is a new tool for molecular microanalysis, its optical, mechanical and system design are described to illustrate the state of development of molecular microanalysis. Applications of infrared microspectroscopy are reviewed by Messerschmidt and Harthcock.Infrared spectral analysis of microscopic samples is not a new idea, it dates back to 1949, with the first commercial instrument being offered by Perkin-Elmer Co. Inc. in 1953. These early efforts showed promise but failed the test of practically. It was not until the advances in computer science were applied did infrared microspectroscopy emerge as a useful technique. Microscopes designed as accessories for Fourier transform infrared spectrometers have been commercially available since 1983. These accessory microscopes provide the best means for analytical spectroscopists to analyze microscopic samples, while not interfering with the FT-IR spectrometer’s normal functions.

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