scholarly journals The prosaic Laplace and Fourier transform

1995 ◽  
Author(s):  
G. A. Smith
Keyword(s):  
Fourier Transform ◽  
Laplace And Fourier Transform

Generalized GL Fractional Derivative and Its Laplace and Fourier Transform

2009 ◽  
Author(s):  
Manuel D. Ortigueira ◽  
Juan J. Trujillo
Keyword(s):  
Fourier Transform ◽  
Linear System ◽  
Fractional Derivative ◽  
Frequency Response ◽  
Fourier Transforms ◽  
Laplace And Fourier Transforms ◽  
Riesz Fractional Derivative ◽  
Laplace And Fourier Transform

It is well known the difficulties that the Riesz fractional derivative present, as the spatial fractional derivative involved in many models of the dynamics of anomalous processes. The generalized Gru¨nwal-Letnikov fractional derivative is analysed in this paper. Its Laplace and Fourier Transforms are computed and some current results criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.

On Dynamics of Bar of Rectangular Cross Section

2000 ◽  
Vol 68 (4) ◽  
pp. 662-666 ◽  
Author(s):  
N. B. Rassoulova
Keyword(s):  
Fourier Transform ◽  
Closed Form ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Original Method ◽  
The Body ◽  
Closed Form Solutions ◽  
Nonstationary Waves ◽  
Parameters Inversion ◽  
Laplace And Fourier Transform

The propagation of nonstationary waves in semi-infinite elastic rectangular bars is studied. It is assumed that two opposite lateral surfaces of the body are free of forces, while the two others are subjects to cross conditions. By introducing three new potential functions, the author succeeded in getting closed-form solutions in Laplace and Fourier transform parameters. Inversion of the transform solutions, carried out by an original method of inversion, is suggested herein.

scholarly journals A mathematical model for the spread of oil spills in high seas

2021 ◽  
Vol 1 (1) ◽  
pp. 9
Author(s):  
Bambang Hendriya Guswanto ◽  
Kiran Nirmala Achfasarty ◽  
Ari Wardayani
Keyword(s):  
Mathematical Model ◽  
Fourier Transform ◽  
Oil Spill ◽  
Oil Spills ◽  
Random Walk Process ◽  
The Fourier Transform ◽  
The Mathematical Model ◽  
Laplace And Fourier Transform ◽  
Oil Particles ◽  
High Seas

This study aims to model the distribution pattern of oil spills in high seas with the influence of wind movements. The mathematical model is derived from the random walk process of the oil spill particles by using a probability measure on a unit circle with the help of Laplace and Fourier transform . The solution to the model is also obtained by using Laplace and the Fourier transform. Based on the analysis of the solution of the model, the oil spill tends to spread in the direction of wind movement.. The speed and direction of the wind movement affect the speed and direction of the spread of the oil spill particles. The larger the speed of wind movement, the faster the oil particles movement.

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.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

Fourier transform infrared spectrum of 13C32S2 in the 3v3 band region

1996 ◽  
Vol 89 (4) ◽  
pp. 1145-1155
Author(s):  
JACQUES WALRAND ◽  
GHISLAIN BLANQUET ◽  
JEAN-FRANCOIS BLAVIER ◽  
HARALD BREDOHL ◽  
IWAN DUBOIS
Keyword(s):  
Fourier Transform ◽  
Infrared Spectrum ◽  
Fourier Transform Infrared ◽  
Band Region
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