Fourier sine transform

The Fourier sine transform F, is obtainable by replacing the cosine by the sine in these integrals. 

The most spectacular success of the theory in its quasistatic limit is to show how to film atomic motions during a physicochemical process. As is widely known, photographing atomic positions in a liquid can be achieved in static problems by Fourier sine transforming the X-ray diffraction pattern [22]. The situation is particularly simple in atomic liquids, where the well-known Zernicke-Prins formula provides g(r) directly. Can this procedure be transfered to the quasistatic case The answer is yes, although some precautions are necessary. The theoretical recipe is as follows (1) Build the quantity F q)q AS q,x), where F q) = is the sharpening factor ... 

In the ease of odd functions a Fourier sine transform is used. Thus, if /(x) is an odd funetion, the Fourier transform is... 

The Fourier transform can be used to solve the Dirichlet problem in the inhnite domain, and the Fourier sine transform can be used in the semi-inhnite domain. The Fourier cosine transform is appropriate for the Neumann problem in the semi-infinite domain. 

If fix) is an odd function, its Fourier transform is a Fourier sine transform ... 

Find the one-sided Fourier sine transform of the function ae ... 

The Fourier sine transform of this function yields the swiming speed distribution... 

Figure 4.4 Gross radial distribution function g (r) of polystyrene given by the inverse Fourier sine transform of qi q) according to (4.22). (From Schubach et al.1)...

Figure 11. Tungsten Lm edge EXAFS Fourier sine transforms for the reaction shown by Eq. (2).

Here, Ffpj) is the Fourier sine transform of/(x). If /(x) is an even function, Equation 5.59 can be reinterpreted as... 

When the probability distribution of equation (6) is converted by Fourier sine transformation (c/. Chapter 1, p. 15) to the electron diffraction intensity expression, it is found that the scattered intensity for a given atom pair contains the term... 

Under the same conditions, define the Fourier sine transform of F(x) as follows... 

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