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Fourier cosine series

If / is an even function on the interval (—it, 7t) its Fourier coefficients have the values [Pg.352]

This is the Fourier cosine series corresponding to / on the interval (0, Jt) with [Pg.352]

A complex number is defined as z = a + ib, where a and b are real numbers and i = V a complex variable is defined as z = x + iy. When complex numbers are involved, [Pg.353]


If the function f x) is an even function, all of the bn coefficients will vanish, and only the cosine terms will appear in the series. Such a series is called a Fourier cosine series. If f x) is an odd function, only the sine terms will appear, and the series is called a Fourier sine series. If we want to represent a function only in the interval 0 < a < L we can regard it as the right half of an odd function or the right half of an even function, and can therefore represent it either with a sine series or a cosine series. These two series would have the same value in the interval 0 < X < L but would be the negatives of each other in the interval — L < jc < 0. [Pg.175]

The series representing fix) is called a Fourier-Sine series. Similarly, we can also express functions in terms of the Fourier-Cosine series... [Pg.664]

COMPASS. COMPASS is an example of a Class II force field parameterized by using an analytic representatiOTi of the ab initio (e.g., HF/6-31G ) potential energy surface. The functional form of the COMPASS force field is the same as CFF93 and includes an out-of-plane potential term (angle X), a U 6-9 potential as well as nonharmonic terms for bond stretching and angle bending, a Fourier cosine series for torsion, and a number of cross-coupled terms for the bonded interactions. The form of the COMPASS force field described in detail by Sun [12] is... [Pg.64]

This assumption may be generalized to include loops having an arbitrary current distribution represented by the following Fourier cosine series (Werner, 1996 Storer, 1956) ... [Pg.1504]

Independent evidence for free rotation in nitromethane has come from an analysis of its microwave spectrum, which has shown that the potential barrier restricting internal rotation is only 25.2Jmol for thermodynamic purposes this barrier is eflFectively zero. The low barrier in nitromethane is believed to be due to the possession of 6-fold S3rm-metry about the internal rotation axis. A Fourier cosine series expansion of the restricting potential in the form ... [Pg.283]

Internal Rotation of an Asymmetric Top restricted by an n-Fold Potential Barrier. A Fourier cosine series expansion of the internal rotation potential for a top having 2-fold symmetry about the axis of rotation may be expressed as ... [Pg.292]

This single-domain SmI sample enables one to obtain high quality X-ray data describing the bond-orientational order. In order to characterize the bond-orientational order quantitatively, a nonlinear least-squares fit of the data between 60° and 120° to the following Fourier cosine series [90]... [Pg.1442]

The detailed solution for Eg. flO.SI will not be shown here only the final result will be presented. The details will be left as an exercise for the reader. Keep in mind that the procedure for solving such a type of PDE is similar to that shown in Sec. 10.7. However, in the final stage, the expansion for f (x), as the initial condition, should become eguivalent to the half-range Fourier series, namely, the Fourier cosine series. [Pg.327]

If the function fix) is an even function, all of the Z> coefficients will vanish, and only the cosine terms will appear in the series. Such a series is called a Fourier cosine series. If / (x) is an odd function, only the sine terms will... [Pg.143]

Exercise 11.5. Find the Fourier cosine series for the even function... [Pg.144]

The linear combination shown in Eq. (14.3-24) is called a Fourier sine series. Fourier cosine series also exist, which are linear combinations of cosine functions. The Fourier coefficients a, a2,... must depend on t to satisfy the wave equation. With the initial condition that the string is passing through its equilibrium position at... [Pg.635]

Both the X-ray scattering,7>i ii and the electron diffraction experiments scan the scattering intensity as function of the angle of rotation in the plane, S(x)- Long range BO order implies a six-fold modulation in S(x)- Indeed, both types of experiments exhibit such a modulation, on both thick and thin films. Quantitatively, this modulation is analyzed using the Fourier cosine series,... [Pg.57]


See other pages where Fourier cosine series is mentioned: [Pg.176]    [Pg.212]    [Pg.164]    [Pg.194]    [Pg.201]    [Pg.248]    [Pg.191]    [Pg.185]    [Pg.352]    [Pg.726]    [Pg.176]   
See also in sourсe #XX -- [ Pg.175 ]

See also in sourсe #XX -- [ Pg.352 ]

See also in sourсe #XX -- [ Pg.175 ]

See also in sourсe #XX -- [ Pg.130 ]

See also in sourсe #XX -- [ Pg.1254 ]




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