For a reduced shear g ~ and unlensed complex ellipticities \ chi _ s ~ and \ epsilon _ s ~, the lensed ellipticities are
32.
The special cases of linear and circular polarization correspond to an ellipticity ? of infinity and unity ( or ? of zero and 45?) respectively.
33.
More accurate methods that consider the Earth's ellipticity are given by Vincenty's formulae and the other formulas in the geographical distance article.
34.
To measure this tangential alignment, it is necessary to measure the ellipticities of the background galaxies and construct a statistical estimate of their systematic alignment.
35.
Typically, the intrinsic ellipticity is much greater than the shear ( by a factor of 3-300, depending on the foreground mass ).
36.
Using mean residue ellipticity facilitates comparing the CD of proteins of different molecular weight; use of this normalized CD is important in studies of protein structure.
37.
The reflected light has a change in Kerr rotation and Kerr ellipticity which is measured by an analyzer and corresponds to either a logical 0 or 1.
38.
The fundamental problem is that galaxies are not intrinsically circular, so their measured ellipticity is a combination of their intrinsic ellipticity and the gravitational lensing shear.
39.
The fundamental problem is that galaxies are not intrinsically circular, so their measured ellipticity is a combination of their intrinsic ellipticity and the gravitational lensing shear.
40.
Cross-coupling can be caused by rotation of Earth leading to mixing of fundamental spheroidal and toroidal modes, or by aspherical mantle structure or Earth s ellipticity.
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