r and [alpha] are the geocentric distance and the orbital

polar angle of the mass center O, respectively.

We can calculate a new distribution function of the

polar angle by this formula.

After solving of the algebraic systems the contact pressure was calculated as a function of

polar angle for different values of the free parameters.

By following the procedure described above, we can obtain the differential elements of effective area as a function of the

polar angle orientation.

Caption: Figure 3: Tangential displacement ([u.sup.*.sub.[theta]]) versus

polar angle at r = b for different wave numbers ([k.sup.(2).sub.2]b) for a tunnel in hard soil.

where [[theta].sub.A] is the

polar angle of any point A on the outer raceway.

where [[theta].sub.mi] is the

polar angle corresponding to the midpoint of the arc between adjacent

polar angles [[theta].sub.i] and [[theta].sub.i+1]; [[theta].sub.mi] [approximately equal to] ([[theta].sub.i] + [[theta].sub.i+1])/2

The amplitude [rho] of a tricomplex number is defined as [rho] = [([x.sup.3] + [y.sup.3] + [z.sup.3] - 3xyz).sup.1/3], the

polar angle [theta] of OP with respect to the trisector line (t) is given by tan [theta] = D/S, 0 [less than or equal to] [pi] and the distance from P to the origin is [d.sup.2] = [x.sup.2] + [y.sup.2] + [z.sup.2].

Depending on the location of the pixel in affine covariant region, the relation between the

polar angle of each pixel and the ellipse orientation is summarized in Table 1.

where, [[theta].sub.0] is the

polar angle of the output rays, i.e., the desired radiation direction.