i.e., the scalar product of r with the

unit vector [??] is the projection of r in the direction of [??].

The other base pairs are represented as the sum of two

unit vectors for each base, as given by the WS-curve method.

The orientation of the optical axis of the camera is determined by the

unit vector [[??].sub.i] = [[d.sub.ix], [d.sub.iy], [d.sub.iz]].

The realization of SEHAPF connected through FSMPWM has been examined and the results are compared with the classical HCC using

unit vector theory.

The origin of the coordinate system is the center of the Earth, while the

unit vector [??] intersects the Greenwich reference meridian at all times, and [??] is aligned with the planet axis of rotation and is positive northward.

as it follows from formula (17), it is straightforward to obtain also the azimuthal angle [theta] in the spherical representation of the invariant

unit vector n and the angle of rotation [phi], respectively, as

Let [[theta].sub.n] denote an arbitrary

unit vector orthogonal to the subspace < [e.sub.-1], [e.sub.0], ..., [e.sub.n-1] > (which also contains vector [r.sub.n-1]), and [E.sub.n] denote the set of vectors {[e.sub.-1], [e.sub.0], -[e.sub.1], -[e.sub.2], ..., -[e.sub.n-1]}.

As a

unit vector [[??].sub.c] is turned by 90 degrees every time differentiated with respect to time, [[??].sub.c] * [[??].sub.c] = 1, [[??].sub.c] * [[??].sub.c] = 0 , [[??].sub.c] * [[??].sub.c] = -[[OMEGA].sup.2])

The normal

unit vector N is equal to d[h.sup.#] = q, and thus

where [??] and [??] are the

unit vectors of the rotational velocity vector w and the translational velocity vector [??], respectively, and [C.sub.m] is the Magnus coefficient that depends on the spin factor S.

The expansion of the 3-dimensional vector x = [[[x.sub.a] [x.sub.b] [x.sub.c]].sup.*] [member of] [X.sup.(3)] along the ZS

unit vector determines the representation of the 3-dimensional vector by two mutually orthogonal components

If N is the

unit vector normal to the associated wave phase, the electron subject to the frequency [v.sub.0] = [m.sub.0][c.sup.2]/h has traveled a distance dN during a time interval dt, so that we may define an electronic phase [[phi].sub.e] which has changed by: