(i) [O.sup.wd.sub.k]:

normalized vector of hourly trips originated in zone k on a weekday

where [F.sup.*.sub.l] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are

normalized vector of [F.sub.l] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [L.sub.2] is Euclidean distance metric.

There are four registers in the diagram block: "num," "row," "fac," and "den"; these registers are temporary locations used together with the "Vector Arithmetic Unit" to perform lightly more elaborate operations on the rows; for example, to execute (16), the term [a.sub.ki] is first saved in the register "fac," and then the

normalized vector is multiplied by this factor and added to the internal row of the Core_lu, which is recorded by the register "row."

Dividing each vector element on sum of all components of vector to get

normalized vector, where--

A Lorentzian manifold ([bar.M], [bar.g]) admits a global decomposition as GRW space-time if and only if it has a timelike gradient conformal Killing vector field K, such that the flow of its

normalized vector field, Z, is well defined and onto a domain I x L for some interval I [less than or equal to] R and some leafofthe orthogonal foliation to K.

The relationship between the

normalized vector and the magnetic sensor raw data can be expressed as [3]:

The co-integration

normalized vector is the following:

The

normalized vector of a vector z is denoted by [bar.z]; the set of

normalized vectors is shown as [bar.Z].

Given a space-like vector x in the Lorentz space (V, B), the

normalized vector x of x is given by

Defining a

normalized vector of time when the measured condition states change as follows:

Therefore, the normalized coordinates x, y and z are actually [c.sup.-1][w.sub.c]x, [c.sup.-1][w.sub.c]y and [c.sup.-1][w.sub.c]z, the normalized momenta nx, ny and nz are similarly [([m.sub.e]c).sup.-1][[pi].sub.x], [([m.sub.e]c).sup.-1][[pi].sub.y] and [([m.sub.e]c).sup.-1][[pi].sub.z] and the

normalized vector potential amplitude [A.sub.0] is [m.sup.-1.sub.e][q.sub.e][A.sub.0].

This class of vector fields properly includes the

normalized vector fields of the nowhere zero conformal vector fields (see Section 2).