Since in practice, the

angle variables are affected by vibrations and hardware error, an appropriate white noise was added to

angle variable to make simulation results much closer to real situation.

According to (3) integration over the spherical angle variable [theta]' has been done independently.

As a test of our numerical calculations we have shown convergence of the results as a function of number of grid points [N.sub.P1], [N.sub.P2], and [N.sub.[theta]] for the momentum and angle variables in Table 4.

Thus, the first variable resulting from the model, and required for the process of dialectic synthesis between opposing pairs, is the Angle variable, which defines proportionality between EM and EF.

Thus, in the formation of typological groups the terms Isoschematic (Iso), Masculine Heteroschematic (MH) and Feminine Heteroschematic (FH) can be respectively designated to the fields formed in the vectorial plane according to the influence of the angle variable.

Trials shown in Figure 1 with the

angle variable set high (+) exposed specimens on racks set at 5[degrees] while trials with the

angle variable set low (-) exposed specimens on racks set at 45[degrees] This represents an example of controlling a variable in a natural weathering DOE without introducing an artificial effect.

We notice that in [39], to overcome the barriers of weak smoothness, they made use of exchange of the role of time and

angle variables skills and showed the existence of Aubry-Mather sets and quasiperiodic solutions by employing a version of Aubry-Mather theorem obtained by Pei [37].

However, there tended to be more variability in the symmetry coefficient values for the moment and power variables than for the

angle variables (Figure 3), even in the low LLI group.