Caption: Figure 2: Effect of the

Gaussian shape parameter ([epsilon] [less than or equal to] 1.5) on the result accuracy for the conventional Kansa scheme computed at Re = 10 with t = 0.5, [DELTA]t = 0.005, and N = 10x 10.

G--line of

Gaussian shape. L--line of Lorentzian shape.

For a case, when the FM index is high, that is, Bv is small enough compared to [square root of ([P.sub.v])], the final spectrum follows the

Gaussian shape.

Figure 4 shows that a cut across this resolution-limited Bragg peak follows a

Gaussian shape function exp[- (x - < x >)2/2[[sigma].sub.x.sup.2]] in the horizontal direction.

The nonlinear interaction has been studied for two wave crests of

Gaussian shapeThe fact that there are very few extreme values, as well as the resemblance with the Gaussian distribution will lead to the conclusion that the resulted distribution will tend to agglomerate near its mean value (for a sufficiently long period of time the Law of Large Numbers (LLN) applies)--the phenomenon is graphically described in Fig.1--keeping the

Gaussian shape, but altering the kurtosis parameter of a normal distribution, becoming, in fact, a normal shaped leptokurtic distribution.

(1) Transform the original data so as to achieve a distribution that is as close as possible to

gaussian shape. The original algorithm used the Box-Cox transformation for this purpose.

The

Gaussian shape of the duty-cycle histogram means this parameter has a central value affected by noise.

The Gaussian filter features a

Gaussian shape in both the time and frequency domains and does not ring like the raised cosine filters.

When the laser beam passes through an absorbing solution, the heat generated in the sample has the same

Gaussian shape as the laser light.

In Figure 3, the u profile is shown at t = 2 and t = 20 in order to illustrate the initial adjustment of the wave profile from its initial

Gaussian shape, the formation of Nor dispersive shock waves behind the leading front, and the number of waves that are formed as functions of the viscosity coefficient.

1(a) that the profile of DP(x, z) does not remain invariant on propagation, but turns into a

Gaussian shape gradually with increasing propagation distance, and the effect of depolarization at the point x = 0 becomes stronger when the QHG beam travels a further distance.

In all of these simulations the two-stage transformation was used to convert the data to a

gaussian shape. The last row of Table 1, referred to as Gaussian*, gives the results for the estimator ([bar.x] + 1.96s), without any transformation being used, using well-known approximate results quoted, for example by Bland (5).

The GOS tends to a

Gaussian shape knwn as the Bethe Ridge with a half width in [nm.sup.-1] approximately given by 35 [square root of ([E.sub.B])] where [E.sub.B] the binding energy is in Hartrees.

To avoid the artificial edge diffraction resulting from the finite length of the simulated rough surface, the incident wave can not be simply chosen as a plane wave, and should be expressed as a Gaussian beam which has a

Gaussian shape with half-width W centered at [r.sub.s] = 0 in the z = 0 plane.