The linear correlation coefficient, as defined by Equation 6 is a dimensionless quantity
. In general, -1[less then or equal to] r [less than or equal to] 1, wherein a "+" sign indicates positive linear correlation, and a "-" sign implies negative linear correlation.
In addition to dimensionless quantity
[theta], for further analysis the dimensionless variables are introduced:
is a dimensionless number group that characterizes the influence of vibration force field on the apparent viscosity of melt; [epsilon] = [A[omega]]/[[pi]D[bar.N]], called vibration impact factor, is a dimensionless quantity
that represents the strength of axial vibration of screw, and [A.sub.z] = [epsilon]xtg[theta], [A.sub.z] = [epsilon]xctg[theta].
In at least one case the author conforms to accepted usage, e.g., the mass-to-charge ratio (m/z) is defined as a dimensionless quantity
, although the physics of the accepted terminology are questionable because a quantity so defined cannot be used in equations of motion for charged particles.
This dimensionless quantity
is defined by the equation
The modal amplitude [h.sub.n] should be found out hereinafter as a dimensionless quantity
. As it follows from Equation (28), the other modal amplitudes, [V.sub.'n] and [I'.sup.n], will be dimensionless, as well.
Another important dimensionless quantity
, the Janeschitz-Kriegl (Jk) number, merely follows the changes in De/St and does not increase our understanding of the problem.
The reference interval width for the W group was compared to that of the T group by using their ratio because this dimensionless quantity
allows for comparisons across analytes.