According to expressions (81)-(84), after the

semiangle [delta] of the sectorial region (82) is given, then we can get the optimal [theta] by maximizing the function R([theta]), and thus the optimal parameters h and v can be computed from the formulas (81).

The external ring of the polar grid defines the feed cone edge with

semiangle [[theta].sub.C].

The probe size for Scanning TEM (STEM) imaging was set to 0.1 nm, with a current of 20 pA and the convergence

semiangle of 24 mrad.

The normalized stress intensity factors are denoted as [Y.sub.I,II] = [K.sub.I,II]/[sigma][square root of ([pi]R sin ([phi]))], and they are plotted as a function of the

semiangle [phi] in Figure 7.

In this study, the rotation quaternion is expressed as q = [(w, x, y, z).sup.T], where w is the cosine of the rotation

semiangle, while x, y, z are the multiplication X, Y, Z coordinates of the rotation axis and the sine of the rotation

semiangle, whereas [w.sup.2] + [x.sup.2] + [y.sup.2] + [z.sup.2] = 1.

We may deduce directly the orbits of rays exiting from the barrier; those falling within a cone of

semiangle [tan.sup.-1] ([square root of 3/2]) = 68.9 degrees go to our telescope at "infinity", forming an image of parallax 6m [square root of 3].

Here, [alpha] is the convergence

semiangle of the lens such that [alpha] = arcsin(NA/n), NA is the numerical aperture, and n is the index of refraction between the lens and the sample.

In Appendix A, a material with uniaxial anisotropy is modeled that has uniform K\n but with each grain having an easy axis randomly selected within the confines of a texture cone, that is, the anisotropy directions are distributed with equal probability within a cone symmetric about the z-axis with

semiangle defined by the variable phideg.

The die geometry for the production of extrudates with the combined properties of high fibril concentration, good structural integrity and auxetic behavior was found to be a die with a cone semi-angle of 45[degrees], die entrance diameter of 15 mm, exit diameter of 9-10 mm and no capillary, and of these parameters, the cone

semiangle was found to be the least significant.

Most people today are using flat-face-geometry dies with a traditional

semiangle of 90 [degrees].

According to (70), we see that once the

semiangle [epsilon] of the sectorial region (49) is given, then one can find the optimal [theta] by maximizing the function R([theta]).