When θ = θ 0, model (3) will undergo a Neimark-Sacker bifurcation at E ( u ∗, u ∗ ) (see Figure 4).
When θ g > θ g ∗ then x g =1 maximizes the function.
Note the expectation E(t ) is taken when the parameters are at Θ(t ).
When TE and TM polarizations are incident at θ = 60°, their simultaneous reflectance spectra in visible wavelengths [400 nm, 750 nm] at three azimuths are shown in Fig. 2.
Given this fundamental design criteria, a dipole antenna was analyzed and built given that it is horizontally polarized around the direction at θ = 90° when horizontally oriented.
The CD8+ replication rate in our model is saturated at θ, and θ/2 occurs when infected cells are equal in number to parameter r, which represents how many epithelial cells need to be infected before half-maximal CD8+ expansion.
On the other hand, although one can always conjecture that, at least when θ is a scalar but P q) and q are still vectors, an equation like (38) below may always be found by proceeding as in the Appendix, the resulting pointwise condition equivalent to (11) will hold in that case only almost everywhere.
When θ ≤ 2, the function f θ ( x ) is strictly increasing; When θ > 2, the function f θ ( x ) has a unique minimum.
Similarly, when k < 1, Fig. 6 also shows that its tangential stress reaches the minimum at θ = 0°and the maximum at θ = 90° both in anisotropic and isotropic formations when θ = 0°.
According to this analysis, borehole wall collapse will occur at the point when θ = 90° and θ = 270°, where the effective pressure differential ( sigma_{theta } - sigma_{r} ) is the greatest.
