According to (49), the distortion caused by PCA can be expressed by J = mathbb{E}left[ {{{left| {textbf{h} - {mathbf{h}bar{mathbf{U}}}{{bar{mathbf{U}}}^{H}}} right|}^{2}}} right] = mathbb{E}left[ {{{left| {textbf{h}Delta textbf{U}Delta {textbf{U}^{H}}} right|}^{2}}} right].
A cause-specific hazard can be expressed graphically, but they are not easy to interpret.
The normal stress and the shear strength caused by the landslide can be expressed as, varDelta sigma =rho left 1-rright){g}_zh (11) varDeleft 1-rrightleft(1-rright){g}_zh (11).
Mass flux J a_no_slip caused by pressure difference can be expressed as J_{{{text{a_no_slip}}}} = - frac{{rho_{text{avg}} R_{0}^{2} }}{8mu } times frac{{Delta p}}{L} (11)and absolute permeability is given by K_{{{text{no_slip}}}} = frac{{R_{0}^{2} }}{8}.
So the mass flux J a_slip caused by pressure difference can be expressed as J_{{{text{a_slip}}}} = - F times frac{{rho_{text{avg}} R_{0}^{2} }}{8mu } times frac{Delta p}{L}, (13) F = 1 + sqrt {frac{8pi RT}{M}} times frac{mu }{{R_{0} p_{text{avg}} }} times left(frac{2}{alpha } - 1 right).
Allowing for different values for every outcome prevented or caused by treatment, this can be expressed algebraically as: (5) where m is the total number of treatment benefits, the benefit(2) to benefit(m) are the benefits other than the target one, and k is the number of treatment harms.
Then, the target phase caused by its cross-track motion can be expressed as (13).
Thus, the cumulate interference caused by SUs in Π I can be expressed as I T = ∑ i ∈ Π I P S i p ( r i ) x i, (15).
The mixed output signal, caused by mixing (i.e., multiplying) and, containing both the sum frequency signal and the difference frequency signal can be expressed as (6).
