By taking the upper limit as i → ∞, we get ε s ≤ lim sup i → ∞ d ( x m i + 1, x n i ).
Firstly, the accurate nonlinear coupled kinematic and dynamic equations of the upper stage body, the two-axis gimbal and the GT are derived by taking the upper stage as a multi-body system.
end{aligned}Now, by taking the upper limit when (nrightarrow infty ) in above inequality we get begin{aligned} underset{nlongrightarrow infty }{lim sup },S y_{n},y_{n},t le 2 underset{nlongrightarrow infty }{lim sup },S y_{n},y_{n},x_{n})+ underset{nlongrightarrow infty }{lim sup },S t,t,x_{n})=0.
end{aligned} (6 Similarly by taking the upper limit when (nrightarrow infty ) in (6), we obtain begin{aligned} S y,y,Ty)=,&& underset{nlongrightarrow infty }{lim } S fx_{2n},fx_{2n},gTx_{2n+1})le q max {S y,y,Ty),0,0,S y,y,Ty))}, end{aligned}that is, again it follows that (Ty=y).
Thus, by taking the upper limit as n → ∞ first, and then m → ∞ the last inequality, it follows from z m → x ˜ and (3.13) that lim sup n → ∞ 〈 f ( x ˜ ) x ˜ →, x n + 1 x ˜ → 〉 ≤ 0. Finally, we prove that x n → x ˜ as n → ∞.
end{aligned} Thus, by taking the upper limit as (ntoinfty) first, and then taking the upper limit as (tto0), it follows from (z_{t,n}totilde{x}) and (3.17) that limsup_{tto0}limsup_{ntoinfty} bigllangle overrightarrow{f tilde{x} tilde{x}},overrightarrow {x_{n+1}tilde{x}} bigrrangle leq0.
By taking the minimum upper bound for each case, the sum-capacity C DDF can be expressed as Fig. 5 The achievable rate regions and sum-capacities of DDF relaying mode for different interferences cases.
By the definition, taking the upper limit on both sides of the above inequality as (t to + infty) results in mathop{overline{lim}}_{t to + infty} V ( y,z ) le R^{2}.
The associated upper and lower 95% confidence limits by weather condition were obtained by taking the exponential of the upper and lower 95% confidence limits of the estimated βs.
My date and I would have an inexpensive, romantic and scenic evening by taking the subway to upper Broadway in Manhattan, walking to Riverside Drive and boarding an open double-decker bus to Lower Manhattan.
The axis separating the two regions is computed by taking the two-thirds upper and one-third lower bounds on all snake points.
