Sentence examples for with some manipulations from inspiring English sources

With some manipulations on (26), we can have the following test statistic z = ∑ i = 1 l m i ( r + s A ) η i γ i - m i r - s A η i γ i + ( γ i - 1 ) ln m i ( r - s A ) m i ( r + s A ) + ln m i ( r - s A ) m i ( r + s A ). (27).

In this way, with some manipulations, the throughput of the basic ARQ approach is found as η Basic = N ∑ m = 1 M + 1 R m ∏ l = 1 m − 1 Pr log ( 1 + γ l ) < R Pr R ≤ log ( 1 + γ m ).

given by (A.5) into the integral in (A.4) with, the coefficient after some manipulations, has the following closed-form expression: (A.6).

Other cases can be similarly derived with some tedious manipulations.

With some straightforward manipulations of (17) and using the fact that, the average sum MSE (objective function of (20)) can be alternatively expressed as follows: (29).

With some algebraic manipulations, we can derive the following expression for the expected value of WTP from Eq. 8. mathrm{WTP}=sqrt{frac{left(exp {left(Eleft({mathrm{WTP}}_i^{mathrm{IHS}}right)right)}^2-1right)}{2}} (12).

With some algebra manipulations, we may express the n-step ahead prediction probability (hat {b}(t + n)) as hat{b}(t + n) = frac{beta}{alpha+beta}-frac{beta}{alpha+beta} (1 - alpha - beta)^{n}+(1 - alpha - beta)^{n}b t).

It has been described that LFS (low-frequency stimulation) and HFS (high-frequency stimulation), respectively, produce striatal LTD (long-term depression), whereas LTP (long-term potentiation) is generated only with HFS or with some pharmacological manipulations (Calabresi et al., 1992a).

As in the calculation of the mean value, one can use the definition combined with some algebraic manipulation to show that, if R has the binomial distribution, then Var R) = npq.

Rather, like FarmVille or SimCity Social or other popular Facebook games, it tugs you to keep playing with some psychological manipulation.

Next, using Eq. (5.11) in [40], with some algebraic manipulation, the average SER for QPSK modulation scheme at high SNRs can be written as bar P_{s_{j}rightarrow r}approxfrac{2(1+K)}{pi}int_{0}^{frac{pi}{2}}frac{e^{-frac{Kbar{gamma}sin^{2}{theta}}{1+K+frac{1}{2}bar{gamma}sin^{2}{theta}}}}{1+K+frac{1}{2}bar{gamma}sin^{2}{theta}}dtheta (27).