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If we choose a conjugate prior, a closed-form expression can be given for the posterior.
For a uniformly sampled data set of impulse response type a closed form expression can be given for the Fisher information using the solution of a Lyapunov equation.
The final expression can be given by begin{array}rcl@ Pleft Sge k right)=1-Pleft(S
The exact BER expression can be given by Figure 6 The allocated power to different ELs with the proposed power distribution scheme and the optimal power distribution scheme.
The Langmuir expression can be given in the linearized form: frac{1}{q_{mathrm{e}}}=frac{1}{X_{mathrm{m}}b{c}_{mathrm{e}}}+frac{1}{X_{mathrm{m}}} (5).
A similar expression can be given for the second order moment: E u 2 | E ≈ ζ 2 ( E, 0 ) + ∑ n = 1 + ∞ ∂ n ζ 2 ∂ ν n w = 0 E ν n n !
Similar(52)
Similar expressions to Equation 26 can be given for u(t) ≤ 0 and g0 ≤ 0. There is one error equation (with g i, a i and u i ) as Equation 24 for each diagonal reaction.
Combing (24) with (20), the exact expression for the intercept probability can be given by P intercept = ∏ m = 1 M λ r m d λ r m d + λ r m e (25).
Therefore, the expression for (u_{b}) and (v_{b}) can be given as u_{b} = - zfrac{{partial w_{b} }}{partial x},quad v_{b} = - zfrac{{partial w_{b} }}{partial y} (3).
Consequently, the expression for (u_{s}) and (v_{s}) can be given as u_{s} = f z frac{{partial w_{s} }}{partial x},quad v_{s} = f z frac{{partial w_{s} }}{partial y} (4).
The success of these revivals is a reminder that such works were written for the stage and, it is often argued, can be given full expression only by stage representation.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com