Sentence examples for analogously obtained from inspiring English sources
The proofs of the next four lemmas involving the (psi_{alpha}) function can be found in [7], whereas the proofs for the function (psi_{alpha, 0 }) are analogously obtained by simply replacing L by (L_{0}).
We show that π (m ˜ | α, S ) = π (m ˜ | α, S α, S m ˜ ) ≈ π (m ˜ | α, S m ˜ ), given that S m ˜ is ε-sufficient for m ˜ : Together with an analogously obtained lower bound, we have that (A8) e − ε π (m ˜ | α, S m ˜ ) ≤ π (m ˜ | α, S α, S m ˜ ) ≤ e ε π (m ˜ | α, S m ˜ ) and again S α can be omitted without much loss, if S α does not provide much further information about m ˜ given S m ˜.
From (2.18), one can analogously obtain (2.32).
we analogously obtain that and the pair satisfies.
end{aligned} For the case when (gamma= frac{alpha- sqrt{alpha^{2} + 4beta}}{2}), (gamma= frac{-alpha+ sqrt{alpha^{2} + 4beta}}{2}), or (gamma= frac{-alpha- sqrt{alpha^{2} + 4beta}}{2}), we analogously obtain (lim_{betatoinfty} | mathbf{A} |_{infty}cdot | mathbf{A}^{-1} |_{infty}= 1).
Analogously, we obtained 12 pathways enriched with driver genes that were associated to under-expressed pathways (Table 2).
Analogously we obtain (2.28).
Analogously one obtains the following result.
Analogously, we obtain the sharp estimates for the best constants in (1.4) and (1.5).
end{aligned} (2.7) Analogously, we obtain biglvert S_{v_{0}}bigl v x,t_{2}) bigr -S_{v_{0}}bigr -S_{v_{1})bigr) bigrvert leq 2max bigl{ 1,K vert Omega vert bigr} (t_{2}-t_{1}) bigl( Vert v Vert _{kappa }+ Vert u Vert _{kappa }^{q} bigr).
Analogously, we obtain 1, 333 orthologous pairs in C. elegans and 1, 351 in D. melanogaster.
