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The lower inverse of a point y ∈ Y of a set-valued map T is the set-valued map T l of Y into X defined by T l ( y ) = { x ∈ X : y ∈ T ( x ) }. Analogously, lower inverse of a subset of B ⊂ Y is defined as T l ( B ) = { x ∈ X : T ( x ) ∩ B ≠ ∅ }.
In contrast, for both CD4 count strata, best fits to the data were obtained with a 40% to 60% increase in the effectiveness of 3rd and 4th line HAART, with analogously lower failure/discontinuation rates.
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Analogously the lower good-deal bound (pi ^{l}_{cdot }left (Xright)) and corresponding hedging strategy can also be computed, but under the worst-case measure (P^{underline {a}}in mathcal {P}_{[underline {a},overline {a}]}) for "minimal" volatility matrix (underline {a}).
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 ˜.
The concept of lower bound is defined analogously.
Analogously, the narrower specimens presented a lower residual flexural strength than did the wider ones.
Analogously, patients with histological MVI had lower median OS compared to those without (P < 0.001; 63 vs. >147 months; Fig. 2A).
One can analogously show that the integral along the lower side tends to the same number.
Analogously, we indicate the negative changes (those lower than the threshold) with an arrow pointing downwards.
Analogously, APAO transcript was confirmed to be lower in tumor samples than in the normal tissue (p < 0.01).
Analogously, Grice et al. (1984) identified a lower bound on UCIP performance, providing a test of extreme capacity limitations.
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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