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Then, they introduced two sets of variables to formulate such problems: ( x in R^{{n_{1} }}, ) represents the vector of decision variables that their optimal values are not dependent upon the realization of the uncertain parameters.
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The straightforward and effective realization of construction projects is heavily dependent upon the planning of the construction process and the response to project modifications during the construction phase.
Like the emperor's clothes, self-belief vanishes upon the realization that mystical powers don't influence performance.
I cried yesterday upon the realization that he, a childhood hero, was no longer alive either.
It can be observed that for each channel realization, there is an optimum value for η that is dependent upon the instantaneous first and second hop channel matrices.
The way this works is similar to how the realization of impermanence, suffering, and no-self (wisdom) in Hinayana Buddhism is dependent on achievement of concentration which is itself dependent upon the practice of morality (keeping of the precepts).
I am totally dependent upon the affection of women.
Aesthetics are dependent upon the passage of time".
Thus, reading comprehension is dependent upon the quality of literary exposure, not upon age.
They are dependent upon the establishment of policy incentives.
Our Framers intended a Congress "dependent upon the People alone". We instead have a Congress dependent upon "the Funders" primarily.
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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