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The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn Banach theorem.
Then, the basic ability of the coupled model to reproduce (1) the drawdown of a surface fluid observed in square-pillar experiments, using pillars filled with only fluid or with fluid and a porous medium and (2) the migration of saltwater (salt concentration 0.5%) in the porous medium using the pillar filled with fluid and a porous medium was evaluated.
Supposing that the system is permanent, the drawdown of a well with r 0 radius is given by Dupuit formula: Delta_{{r_{ 0} }} = frac{Q}{2pi T};; times ;;{text{Log}};;frac{R}{{r_{0}^{2} }}.
They are responsible for the slowest economic recovery ever, the biggest debt increases ever, a massive tax increase on the middle class, the relentless buildup of the regulatory state, and the swift, mindless drawdown of a military that was generations in the making".
Similar(56)
In the 10 days since bin Laden's death, many legislators have called for the United States to speed its withdrawal from Afghanistan, beginning with Obama's planned drawdown of an unspecified number of troops this summer.
I think the ultimate question, when you talk about a withdrawal, or a drawdown of any sort, is what comes after, and what's the Afghan part in this?
Assuming the recommended drawdown of 4 percent a year, a nest egg of $750,000 might be needed.
In that event, pressure would build for repeated drawdowns of a reserve intended for use only during genuine threats to national security.
Mr. Bush's claim that things were going so well in Iraq that he could "accept" his generals' recommendation for a "drawdown" of forces was a carnival barker's come-on.
He said such a strategy could lead to a significant drawdown of troops within a year or slightly longer.
A classic example is the debate over when we're due for a market correction (a drawdown of at least 10 percent) or a bear market (a drawdown of 20 percent or more).
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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