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The solution of the problem is reached as the limit of a sequence whose elements are obtained from the minimization of a functional.
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Mr. Edwards's biggest problem is reaching enough voters quickly enough.
For Edward Serotta, as for many other people, the problem is reaching that state of flow to begin with.
With state revenues in free fall, the problem is reaching crisis proportions and creating a legal and moral challenge for the criminal justice system, state legislatures and the legal profession.
His problem is reaching out to swing voters at a time when the number of self-identified Republicans is up to ten points lower than the number of self-identified Democrats.
The problem is reaching near-crisis proportions while President Park Geun-Hye calls for "a second miracle on the Han River" – the broad, twisting waterway that bisects Seoul.
Using antimicrobial drugs (not just antibiotics but also drugs against fungal, viral, or parasitic infections) invariably leads to the spread of pathogens that can tolerate them, and the problem is reaching crisis proportions, health experts widely agree.
Its chief executive, Anna Feuchtwang, said: "With a quarter of 14-year-old girls showing signs of depression, it's now beyond doubt that this problem is reaching crisis point.
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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