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If, in addition, t is a prime number, then the multiples of a non-zero residue class run through all the residue classes' mod t, thus a single singular dimension would imply complete singularity which cannot be the case, proving (ii) and the theorem.
After 22 years under the reign of a single, singular mayor and much of the last half-century with someone named Daley at the helm, even the slightest adjustment would feel enormous to Chicago.
The result implies that in the conformal class of the unit Euclidean ball there exist metrics with a single singular boundary point which have flat Q-curvature and constant boundary Q-curvature.
Throughout this section, we focus on solving θ → i = arg min J ( θ → i ) as a least square solution for a single singular vector u → i [ k ], so we drop the subscript "i" from the quantity θ → i and use F and f →, instead of F M ( u → i ′ ) and f → M ( u → i ′ ) to simplify the notation.
In this paper, for each parameter combination, we always found a single singular strategy that was both evolutionary and continuously stable, that is, the singular strategy is a continuously stable strategy (CSS; Maynard Smith 1982).
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(a) The single singular soliton solution (H x,t)) for (k_{1}=0.4).
When he wrote that letter, Melville's scattered ambitions had already consolidated into a single and singular effort.
During four weeks this spring at Danspace Project, the choreographer Melinda Ring has redefined the organization's Platform series by paying homage to a single and singular dance artist: Susan Rethorst.
Directed by Rachel Chavkin ("Natasha, Pierre and the Great Comet of 1812"), one of the show's six co-creators, this play is centered on a single and singular personage named Ann Libby Kingg), a lesbian who works on the floor of a meat processing plant in South Dakota.
If has identical elements, then it has rank one and hence only a single nonzero singular value, that is,.
While there hasn't (thankfully) been a single, sharp, singular defining atrocity in the Middle East like 9/11, the earnestness of the Qatari messaging about the badness of the Islamic State is reminiscent of post-9/11 counterterrorism discussions in the US.
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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