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Clearly and are not the solutions of (5.1) and Moreover, the assumptions, and of Theorem 3.1 are satisfied by choosing Thus, the conclusion of Theorem 3.1 applies to the problem (5.1).
Laws that discriminate and deny to members of certain groups the right to marry the person of their choosing thus contravene the original meaning of the Fourteenth Amendment.
She said visas are issued about a week before the trip and picked up at Tripoli Airport; the online itinerary, however, includes the following warning: "The Libyan government reserves the right NOT to issue visas to any individual of their choosing, thus visa clearance cannot be guaranteed by Cox & Kings, USA".
Neither I, nor our team, feel it best serves the core message and goals we are seeking to accomplish to be in a fight on an issue not of our choosing, thus I respectfully withdraw my acceptance of the President's invitation.
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Maybe she was chosen thus.
Standard designs and material properties were chosen, thus making the process as realistic as reasonable even at the cost of reducing the options (design variables) available for optimization.
At once a voice arose among The bleak twigs overhead In a full-hearted evensong Of joy illimited; An aged thrush, frail, gaunt and small, In blast-beruffled plume, Had chosen thus to fling his soul Upon the growing gloom.
"You may argue that only two or three nominees are allowed for us to choose, thus virtually barring any chance for a pro-democracy candidate to be considered.
In fact, we choose,,, thus for,.
As in [9], we choose,, thus.
To fulfill property (i) of Theorem 2.8, we choose, thus.
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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