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This shows that ({underline{mathbf{X}}}) = ({underline{mathbf{Y}}}) for all states connected toward Y. Now this argument can be repeated for all states connected toward Y instead of X.
Let Y be a state and (X_{1}, ldots, X_{k}) the states connected toward Y. Then the following hold.
In this manner, the following criteria can be found: Let Y be a state and ( X_{ 1}, ldots,X_{k} ) the states connected toward Y.
Therefore, the assumption that for some state X connected toward Y it holds ({underline{mathbf{X}}}) ({underline{mathbf{Y}}}) cannot be true.
If for some state Y at time t for all states X connected toward Y it holds (X t)) (ge Y t),) and at least one state X connected toward Y exists with (X t) > Y t)) then (Y t)) is strictly increasing at (t,mathbf{d}Y t)/mathbf{d}t > 0).
If for some state Y at time t for all states X connected toward Y it holds ( X t) le Y t),) and at least one state X connected toward Y exists with (X t) < Y t)) then (Y t)) is strictly decreasing at (t:mathbf{d}Y t)/mathbf{d}t < 0). .
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The diffuse vascular bundles of node I are assembled in internode I to form large vascular bundles that connect toward the panicle tissues [ 26, 35].
The tits on stage were more like udders, pulling the 50-year-old frames they were connected to toward the floor.
The endpoints are next connected together toward the center of the cornea, forming a curve that resembles spiral patterns.
After most of his shots that connected, Miller turned toward the Sixers' fans in the front row and stared as he trotted down the court.
And with the latest arms sales, important pieces are coming together that, when connected, will bring toward fruition a project that American officials have pursued for years.
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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