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It is shown that for any continuous flow reactor, isothermal or not, supporting any system of first order reactions, there exists always a batch reactor or plug flow reactor whose performance is better (or at least no worse) for that reaction system.
and clearly it exists always a set of positive values p k, m q, p q max ( k ) ∈ R + such that p q max ( k ) > p k, m q ≥ ( e R q 0 − 1 ) 1 a I q ( k, m ) ∀ k ∈ V N q, m ∈ V M q, q ∈ Ω. (75).
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It is well known that (A^{dagger}) always exists for any A and is unique; see, e.g., [3 5].
I'm not sure why, but the idea that Truth existed was always an issue beyond debate for me.
There always exists a value for a real-time user utility function parameter when, indicated as such that when then there is no such that (C.1).
There always exists a value of a real-time user i utility function parameter when, denoted as, such that, and hence when.
We remark that for an arbitrary gauge δ on [ a, b ] there always exists a δ-fine partition of [ a, b ].
For strained 2D islands there always exists a total energy minimum for a particular island size [23, 30].
There always exists a subset of patients with a very aggressive natural history, who are likely to fail to respond to chemotherapy.
These works assume that the set of given links is always feasible, i.e., for such a set, there always exists a solution to the power allocation problem.
There always exists an upper bound of a real-time user's utility function parameter, when, denoted as, where (D.1).
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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