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Because the two parts of the Liouville operator do not commute L1 L2 ≠ L2 L1, one must rely on the Trotter theorem [ 5] to develop the argument of the exponential: (49) exp i L Δ t = exp i L 1 + L 2 Δ t ≈ exp i L 2 Δ t 2 exp i L 1 Δ t exp i L 2 Δ t 2 + O Δ t 3.
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JS, FO, FB and PV have made substantial contributions to developing the arguments of the article, critically revised the article for important intellectual content, and read and approved the final version of the manuscript.
Let us develop the argument under one of these stronger assumptions.
NB: The analytical approach used to develop the argument, and several of the terms used in the following section pertain to the fields of risk analysis and systems engineering.
Since a review of the relationship between mortality and quality of care found no empirical studies that directly report the relationship between SMRs and preventable mortality, 21 we develop the argument from a number of plausible scenarios using a mathematical model for hospital mortality rates.
And while they did retain an expert on substance abuse, they did not develop the argument that Ms. Johnson's history of drug abuse (she was a methamphetamine-user) influenced her conduct.
Like their critics, however, they fail to develop the argument, or to confront the association of textualism and conservatism in contemporary legal and political rhetoric.
This essay develops the arguments for a radically different definition of a biomaterial.
From these premises she developed the argument that mothers, by virtue of their maternal work, cannot countenance violence, whether in social settings like the playground or the workplace, or as an instrument of state policy.
Second, it develops the argument that on the basis of their great potential for (a) promoting economic growth and (b) enhancing place identity of cities, both built heritage and innovative design of space appear to be expansively used as major components of contemporary strategic plans of cities for the transformation and improvement of urban landscape.
KP & LD (a) contributed substantially to developing the line of argument and the interpretation of data over the last 7 years, and (b) reviewed and revised the manuscript critically for important intellectual content.
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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