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In fact, he was dubious that such an optimum exists.
In the theory of the firm, an optimum allocation of outlays among the factors is the same for all factors; the "law of eventually diminishing marginal utility," a property of a wide range of utility functions, ensures that such an optimum exists.
In one limiting case that will be presented, the use of the wrong efficiency definition can lead a process engineer to believe that a theoretical maximum in fuel processor efficiency exists at a particular operating condition, when in fact no such efficiency optimum exists.
If the optimum exists, the algorithm can identify it.
p is strictly convex with respect to the q that ensures an optimum exists.
Comparing the on axis beam number density for various nozzle opening angles, we can see (Fig. 16) that an optimum exists for angles of 40 60° (full cone angle).
Similar(54)
Future work will use elementary mode analysis [ 33] to determine if multiple pathways that lead to the same optimum exist, which is highly likely due to the size and complexity of the network.
It is found that two local optimums exist, where the optimal excitation frequency and electrical damping are analytically obtained.
If this is not the case then this means that another local optimum apparently exists and the analysis should be repeated starting from this optimum.
We derive certain important conditions to determine whether an optimum solution exists.
The DOE results suggested that the optimum point exists at the corner point (not at center point).
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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