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The phrase "a minimum is achieved" is correct and usable in written English.
It can be used in contexts where you are discussing optimization, performance, or measurements, indicating that the lowest possible value has been reached.
Example: "After several iterations of the algorithm, a minimum is achieved in the error rate, leading to improved accuracy."
Alternatives: "a minimum has been reached" or "a minimum value is obtained."
Exact(2)
For locations south of the southern hemisphere current focus but still away from the auroral region, H decreases from dawn to about noon, when a minimum is achieved; it later increases up to dusk (the overhead vortex in the northern hemisphere circulates anticlockwise while the overhead vortex in the southern hemisphere moves clockwise).
When first trained with a novel object at a single orientation, subjects learn to recognize the object with progressively smaller reaction times until a minimum is achieved [ 36].
Similar(58)
In addition, since the full minimum for the first of (24) may be not available, we relax the result by assuming that a local minimum is achieved and that the target function in this local minimum x t+1 is smaller than or equal to the function value in x t.
But when that minimum is achieved, everything is possible.
Clearly this minimum is achieved when.
and the minimum is achieved when U Y = Ur,1.
The minimum is achieved for, with satisfying the recursive equation: (16).
The treatment level at which this minimum is achieved will be referred to as the optimal constant level.
Moreover, setting ni = N/ k into (1.10) shows that the minimum is achieved at the optimal number of subnets k = N, irrespective of the functional form of f.
Table 1 Result table (AMOS 22 Output) Minimum was achieved Chi square = 25.212 Degrees of freedom = 17 Probability level = 0.090.
Concentrations of 2−3 nm neutral particles and ions decreased by approximately the same factor, and their concentration minima were achieved a bit later than those of smaller particles.
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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