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The phrase "active core" is correct and usable in written English.
It can be used in contexts related to fitness, biology, or systems theory, referring to the central or most important part that is engaged or functioning actively.
Example: "To improve your overall strength, it's essential to focus on exercises that target your active core."
Alternatives: "engaged center" or "dynamic nucleus."
Exact(56)
A structure activity relationship study indicated that the active core of DH is the C-terminal hepta-peptide, LWFGPRLa.
The C-terminal hexapeptide proved to be the active core, the minimum sequence required to retain significant diuretic activity.
An increase in the number of hydrophobic atoms in the active core of drug -target interface further increases the biological activity of the drug lead.
A cross-talk between the active core and the regulatory domain in CBS modulates its enzyme activity.
In more conservative dioceses, especially, they're often the active core of parish life, fundraising, community service and so on.
The active core of a nuclear reactor splits atoms in two to produce bursts of energy and, as a byproduct, large masses of highly radioactive particles.
It may seem odd at first, but the casual watersport is a pleasantly easy way to admire the skyline from the lake, and getting a surprisingly active core workout at the same time.
The active core of these systems is the biomixture.
The active core of QDCL is based on a bound-to-continuum design.
Similar(2)
A significant decrease over time in the hemodynamic values, respiratory rate, and shivering was seen in the active core-rewarming group when compared with the controls.
Data are expressed as mean (s) *Significant differences between active-core rewarming and passive-external rewarming (P < 0.05).
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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