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The phrase "a function of the square" is correct and usable in written English.
It can be used in mathematical or scientific contexts to describe a relationship where one quantity depends on the square of another quantity.
Example: "The area of a square is a function of the square of its side length."
Alternatives: "dependent on the square" or "related to the square."
Exact(24)
Figure 5: Drop deformation as a function of the square of the electric field strength.
Temperature gradient ∇T along the sample as a function of the square of the heating voltage VH at different base temperatures, which is proportional to the heating power.
In particular, the rotational spring stiffness of HBM is a function of the square of cross-sectional area of columns with regular polygonal or circular cross-sectional shape.
Centrifugal force is a function of the square of the train's velocity divided by the radius of the curve; the smaller and tighter the curve, or the faster the train, the greater the centrifugal force.
A plot of the transient charges as a function of the square root of the measuring time gives rise to a non-linear relationship for short times.
Design of a Multiple Compound Parabolic Concentrator, or MCPC, was performed by taking into account both that photocatalytic degradation efficiency is a function of the square root of photon flow intensity that excites the photocatalyst and that TiO2 is able to absorb more sunlight (photons) than the provided in utilising a 1-sun geometric concentration ratio (CR).
Similar(36)
Due to SNR scaling as a function of the square-root of the number of stimuli, we required a minimum of 100 novelty stimulus repetitions to achieve an SNR of 2. 38 The basic stimulus block comprised 1,050 stimuli (100 novel stimuli, 100 deviants, and 850 standards).
b The plots of impedance as a function of the inverse square root of angular frequency in the Warburg region.
Peak signal-to-noise ratio is a standard metric of video quality and is a function of the mean square error between the original and the received video frames.
Each frame also has a peak signal-to-noise ratio (PSNR) [27], which is defined as a function of the mean square error (MSE) between the original and reconstructed frames.
The inertia is the whole table is a function of the Chi-square statistics χ2.
More suggestions(16)
a function of the surface
a function of the space
a function of the acreage
a function of the sphere
a function of the starting point
a function of the between
a multiple of the square
a resident of the square
a fan of the square
a revolution of the square
a percentage of the square
a result of the square
a ratio of the square
a centerpiece of the square
a magnification of the square
a glimpse of the square
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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