The phrase "a linear dependence over" is correct and usable in written English.
It is typically used in mathematical or theoretical contexts to describe a relationship among vectors or functions in a vector space.
Example: "In this case, we can conclude that there is a linear dependence over the set of vectors provided."
Alternatives: "a linear dependence among" or "a linear dependence within".
The electrochemical sensing of nitrite offered a linear dependence over the range of 1 12 μM nitrite.
The APS-Au NPs electrode was highly sensitive, which offered a linear dependence over a wide range of sulfite concentrations from 100 nM to 150 μM.
The APS-Au NPs electrode was found to be highly sensitive, and the amperometric response was very stable, which offered a linear dependence over a wide range of hydrazine concentrations (10 nM–12 μM).
These measurements yielded a linear dependence over a biologically-relevant concentration range that agrees with previously published direct refractometry measurements of bulk hemoglobin samples.
Electrodes modified with the Fe@Fe-O@Ag nanocomposite showed a stable and sensitive response towards hydrogen peroxide reduction, exhibiting a wide linear dependence over H2O2 concentrations from 5 μmol L−1 to 1 mmol L−1 with a sensitivity of 460.34 μA μM−1 cm−2 and detection limit of 5.19 × 10−9 mol L−1.
By contrast, AE shows a continuous, linear dependence over the whole pKa range, indicating that the rate-limiting step does not change.
Specifically, Young modulus, yield strength and ductility show a linear dependence upon the nanotube content over the range of compositions explored; in particular with respect to neat PP fibers filaments containing 0.2 vol% of single wall carbon nanotubes show increases of approximately 16% and 6% in the modulus and the yield strength, respectively, while the ductility decreases of about 65%.
The regression plots showed a linear dependence of RSFI values on drug concentration over the range cited in Table 1.
The results show that the catalytic activity of isopropylbenzene cracking over the catalysts has a linear dependence with their hierarchy factor (HF).
Furthermore, PL intensities exhibit a linear dependence (see the inset of Figure 2) on incident power, over the excitation range examined.
In contrast to the behavior of the wild-type enzyme, a linear dependence of formed DCD on chlorite concentration was observed only over a small concentration range [0 10 μM for R173A and 0 100 μM for R173K].
