The phrase "a linear function over" is correct and usable in written English.
It can be used in mathematical or technical contexts when discussing functions defined over a specific domain or set.
Example: "In this analysis, we will consider a linear function over the interval [0, 1]."
Alternatives: "a linear function defined on" or "a linear function with respect to".
LP focuses on maximization or minimization of a linear function over a polyhedron [15].
For the HYBRID and the MPDM, the mean θ followed a linear function over δ with group-specific slopes ρ g (Eq. 6).
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank.
The relation between PM2.5 exposure and excess mortality RR is not necessarily restricted to a linear function over the range of human exposure to PM2.5 from diverse sources (Pope et al. 2009, 2011b).
Response was a linear function of concentration over the range of 0.2 to 2 μg/ml which was used as the working range of the method.
Response was a linear function of concentrations over the range of 20 80 μg mL-1 for moxifloxacin (r2 ≥ 0.998) and 40 160 μg mL-1 for prednisolone (r2 ≥ 0.998).
Second-order cone programming (SOCP) problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the Cartesian product of second-order cones [3 6].
Conversely, in the intensive group, the log(HR) increased as a linear function of the A1C over the range of A1C values, i.e., a positive rather than a negative association, resulting in an HR of 1.66 per unit A1C increase (P < 0.0001), the difference in the risk gradients between groups also being statistically significant (P = 0.0007).
Furthermore, the averaged numbers of memory patterns retrieved during contextual recall in six recorded mice also exhibited a near linear function over averaged freezing responses (Fig. 4I, r = 0.8956, p<0.05).
The average decline in GFR over the years can be described by a linear function Extrapolating the average decline found over the initial 6 months will not overestimate the decline in the following periods.
In women, the association between SRH and year of investigation followed a linear function, with gradually decreasing SRH levels over time, and in men the association followed a third-degree polynomial function with fluctuations but no persistent decrease over time.
