"under equation" is a correct and usable phrase in written English.
It is commonly used to describe a situation where something is being compared or considered in relation to an equation, formula, or mathematical concept. Example: "The data shows a clear correlation between temperature and productivity, as seen under the equation P = T x 0.5."
The functionals (E v)) and (F v)) defined above are conserved quantities under equation (2.1).
The matrices Γ 0 and Σ i are defined under Equation 16 and in Equation 21, respectively.
To give an example, in Figure 1 we plot the dynamics for the evolution under equation (1).
We start with decomposing B i defined under Equation 22 as B i = I + ∑ k = 1 ( ≠ j ) N γ k Φ i, k Φ i, k T + γ j Φ i, j Φ i, j T = B i, - j + γ j Φ i, j Φ i, j T, where B i,-j is B i with the contribution of the column Φ i,j in the matrix Φ i removed such that we have det B i = det B i, - j det 1 + γ k Φ i, j T B i, - j - 1 Φ i, j.
For later exposition, we denote the log-likelihood of an observation x under Equation (2) as γ(θ(t )\ u ; x)=logℙθ(t )\ u (x u | x\ u ).
Uncertainties in the parameters estimated under Equation 1 and Equation 2 were evaluated via bootstrap resampling with replacement (n = 1,000, implemented with the SAS macro %boot).
Least mean absolute (LMA) based adaptive algorithms are developed for designing these filtering structures under the equation error formulation framework.
In the following theorem, sufficient conditions under which equation (1) has no asymptotically periodic solution are given.
As a consequence, a probability distribution can be obtained that leads directly to the definition of an entropy of the system under consideration (Equation (3) and Equation (4)).
The Owen equation under-predicted RMR in both sexes, all three BMI categories, 18 49 year olds and White participants.
The impact angle exponent was increased in order to reduce the equation under-prediction for the oblique incidence data.
