Sentence examples for equations can be modified from inspiring English sources
It was shown, that existing penetration equations can be modified to account for the shape of the projectile by introducing a single factor fn. From the experimental and simulation data available in this study, n=0.45 was derived as a suitable exponent to describe the shape effect.
(These equations can be modified as desired to reflect for example new quantitive findings as these emerge or to explore the role of TGF-β1 in abnormal wound healing).
The equations can be modified to require that at least 2 inserts overlap a breakpoint.
Assuming var (ε + e) is a scaled identity matrix facilitates the computing involved in fitting this model, as the relevant mixed model equations can be modified by multiplying the left- and right-hand sides by the unknown scale parameter as is typically done in single trait analyses.
Equation (7) represents the LMP change equation for Case 4. This equation can be modified to illustrate the other three cases with varying conditions for network congestion and marginal units due to topology error.
This equation can be modified to demonstrate linearity of data, if the Eq. (2) is given by ln left({C}_0/{C}_tright)=kt (3)where k is the constant of the pseudo-first-order rate.
(5) This equation can be modified using the first-order approximation to _{0}^{CF} D_{t}^{alpha} bigl(f( t_{j} ) bigr) = frac{M alpha)}{1-alpha} sum_{j=1}^{n} int_{(j-1 k}^{jk} j-1 k( frac{f^{k+1} - f^{jk}{Delta t} +O(Delta t) biggl) exp biggl[ -alpha frac{f^{k+1-x}{1-alpha} biggr],dx.
Finally, the last equation can be modified to C N = N - 2 N C N - 1 + 1 N μ 13 X, Y + N + 2 N N - 1 x N y N 3 - 3 x N y N μ 02 X, Y - 3 y N 2 μ 11 X, Y, where μ nm X, Y = 1 N - 1 ∑ i = 1 N - 1 x i n y i m is the estimator of E(X n Y m ) using N-1 samples.
