(9)–(11), becomes a polynomials for f i (i = 0, 1, 2, 3) and f j g(j = 0, 1, 2), setting the coefficients of the polynomials to zero yields a set of algebraic equations.
Step 3: Substituting (44), (45) and (46) into (43) and setting the coefficients of the powers of i to be zero, one can obtain an over-determined nonlinear algebraic system in a i ( i = 1, …, n ) and c.
The governing equilibrium equations can be derived from Eq. 26, by integrating the displacement gradients by parts and setting the coefficients of δu 0, δv 0, δw 0, and δθ x,y to zero (Ferreira and Roque 2007, 2009).
Substituting Equations (9), (10), and (13) into the above equation, using variation technique and setting the coefficients of δu i, δw i, and δθ i equal to zero results into the following differential equations of motion for a DWNT ∂ N xi ∂ x = ρ A i ∂ 2 u i ∂ t 2, Open image in new window (15a).
where satisfiy (4.5), with the aid of Mathematica software; substituting (5.5) along with (4.5) into (5.2) and (5.4) yields a set of algebraic equations for setting the coefficients of these terms to zero yields a set of overdetermined algebraic equations with respect to, and.
(4), (6) and (7) into Hamilton's principle ∫ 0 L (δT − δV s + δV e )dt = 0, integrating by parts and setting the coefficients of δW, δU and δψ to zero leads to the differential equations of motion as δ U : ∂ N x ∂ x = 0 Open image in new window (10-a) δ W : ∂ 2 M x ∂ x 2 = m ∂ 2 W ∂ t 2 − ∂ ∂ x N x ∂ W ∂ x − ∂ ∂ x N x ∂ Z ∂ x − ∂ Q x ∂ x + f e Open image in new window (10-b).
A simpler model is obtained by setting the coefficient of log(Days) equal to 1 and fitting a linear model to log(Orangs1/Days1), the logarithm of the daily abundance.
In this analysis, differences in genotype frequency among populations were measured by GST [ 73, 74] Selection coefficients of the inoculated isolates within each host treatment were estimated simultaneously by setting the coefficient of the most-fit isolate (the isolate with the greatest increase in frequency over the considered time period) to zero as described previously [ 32].
set the coefficients of the to rows of to.
set the coefficients of the first and last rows of to.
In the case of training data set, the coefficient of determination (R) and absolute average deviation (AAD) were 1 and 0.1%, respectively, whereas for the testing data set, R2 was 1 and AAD was 0.231% (Table 4) and for validating data sets R2 and AAD were 0.989 and 0.059%, respectively (Table 5).
