For irregular, natural clasts with unknown axial dimensions, a polynomial equation of the same form is applied, but with different coefficients.
Low-field magnetic susceptibility shows positive correlation with SIRM and χARM, but with different coefficients.
For our purpose of this paper, together with the problem L defined by (1.1 - 1.2 1.1 - 1.2ider another problem (tilde{L}) of the same form but weth different considerents (tilde{p}(x)), (tilde{q}(x)), (tilde{another, (tilde{beta}).
We consider the boundary value problem L ˜ with the same form of L but with different coefficients q ˜ ( x ), θ ˜ i, γ ˜ i, δ ˜ j, θ ˜ j ′, γ ˜ j ′, i = 1 − 6, j = 1, 2. If a certain symbol α denotes an object related to L, then the symbol α ˜ denotes the corresponding object related to L ˜.
We consider the boundary value problem L̃ which has the same form as L but with different coefficients (tilde{Omega}(x)), (tilde {alpha }_{j}), (tilde{gamma}_{j}), (tilde{alpha}_{j}^{prime}), (tilde{gamma}_{j}^{prime}), (j=1,2), such that tilde{Omega}(x)= begin{pmatrix} tilde{p} ( x ) & q(x) q(x) & tilde{r} ( x ) end{pmatrix}.
Such multiple analyses were applied for an overall comparison of the mating success of (1) females (full sisters) displaying a similar coefficient of relatedness (r) to the parental strains but emitting different pheromone types and (2) females with similar pheromone types but with different coefficients of relatedness (r) to the parental strains.
At the new scale, the same set of equations is applied, but possibly with different coefficients.
"We have a software specialist who has spent his whole career, thirty-five years, coming up with different coefficients for chemicals in chewing gum," Hagen told me.
Bioregenerative life support systems (BLSS) with different coefficients of closure are considered.
We selected a variance function structure with different coefficients of the variance function for different strata to avoid heteroscedasticity (varIdent R function)47 and a compound symmetry as the spatial autocorrelation structure function (as two plant individuals grew in the same pot).
The uncertainty analysis was performed for different scenarios of potable water demand with stochastic variations in a normal distribution with different coefficients of variation throughout the simulated period.
