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A neural network model is developed for predicting, with sufficient approximation, relationship between the factors affecting resilient modulus (inputs: curing time, cement addition level, and residual asphalt content) and the resilient modulus (output) of emulsified asphalt mixture.
Here, we obtain the approximation relationship between the minimum window and the transmission probability.
We employ the following approximation relationship: begin{array}rcl@ limlimits_{c rightarrow 0} e^{-c} approx 1-c+frac{1}{2}c^{2} end{array} (22).
In the proposed method, if both of the target low-frequency and high-frequency components are perfectly represented by the nonlinear eigenspaces of cluster k, the approximation relationship in Equation 32 becomes the equal relationship.
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For statistical analysis, the Wilcoxon signed rank test was used to compare average values (two-sided, exact version for at most 40 cases involved, otherwise using the t approximation); relationships were quantified by linear regression and Spearman's rank correlation coefficient.
Based on this approximation, the relationship between system response speed and steady state variance is obtained.
It has been shown that there is an approximation linear relationship between the dimensionless back face displacement and the dimensionless impulse for all aluminium alloys investigated here.
The model adequacy can be judged from residual's least square which is important to ensure for providing maximum approximation on relationship between factors and response when normal probability is checked by normal probability plot of residuals.
Using a discrete approximation, the relationship between the cumulative incidence at time t and that of time t+1 is [ F (t + 1 ) - F (t ) ] / F (t ) = λ, where λ is the per capita infection rate per time unit.
Polynomial approximations of relationships implied by the model for the combinations of the following exposure and annoyance measures are presented: DNL or DENL, and percentage "highly annoyed" (cutoff at 72 on a scale of 0-100), percentannoyednoyed" (cutoff at 50 on a scale of 0-100), or percentage (at least) "a little annoyed" (cutoff at 28 on a scale of 0-100).
The graph of the estimated regression equation for simple linear regression is a straight line approximation to the relationship between y and x.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com