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Each response prediction equation can be evaluated statistically against the original data to generate the mean and standard deviation of the model predictions.
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It is demonstrated that for BIEs associated with the Laplace and Helmholtz equations, the kernel in the reduced equations can be evaluated very rapidly by exploiting recursion relations for Legendre functions.
The basic equations of fluid mechanics are transformed into the SPH equation, which can be evaluated by the kernel function.
Using Equation 7, p wu can be substituted in terms of p ap; thus, the system throughput in Equation 9 can be evaluated as follows, S =frac{(1+k)mgamma p_{text{ap}} 1-p_{text{ap}})^{m+n-1} 1-p_{text{ap}}}}(frac{text{km}}{n}-1))^{n}+frac{1-T}{T}(1-p_{text{ap}})^{m+n}}.
We note that the IBI computation equation (19) can be evaluated directly.
Hence a pseudo first order model, as per Equation 4, can be evaluated.
Equation 6 can be evaluated numerically and analytically for GTO basis sets, and numerically only for STO basis sets.
Thus, Equation 16 can be evaluated to give the following solution, centering p_{text{ap}}approxfrac{sqrt{(m+n)^{2}+2Q}- (m+n)}{Q} (18).
Equation 10 can be evaluated more quickly if we skip the addition of all terms where (alpha _{m,n} vec {r}_0)=0).
Equation (34) can be evaluated by an M-point IFFT for each m value and by a subsequent index-finding among the stored values using the periodicity of the complex exponential kernel with period M. Equations (35) and (37) require an M-point IFFT and an N-point IFFT, respectively, and subsequent index finding stages.
In this model, the buffer capacity of the CK system is computed by the following relationship: (5) d [ CrP ] c d | Δ G ATPase | = C. Based on the simulations of [CrP]c and Δ GATPase at varying cardiac work rates in the normal system (illustrated in Figure 7), Equation (3) can be evaluated based on finite differences.
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