Integrate the sum of the γ times of the first equation and the δ times of the second equation in (1.1) on Ω by parts, begin{aligned}[b] frac{d}{dt} int_{Omega }gamma u+frac{d}{dt} int_{Omega }delta v=-a gamma int_{Omega }u+rdelta int_{Omega }v-frac{rdelta }{K} int_{Omega }v^{2}.
Clearly, the power of, and can be calculated by integrating the power spectrum of the sum frequency noise of, and within the bandpass filter frequency range.
If they do represent one molecule, then estimating its relative abundance by integrating the areas under the peaks, and comparing the sum to the integrated peak areas associated with DHPG, suggests that this molecule could account for ∼1% of the sample.
The algorithm of DFA consists first in integrating the series x t), and calculating for every t the cumulated sum of the deviations of the mean.
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The scaled input function is then integrated analytically (using the sum of exponential models) and a formula for K m (called P 2 in that paper) derived that is essentially equivalent to our Equation 2. Finally, these authors propose to use c t /AUC for K m estimation, thus neglecting the influence of the term proportional to V r in Equation 4 completely.
Linear algebra shows that, once we identify TM, TN with their dual bundles via the Riemannian metrics, (|Df|^2 = Tr ( (Df)^{vee } circ Df )), hence we integrate over M the sum of the eigenvalues of the endomorphism ((Df)^{vee } circ Df : TM rightarrow TM).
Raman chemical images were generated by using a sum filter, which integrates the signal intensity over a defined wavenumber range that is representative of the molecular species of interest and subtracts the background as a linear baseline from the first to second border as defined by the sum filter.
An objective functional, that integrate the beneficial advantages of the least trimmed sum of absolute deviations (LTA) estimation and the combinational M-estimation, is proposed.
