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After the determination of the rate constants, the relative populations of the three lower levels of Tm3+ as a function of temperature were determined using the rate model and the temperature dependencies of Equations 4 and 5 for cross-relaxation processes C1 and C2, respectively.
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Our discussion of stability in Sect. 4 does rely on the choice of specific model equations; here we use the rate models introduced by others.
This subspace is flow-invariant for the dynamics; moreover, if one uses the rate models (10) (without lateral coupling), then there are regions in parameter space where the dynamics are attracting to S. We mention this for two reasons.
Therefore substantial reduction in column height can be achieved by designing individual sections using the rate-based model.
The case study was performed using the rate-based model of the PCC process.
Finally, we sought to assess the instrument's psychometric properties more deeply through Item Response Theory (IRT) by using the Rating Scale Model (Andrich 1978).
We first estimated the difficulty calibration of each item for each mode separately using the rating scale model to avoid correlation problem.
All trees were generated using RAxML [ 39] using the PROTCAT rate model and the ProtTest-determined amino acid substitution model.
The burning rate of the carbon in coal particle is calculated using the finite rate model proposed by Smith [6, 23, 24].
This work presents a systematic procedure for using the general rate model to predict experimental chromatograms.
Luan et al. [2] studied the simulation of the coal combustion and gasification processes in a two-stage entrained-flow gasifier using the finite rate model for heterogeneous reactions.
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