Data fitting results

Time t,h Experimental data Fitted results Error-free results ... 

Figure 8.11 Example of data fitting results - concentrations of sitosterol, campesterol, and the products in the hydrogenation of sitosterol to sitostanol (increasing curve) on Pd/Sibunit. The lower curves represent campesterol and campestanol.

Some data fitting results are displayed in Figures 12.1 and 12.3. The general conclusion is that both models describe the behaviours of the main components, lactose and lactitol very well, both for sponge nickel and ruthenium catalysts. In this respect, no real model discrimination is possible. Both models also describe equally well the behaviour of lactobionic acid (D), including its concentration maximum when the reversible step is included (ks) (Figure 12.3). 

The example of data fitting results are shown in Figure 7. It shows that predicted results represent experimental data well throughout the operation though operating conditions are frequently changed. 

Illustration of Typical Data Fitting Results for an Ionic Conductor... 

Application of equation 10 to the experimental D vs. [HSOIJ] data determined at 25°C and both 1 and 2 M acidity yielded straight line plots with slopes indistinguishable from zero and reproduced the Bi values determined in a non-linear regression fit of the data. This result implies no adsorption of PuSO by the resin and justifies use of the simpler data treatment represented by equation 2. A similar analysis of the Th(IV)-HSOiJ system done by Zielen (9) likewise produced results consistent with no adsorption of ThS0 + by Dowex AG50X12 resin. 

For completeness, the results of the 3-state (B/B/B) model are also included in Table VIII and Table IX. As expected, the data fitted three Bemoullian polymers very well with the following Bemoullian probabilities ... 

After treatment at 373 K in helium flow, the coordination numbers of Mo-0, Mo-S and Mo-Mo were not largely different from those in the cluster 1 and the distances of Mo-0, Mo-S and Mo-Mo were hardly changed. After treatment at 573 K in He flow, however, the color of NaY changed from brown to black and the curve fitting results of the EXAFS data exhibited lower coordination numbers of all interactions than those of the cluster 1. The decrease in the coordination number seems to be not due to the decrease in sulfur amount in the catalyst but to the disordering of each interaction since the S/Mo ratio hardly decreased after thermal treatment. These results show that the structure of the cluster 1 loaded on NaY was maintained at 373 K, but lost at 573 K. 

Fitting the data in Figure 54 using the relationship p / = c, with c a constant that could represent. shows that several combinations of the powers a and b can be used, as long as the exponents a and b are related as 6 % 0.45a. These fit results are inconsistent with the mentioned values for a and b hence the sheath thickness probably is not constant. This was also deduced from direct measurement of the lEDs [161, 235,486, 487]. In contrast, a recently developed method to determine the sheath thickness directly from deposition experiments [ 150,151, 488] revealed that the value of is constant for the conditions where pco - is constant [487]. 

The analysis of absorption data in humans has moved away from the more traditional modeling and data fitting techniques [35]. Absorption processes are now more often characterized by a mean absorption (or input) time (i.e., the average amount of time that the drug molecules spend at the absorption site) or by a process called deconvolution. The former analysis results in a single value (similar to absorption half-life) and the latter results in a profile of the absorption process as a function of time (e.g., absorption rate or cumulative amount absorbed vs. time). These approaches offer additional ways of interpreting the absorption process. 

Spirodela intermedia, L. minor, and P. stratiotes were able to remove Pb(II), Cd(II), Ni(II), Cu(II), and Zn(II), although the two former ions were removed more efficiently. Data fitted the Langmuir model only for Ni and Cd, but the Freundlich isotherm for all metals tested. The adsorption capacity values (K ) showed that Pb was the metal more efficiently removed from water solution (166.49 and 447.95 mg/g for S. intermedia and L. minor, respectively). The adsorption process for the three species studied followed first-order kinetics. The mechanism involved in biosorption resulted in an ion-exchange process between monovalent metals as counterions present in the macrophytes biomass and heavy metal ions and protons taken up from water.112... 

Here, we assume that the data fitting allows us to recover the time constant of the dominant pole reasonably well, and the dead time is roughly 0.9 s. We are not adding exactly 0.2 to 0.725 as a way to emphasize that in reality, we would be doing data fitting and the result will vary. How good an approximation is depends very much on the relative differences in the time constants. 

Equation (31) has also been used to correlate results obtained in annular channels with insufficient hydrodynamic entrance length (B2, B3). Some of the data fit Eq. (31) with a slightly smaller coefficient. A similar expression, including terms for the hydrodynamic entrance length, was used by Pickett and Ong (P3a). 

In addition to the Rouse model, the Hess theory contains two further parameters the critical monomer number Nc and the relative strength of the entanglement friction A (0)/ . Furthermore, the change in the monomeric friction coefficient with molecular mass has to be taken into account. Using results for (M) from viscosity data [47], Fig. 16 displays the results of the data fitting, varying only the two model parameters Nc and A (0)/ for the samples with the molecular masses Mw = 3600 and Mw = 6500 g/mol. 

The Instantaneous values for the initiator efficiencies and the rate constants associated with the suspension polymerization of styrene using benzoyl peroxide have been determined from explicit equations based on the instantaneous polymer properties. The explicit equations for the rate parameters have been derived based on accepted reaction schemes and the standard kinetic assumptions (SSH and LCA). The instantaneous polymer properties have been obtained from the cummulative experimental values by proposing empirical models for the instantaneous properties and then fitting them to the cummulative experimental values. This has circumvented some of the problems associated with differenciating experimental data. The results obtained show that ... 

The data of Loukidou et al. (2004) for the equilibrium biosorption of chromium (VI) by Aeromonas caviae particles were well described by the Langmuir and Freundlich isotherms. Sorption rates estimated from pseudo second-order kinetics were in satisfactory agreement with experimental data. The results of XAFS study on the sorption of Cd by B. subtilis were generally in accord with existing surface complexation models (Boyanov et al. 2003). Intrinsic metal sorption constants were obtained by correcting the apparent sorption constants by the Boltzmann factor. A 1 2 metal-ligand stoichiometry provides the best fit to the experimental data with log K values of 6.0 0.2 for Sr(II) and 6.2 0.2 for Ba(II). 

Sterically compact ortho substituents such as Me, OH, anti-OMe, F, Cl, and CN destabilize the ground and transition states to a similar degree. As a result, changes in the activation energy are minor. The net effect of these substituents on the cyclization rate is similar to that of the para substituents, and the corresponding computational data fit well into the correlation in Fig. 12.49... 

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