Computer curve fitting

Using modern computer curve-fitting techniques,102 equations (17) and (27) can be fitted simultaneously with variables X, log CH+ and D, obtaining pATBH+. m, DB and DA as coefficients, which is a more precise technique than calculating log/ values first and using equation (17) and the error function61 discussed above. 

Dr. Spijkerman No, that will not do. The spectral lines should be resolved otherwise manual and computer curve fitting could give diflFer-ent results. 

If two or more transitions overlap, the quantitative interpretation of the MCD spectrum becomes much more difficult and computational curve fitting that requires simple band shapes is needed. Often, the vibrational structure of the MCD spectrum, which will in general be different from the one in the absorption spectrum, will be so pronounced that this assumption is not fulfilled. Although uncommon, there are some cases known where some sections of the vibrational envelope associated with a single electronic transition are positive and some negative. Thus, the appearance of both positive and negative MCD peaks in a spectral region does not necessarily mean that... 

Another important issue in the determination of possible drug activity is the observation of incomplete curves. This is especially important in the confirmation of weak activity since the concentrations needed to delineate the complete curve may not be run in the experiment (either through the design of the experiment or because of solubility constraints). For example, apparent curves such as those shown in Figure 12.12A are obtained. The question is, how can a unique parameter characterizing the potency of such compounds be calculated Computer curve-fitting... 

Flash-induced absorbance changes at 819 nm are shown in Fig. 6 (A). Since the decay is multiphasic, the absorbance changes are presented on different time scales as indicated for each signal. The number of kinetic phases, as well as the 6/, value and amplitude of each kinetic phase, were determined by a computer curve-fitting program. As seen in panel (A), the AA signal shown at top has one very fast phase that decays in a few nanoseconds and is most likely due to antenna chlorophyll molecules. 

P. A. Linfors, "Computer Curve Fitting of ESCA Data to Aid Interpretation," 3rd Symposium on Applied Surface Analysis, Dayton, OH., 1981. 

This analysis is complex, but follows the pattern given for the dibasic acids. The solutions of the final equations have to be found by successive approximation, or else by computer curve fitting to the whole titration curve. In practice, this is how the analysis will be carried out. 

LJtotai [LJactuai values, valucs of M for any given [L]totai and [MJ tai can be calculated and a graph of n vs. [LJactuai drawn. Values of the s appearing in Equation (7.58) can be found by computer curve fitting techniques, or by successive approximations. 

If three or more complexes are present computer curve fitting, or successive approximations, is necessary. 

Ypv The points are computer curve fitted to a second order polynomial and the intercepts are taken from that curve fit. (Reproduced with permission Ref. 18. Copyright 1981, Elsevier/North Holland Press). 

Concentration is the independent variable, and the relative intensity or intensity ratio is the dependent variable. Some analytical curves are plotted on logarithmic coordinates, but computer curve-fitting procedures readily allow wide-range rectilinear calibrations, as well as calculation of the concentration values for unknown samples. For very accurate work, emulsion calibrations are repeated for each spectrum by adopting the sample spectrum as the source of the emulsion calibration. 

The four-parameter computer curve fit to the data is shown as open circles in Figure 5 and the figure shows that 50% inhibition occurred at a dilution of the sample of 0.02 (i.e., 1 50) and that the residual sum of squares (a measure of the quality of... 

With an appropriate choice of the V-dependence of k.. and ki the model is complete and may be evaluated on a computer. It turns out that the parameters of the model can be adjusted in such a way that the computed curves fit the experimental ones sufficiently well. We do not want to go into any details of this evaluation but once more stress the feedback character of the model. This latter point will lead... 

These data are from [ 1 ], which shows such tables for 21 mixtures. Dataon466 such mixtures are given in [2]. Very extensive compilations are givenin [3,4]. For binary mixtures (mixtures with only two species) the table shows only one mol fraction in each phase the other is found by subtracting this value from 1.0. These values and the values shown in most such tables are not direct experimental values. Rather, the experimental data points are plotted as in Figure 8.4, and then the appropriate temperatures and vapor mol fractions are read from those curves (by eye or by computer curve fit and computer lookup) at the even values of the liquid mol fractions as shown in this table. 

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