Curve fitting program

In the first pari of this project, the analytical form of the functional relationship is not used because it is not known. Integration is carried out directly on the experimental data themselves, necessitating a rather different approach to the programming of Simpson s method. In the second part of the project, a curve fitting program (TableCurve, Appendix A) is introduced. TableCurve presents the area under the fitted curve along with the curve itself. 

Solved using the BASIC curve fitting program QLLSQ we get as a partial output block 10 POINTS, FIT WITH STD DEV OF THE REGRESSION. 2842293... 

Activation energies are found from the Arrhenius equation (Eq. 13). We plot In k against 1/T, with T in kelvins, and multiply the slope of the graph by — R to find the activation energy, with R = 8.3145 J-K 1-mol l. A spreadsheet, curve-fitting program,... 

Special attention was paid to the detection of residual Cu-fl quantities accompanying the metallic Cu. The relative amounts of Cu+1 and Cu were determined by curve-fitting the Cu (LMM) spectra using the Physical Electronics Version 6 curve-fitting program. The catalyst showed reduction of Cu+2 Into a mixture of Cu+1 and Cu after reduction In H2 at 250 C for one hour (Figure 6) as evidenced by the two resolved peaks In the Cu (LMM) spectrum at 568.0 and 570.3 eV which are characteristic of Cu and Cu+1, respectively, and by the disappearance of the Cu+2 2p satellite structure. It could be shown that less than 2%, If any, of the total Cu could be present In the +1 oxidation state during methanol formation. However, when the catalyst was briefly exposed to air (1 minute), a few percent of Cu+1 readily formed (7). Thus, any kind of oxidation environment has to be avoided between methanol synthesis and catalyst analysis. Otherwise, appreciable amounts of Cu+1 will be detected. 

IC50 (concentration that inhibited 50% of specific binding) was calculated using an iterative curve fitting program (McPherson 1983). Nonspecific... 

The complexity of the integrated form of the second-order rate equation makes it difficult to apply in many practical applications. Nevertheless, one can combine this equation with modem computer-based curve-fitting programs to yield good estimates of reaction rate constants. Under some laboratory conditions, the form of Equation (A1.25) can be simplified in useful ways (Gutfreund, 1995). For example, this equation can be simplified considerably if the concentration of one of the reactants is held constant, as we will see below. 

The curve fitting programs cope better with fewer variables in the equations. Try to reduce the number of variables. For example, suppose you have to fit a multiphasic curve to three exponentials that are moderately separated in time. There are seven unknowns three rate constants three amplitudes and an endpoint. If the slowest phase is sufficiently separated from the second, first fit the tail of the slowest phase to a single exponential. Then fit the whole curve to a triple exponential equation in which the rate constant and the amplitude that were derived for the third phase are used as constants. Use a time window that focuses on the first two phases and not the whole time course. Similarly, if the first phase is much faster than the second and third, fit the tail of the process to two exponentials. Then fit the fast time region to a triple exponential in which the last two phases have fixed rate constants and amplitudes. 

For butane (Fig. 3.5), using Eq. 3.4 and experimenting with a curve-fitting program shows that a reasonably accurate torsional potential energy function can be created with five parameters, k0 and ki k4 ... 

These formatted outputs are stored on a flexible disk exactly the same as printed. Later the data on the disk are stored by sample number and project. All raw and reduced data for a project are stored on a single flexible disk. After the data have been stored on a flexible disk, it is a simple matter for the computer to make summaries or do trend analyses. An example of one of these summaries is shown in Figure 5. In this example, the percent of 1 C remaining in the peel and fruit at various time periods after spraying apples with a 1 C labeled compound, was analyzed by a curve fit program. 

The carbon Is spectra were deconvoluted into six peaks using a nonlinear least-squares curve-fitting program. Peaks centered at 293.3, 291.2, 289.5, 288.3, 286.6, and 285.0 eV are due to CF3, CF2, CF-CF , CF, C-CF , and C, respectively. Large numbers of CF3 and CF2 groups and small numbers of C group are present in the polymer prepared in the monomer-deficient (energy-saturated) domain, and the F/C ratios are approximately 1.6. 

Jandel Scientific), a non-linear, least-squares, curve fitting program. Errors given are from the best fits of the data. 

The fluorescence lifetime is obtained from this curve by an iterative curve-fitting program that deconvolutes the lifetime from the instrument-response profile (IRF). This describes the response of the instrument to scattered excitation pulses. A typical... 

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. 

The rate constants r and /and other parameters consist of M, J, Xmax and Y evaluated by fitting equation (2) to a non-linear least-squares curve fitting program KINFIT. ... 

Dye JL, Nicely VA. A general purpose curve fitting program for class and research use. J Chem Edu 1971 48 443-8. 

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