Computer-generated fitting

Fig. 15 (A) Time-resolved nanosecond absorption spectra of the anisole cation radical following the 355-nm irradiation of the anisole/MeOPyNOj complex in acetonitrile with a 10-ns (FWHM) laser pulse (recorded at the indicated times). (B) Spectral decay of AN+ monitored at 440 nm, with the smooth curve representing the computer-generated fit of the data to second-order kinetics.

Table 1. Interpretation of the data from computer-generated fitting of the surface charge of AI2O3 by Westall and Hohl (12)...

Fig. 15. Typical time development of a passivation profile measured on a gold-silicon Schottky diode by the C-V method during the hydrogenation process (Seager and Anderson, 1988). Ordinate is the net density of fixed negative charge, i.e., B minus H+. Hydrogenation was at constant ion flux, 298 K, and with the gold film held at 3 V positive with respect to the silicon base. The lines are computer-generated fits to the model described in the text.

A detailed analysis of the spectrum and temperature dependent lifetime of the emission of crystalline K3Co(CN)e and comparison with a computer-generated fit have given information about the geometry and energy of the E( T ) state.103 The effect of the counter-ions K+, Cd2+, and Ir3+ on the low-temperature emission of M(CN)63- (M = Co, Rh, or Ir) has been discussed.104... 

SKF-10,047 to rat brain membranes. Membranes were incubated with 8 nM (+fH-SKF-10,047 and various concentrations (1 - 64,000 nM) of (+)SKF-10,047 for 45 min at room temperature. Results are from a single experiment and values are the average of duplicate determinations. Lines indicate the high (KD 45 nM Bmax 22 pmol/g) and low (KD HO nM Bmax 86 pmol/g) affinity components of total specific binding. Also shown is the computer-generated curve of best fit for the data points. 

Fenvalerate Data. Calibration data for the GC measurement of Fenvalerate were furnished by D. Kurtz (17). Average responses for five replicates at each of five standard concentrations are given in Table III. It should be noted that the stated responses are not raw observations, but rather on-line computer generated peak area estimates (cm ). (Had we started with the raw data [chromatograms], the problem would actually have been two-dimensional, including as variables retention time and concentration.) The stated uncertainties in the peak areas are based on a linear fit (o a+bx) of the replication standard deviations to concentration and the "local slopes" [first differences] in the last column of Table III are presented... 

R.I. Jennrich and P.B. Right, Fitting systems of linear differential equations using computer generated exact derivatives, Technometrics,... 

The computer generated model in Figure 1.6 shows the perfect fit of the exo-adduct inside the 2,2,2-trimer cavity. The smaller 1,1,2-trimer showed a stereoselective bias towards the endo-product at 30 °C however, this stereoselectivity is lost at higher temperatures (a mixture of both the endo- and exo-products was observed at 60 °C). The reversal of the stereochemical outcome of the Diels-Alder reaction between the two cyclic dimers (30 °C) appears to lie firstly in a large (500-fold) endo acceleration... 

The analysis of the autocorrelation function data by the Coulter Model N4 is carried out by the Size Distribution Program (SDP), which gives the particle size distribution in the form of various output displays (see Section 10.4). The SDP analysis utilizes the computer program CONTIN developed by S.W. Provencher (ref. 467-470 see also Section 10.2). (This program has been tested on computer-generated data, monomodal polystyrene samples, and a vesicle system (ref. 466-468,471).) Since the SDP does not fit to any specific distribution type, it offers the ability to detect multimodal and very broad distributions. 

Figure 4. Computer fits to the room-temperature X-band SPR spectra with the joint distribution density of eq. (16). (a) Experimental spectra (full lines) and the best-fit computer-generated spectra (dashed lines) (b) reconstructions of the best-fit joint distribution density of diameters and demagnetising factors. Top, left the borate glass annealed at 465 °C top, right the borate glass annealed at 475 °C bottom, left the borate glass annealed at 480 °C and bottom, right the sol-gel silica glass. See table 5 for the simulation parameters.

The maximum entropy method (MEM) is based on the philosophy of using a number of trial spectra generated by the computer to fit the observed FID by a least squares criterion. Because noise is present, there may be a number of spectra that provide a reasonably good fit, and the distinction is made within the computer program by looking for the one with the maximum entropy as defined in information theory, which means the one with the minimum information content. This criterion ensures that no extraneous information (e.g., additional spectral... 

Redox potentials have been determined for each of the steps of reduction of the trypsin-solubilized reductase (403) step 1, one electron consumed, Eo = —109 mV step 2, two electrons consumed. Eg = —276 mV and step 3, one electron consumed. Eg = —371 mV at pH 7.0, 26°. As expected, the redox potential of step 3 is more negative than the potential of the NADPH-NADP+ couple and was determined from the dithio-nite titration. The overall potentiometric—spectrophotometric titration curves could be very closely fitted with a computer-generated curve based on the assumptions of four one-electron reduction steps and octinction coefficients of 4.9 and 4.5 mM cm for the semiquinones, FliH and rijH the Eg values assumed for steps 2 and 3 were —270 and —290 mV. The precise fit was very sensitive to all of the assumptions (40 ) ... 

Obviously, at a given field strength, the same value of a should and does come out of fitting all six computer-generated (e z). This is a good check of the consistency of the computer simulation method, and it would be interesting to make further computations along these lines with different types and durations of external force fields. 

Keller and Sadler s model fits the shape of the scattering curve, but fails by a factor of two in absolute intensity but how reliable are the absolute intensities in neutronscattering measurements A factor of two is quite a lot to laugh off. Yoon and Flory produce a computer-generated stochastic model which buys agreement in shape and intensity at the expense of unacceptably large variation in real space density, as... 

The values of temperature, [CO] and [O2] at the time (f -l- 10 " ) s were fitted as a function of the three variables at time t. The fitted functions were fourth-order polynomials with between 22 and 25 non-zero parameters. The average deviations between the results of detailed simulations and values calculated from the polynomial were below 0.26% over the range of conditions covered. A FORTRAN program was used to convert the polynomial coefficients into FORTRAN functions optimized for multiplications. An example of such a computer-generated function is given in Fig. 4.17. 

Figure 1 Computer-generated curves of the flux vs. increasing concentrations of substrate transported by either a simple diffusion process fit to the equation J = 5(S) or by a facilitated diffusion process fit to the equation J = 100(S)/(0.4 + S).

Transistors overcame most of the limitations of vacuum tubes. They generate very little heat, and they are much smaller than vacuum tubes. With transistors, computers that fit into a single room could be made. As manufacturing techniques have become more precise, transistors have gotten smaller and smaller. Today, five million transistors can fit into an area smaller than a thumbnail. 

Figure 4.2 presents a computer-generated profile of this type and its best fit by the series 4.19. [9] On this occasion the approximation is better than that provided by 4.20. As could be expected, the Gram-Charlier series experiences problems in fitting the exponential tail of the profile. 

Computer-generated receptor models for protein-G finked receptors are now available,and Figure 26.2 illustrates the fit of R( )-adrenafine into the active site of the (32-adrenergic receptor. It appears clearly that the docking involves more interactions than only the above-mentioned three points ... 

Fig. 3.3 The raw data output of ITC is transformed to show the heat exchange at each injection (kcal mol of injectant), obtained by integration of the area of each spike in the raw data output, as a function of the molar ratio of the protein-ligand binding interaction. The curve is then computer-generated as the best fit to either a one-site or multi-site binding model.

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