Absolute-value display

FIG. 12. Experimental absolute-value display of the two-dimensional J-spectrum of the AB spin system provided by methyl 5-nitrofuran-2-carboxylate in (CD3)2CO. The four traces on the right are theoretical simulations with Lorentzian line-shapes. From ref. 149. 

Electron densities, bond densities, and spin densities, as well as particular molecular orbitals may be displayed as graphical surfaces. In addition, the value of the electrostatic potential or the absolute value of a particular molecular orbital may be mapped onto an electron density surface. These maps provide information about the environment around the accessible surface of a molecule. Electrostatic potential maps show overall charge distribution, while orbital maps reveal likely sites for electrophilic and/or nucleophilic attack. Surface displays may be combined with any type of model display. 

One set of experiments was done with both Q and B present at initial concentrations much higher than that of A. With k, kx, and k-j known from other work, the value of k was then estimated, because under these conditions the steady-state approximation for [I] held. To check theory against experiment, one can also determine the products. In the case at hand, meaningful data could be obtained only when concentrations were used for which no valid approximation applies for the concentration of the intermediate. With kinsim, the final amount of each product was calculated for several concentrations. Figure 5-3 shows a plot of [P]o<4R] for different ratios of [B]o/[Q]o the product ratio changes 38-fold for a 51-fold variation in the initial concentration ratio. Had the same ratios of [B]o/tQ]o been taken, but with different absolute values, the indicated product ratios would not have stayed the same. Thus, this plot is for purposes of display only and should not be taken to imply a functional relationship between the quantities in the two axes. 

Calculate the correlation coefficient r for every combination of columns, and display the results in a triangular matrix (an absolute value just under 1.00 indicates a strong correlation between the measurements in columns i and j a minus sign indicates that the slope is negative). 

Absorption-mode spectrum The spectrum in which the peaks appear with Lorentzian line shapes. NMR spectra are normally displayed in absolute-value mode. 

Sine-beU An apodization function employed for enhancing resolution in 2D spectra displayed in the absolute-value mode. It has the shape of the first halfcycle of a sine function. 

The behavior of the detection algorithm is illustrated by adding a bias to some of the measurements. Curves A, B, C, and D of Fig. 3 illustrate the absolute values of the innovation sequences, showing the simulated error at different times and for different measurements. These errors can be easily recognized in curve E when the chi-square test is applied to the whole innovation vector (n = 4 and a = 0.01). Finally, curves F,G,H, and I display the ratio between the critical value of the test statistic, r, and the chi-value that arises from the source when the variance of the ith innovation (suspected to be at fault) has been substantially increased. This ratio, which is approximately equal to 1 under no-fault conditions, rises sharply when the discarded innovation is the one at fault. 

As pointed out above, the RPA theory predicts that the dynamics of the respective homopolymers should be observed at high Q in the Rouse regime. While the experiment shows that the predicted Q dependencies are reproduced well by the data, the absolute values for the observed relaxation rates disagree with the predictions (see Table 6.2). In particular the observed Rouse factors for PE are considerably smaller than predicted, (Wf )expt=2xl0 s" compared to Wf pa=3.8x 10 A s at T=473 K. At low Q values, the two blocks display the same single chain dynamics. 

The Romans were the first to discover the vicissitudes of a culture a that derives its power from finance. Gold, like any other commodity, I does not have an absolute value it depends on how much of it there is around. The gold denomination of the Roman Empire was the aureus, which was worth twenty-five silver denarii. But the later emperors were prone to grotesque displays of wealth - Nero constracted a Golden House with jewel-encrusted walls. These excesses removed so much gold and silver from circulation that the coin minters were forced to add other metals to the aureus and the denarius. By the third century ad the denarius was 98 per cent copper. Naturally, a trader will not give as much for a coin that is mostly copper as for one that is pure silver, even if they are called the same thing and bear the same stamp. 

A number of points should be noted concerning the statistics displayed In the table. First, If the researcher wishes to rank the variables In order of their Importance within the equation, absolute values of the beta values are the appropriate Indicators of rank (7, p. 284). Second, the t-values of the regression coefficients give us estimates of the statistical significance of the Independent variables used. Third, the R-square, or coefficient of determination. Is an estimate of the percent of variation In the dependent variable (the functional property) explained by the corresponding regression equation. 

In the fully chaotic regime, the repeller, which is highly unstable, can be constructed as explained above in terms of the sum of absolute values of the forward and backward escape-time functions, which displays the folding... 

Figure 2.7 Display of the absolute value of Ig[m+[X)) along the ray displayed in Figure 2.6, see Ref. [41], Figure 2.14 for details. Published with permission from American Institute of Physics.

The jump in the m-function at the "tilted cut" is complex therefore, we will display the absolute value of the generalized imaginary part of m+ given by... 

Figure 6 shows the calculated absolute value of the 2D PE signal S( 22, 2i). The resonances representing various correlations between one-exciton states (—ea, ea) (diagonal peaks) and (sa, sb) a / b and a, b = 1,..., 5 (off-diagonal peaks) as well as between one- and two-exciton states (—ea, b — a ), a, b = 1,..., 5 (cross-peaks) are well resolved in model A. Model B has the same resonant energies, but since the homogeneous broadening is comparable with the anharmonicity and coupling energies, many resonances are unresolved. Five slices of the 2D spectra along the 0.2 direction at 2i = — ea, a = 1,..., 5, for models A and B are displayed in Fig. 7. The well-resolved resonances in model A are marked in the plot and identified in Table 1 the broader curves represent model B.

Equation 10.9 represents a complicated line shape, which is a mixture of absorptive and dispersive contributions. Figure 10.11 gives an example of such a phase-twisted line shape. The broad base of the line, caused by the dispersive contribution, and the difficulty in correctly phasing such a resonance make it unattractive for practical use. The phase twist problem can be alleviated by displaying only the absolute value mode... 

Figure 1 Two-pulse or primary ESEEM data collected for the type-1 Cu(II) site of the Fet3p enzyme. Figure 1(a) shows the time domain data recorded under the following conditions microwave frequency, 9.6883 GHz field strength, 337.0 mT pulse power, 250 W 90° pulse length, 16 ns full width at half maximum (FWHM) sample temperature, 10 K. Figure 1(b) shows the ESEEM spectrum derived from the data of Figure 1(a) by subtraction of a biexponential decay function, application of a Hamming window function, and Fast Fourier Transformation (FFT). The absolute value spectrum is displayed...

It is therefore possible to display either one of the four real components S (o)i,0)2) etc., or to plot an absolute value spectrum S (o)i,co2) defined by ... 

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