Shape fitting

A rubberised fabric belt used for the transmission of power. In cross-section the belt is rectangular with sloping sides similar to the upper part of a letter V it operates between sheaves into which the V-shape fits. 

Calculated with band shape fitting programs to provide acceptable fits in both the absorption and the associated NCD spectrum. 

Figure 8. (a) Relative surface energy versus polar angle obtained by Legendre transform of shape in fig.6a. (b) Shape, fitting of experimental data by eq. (9). 

Fig. 3.36. Fano line shapes fitted to the measured absorption profile of the Ri (0) transition of HD at 77 K for densities from 28 to 138.5 amagat. Reproduced with permission by the National Research Council of Canada from [345].

Fig. 5.8. Root mean square relative errors of model line shapes fitted to a quantum profile, the quadrupole-induced (XL = 23) component [69], The abscissa gives the ratio of peak intensity and wing intensity of the fitted portion of the exact profile. The superiority of the BC model (lower set of data points) over the desymmetrized Lorentzian (upper set) is evident.

Like the items for sample collection, the more than 50 different items of equipment for sample preparation are packed in four transport boxes (weight 170 kg) in shape-fitted compartments or drawers (see the picture in Chapter 2). The sample preparation equipment is tailored to the approved sample preparation procedures (see Section 3.4). 

Seebach and coworkers18 have reported that a combination of integration and NMR line shape fitting establishes that in THF-d8, w-butyllithium-6Li, 12, consists of an equilibrium between interconverting dimers D and tetramers T (equation 74) with K = (D)2 / T) being 2.6 x IQ-2 M at 185 K. 

Nickel(ii) and cobalt(ii) complexes continue to be the most widely studied first-series transition metal complexes. The well resolved NMR spectra arise from the very rapid electron-spin relaxation which occurs as a result of modulation of the zero-field splitting of these ions. In the case of 4-coordinate nickel(ii), only tetrahedral complexes (ground state Ti) are of interest since the square-planar complexes are invariably diamagnetic. Many complexes, however, undergo a square-planar-tetrahedral dynamic equilibrium which can be studied by standard band-shape fitting methods (Section B.l). 

FIGURE 6 Shape fitting of similar molecules A) and (S) One-to-one correspondence of surface elements of the same class (schematically). 

Curve) shape fitting as in electron spin resonance and gas electron diffraction. 

The practitioners of shape fitting may rightly claim some neglect The data analyst/statistician papers here presented have emphasized the other two types of problems, not because it was felt that shape fitting offered no important data-analytical problems, but rather because the purely data-analytical problems of intensity fitting and location... 

The history of shape fitting in any field seems to follow a standard pattern ... 

The same essentials will be there for shape fitting as for intensity fitting or location fitting ... 

DATA DISPLAY AND GATHERING Back to Shape Fitting... 

There is one distinctive feature of shape fitting—one opportunity to choose for better or worse not shared by intensity or location fitting. This is the choice of how one looks at the curve. In electron spin resonance, for instance, it is commonplace to look at a curve that comes close to representing the first derivative of the absorption. It would be possible to look at a wide variety of other presentations suggestions of sharpening 1 only scratch the surface of the possibilities. All that should be said here is that this is not a simple problem-surely not one for which an a priori calculation can give a satisfactory answer-and that it is hard to see why something close to a first derivative is the best choice. 

In Chapter 13 we saw that the mechanism of enzyme catalysis is highly specific—an enzyme can facilitate reactions only of substrates whose shapes fit its receptor site. Two other biological processes that also require a high degree of specificity are smell and taste. 

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