Spatial distance

In the calculation of a 3D autocorrelation vector the spatial distance is used as given by Eq. (20). 

NOE Nuclear Overhauser effect, change of signal intensities (integrals) dining decoupling experiments decreasing with spatial distance of nuclei... 

Lee s point of departure is to question the veracity of the concept of locality. Consider two points, A and B, separated by some spatial distance Sx and time dif-... 

If / (x) is a wave packet solution that vanishes for large spatial distances, then the surface integral over 8 extends over the two space-like surfaces alf o2 bounding Q (see Fig. 10-8). 

In order to remove the perturbation h t) from the integral we supposed that the period of the gravitational wave was much longer than the round trip time of light). The observer now concludes that the spatial distance Lg between the two mirrors is ... 

Now if there is a third mirror with spatial coordinates (0,L,0), the spatial distance between this mirror and the mirror at (0,0,0) will be... 

Spatial distances between object points, each of them characterized by given indices, can be measured and calculated. 

Images have a certain resolution both in spatial distances and intensity. 

The different length scales involve different time scales with different types of motion. For short times corresponding to spatial distances shorter than the entanglement distance, we expect entropy-determined dynamics described by the so-called Rouse model [6, 35.]. As the spatial extent of motion increases and... 

Figures 4.6—4.8 are the results for the stoichiometric propane-air flame. Figure 4.6 reports the variance of the major species, temperature, and heat release Figure 4.7 reports the major stable propane fragment distribution due to the proceeding reactions and Figure 4.8 shows the radical and formaldehyde distributions—all as a function of a spatial distance through the flame wave. As stated, the total wave thickness is chosen from the point at which one of the reactant mole fractions begins to decay to the point at which the heat release rate begins to taper off sharply. Since the point of initial reactant decay corresponds closely to the initial perceptive rise in temperature, the initial thermoneutral period is quite short. The heat release rate curve would ordinarily drop to zero sharply except that the recombination of the radicals in the burned gas zone contribute some energy. The choice of the position that separates the preheat zone and the reaction zone has been made to account for the slight exothermicity of the fuel attack reactions by radicals which have diffused into...

As seen, cyclophane structures shown in Schemes 1.4b through 1.4e have the following unique feature The through-bond distance within the paracyclophane fragment is held constant, whereas the spatial distance between the ion-radicalized and neutral moieties is changed. Therefore, the relative importance of through-bond and through-space mechanisms for intramolecular electron transfer can be learned directly from experimental data on these molecules. 

The photostimulated reaction of 4-chlorocamphor (in which the spatial distance between the leaving chloride and the C=0 function is increased with an extra C-C bond) yields, after oxidation, an organophosphoric product in 80% yield (Rossi et al. 2003 Scheme 7.65). 

The facial region is morphologically assessed for developmental integrity of the nasal prominence, optic and otic placodes, as well as the relative spatial distance between the placodes as it pertains to the formation of the mesencephalic flexure (Fig. 13). 

Interactions between different genes - possibly located in spatial distance to each other - can hardly be detected by analyzing the genome. 

Recently, the two-dimensional 13C H heteronuclear correlation (HETCOR) NMR method, using the frequency-switched Lee-Goldberg (FSLG) H decoupling sequence55 at high MAS rates, has been developed, in order to provide intermolecular and spatial distance information. The HETCOR spectrum often has multiple proton cross peaks for each carbon, and these cross peaks can be extremely helpful for assigning the spectrum. Thus, this method can be used to characterize the structure of polymers in solids.55 71... 

Properties of Diastereomers In contrast to enantiomeric pairs, the correpond-ing spatial distances in diastereomeric pairs are not all identical. For example, errand trans-1,2-difluoroethene (Figure 1.2.4), differ in their F-F and H-H distances. This results into different energy contents and different properties between diastereomeric molecules. The difference in properties of diastereomers is illustrated with cis- and trans-1-phenyl-1,3-butadiene, which show markedly different physicochemical properties [12] (Figure 1.2.5). Further investigation of stereochemical isomers is beyond the scope of this book, and discussion in subsequent chapters is limited to constitutional isomers. 

Fig. 11.2. Conformational variables of pair interactions shown on a ball-and-stick model of a protein segment, a, b amino acids c, d atom types r spatial distance (treated in discrete intervals) k separ ation along die sequence (=5 here).

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