Correspondence graph illustration

The corresponding graph is illustrated in Fig 3(a). The Langmuir-Hinshel-wood mechanism contains a step which is an interaction between intermediates (step 3)... 

Fig. 4. Doping-induced changes to the totally symmetric modes of vibration of C60. The graphs illustrate the shift in frequency, measured relative to the uncharged molecule, caused by the addition of n electrons. The data points correspond to experimental data collated in Ref. [7] and the lines are least squares fits to the theoretical expression in equation (8).

The notion of a stable neighborhood of a synthon will be illustrated by using the subfamily J fA) displayed in Fig. 7, the corresponding graph of reaction distances is given in Fig. 8. Now we will assume that the synthons S3(A), S9(A), and Si 3(A) are the only stable synthons (they are denoted by encircled vertices), see... 

Graphs illustrating a distribution of the electric field in a medium at an arbitrary moment are shown in Fig. 9.4. Index of curves is parameter qt. As is seen from curves for small values of qt a maximum of the electric field corresponds to the first arrival, and with approaching to the source the field linearly decreases. But with an increase of parameter qt the different behavior is observed, namely, intensity of the first arrival becomes much smaller for points located closer to the dipole. 

Figure 5a illustrates how the delocalized bonding in benzene from the Q overlap of the unique internal orbitals, namely, the p orbitals, leads to aromatic stabilization. In a hypothetical localized cyclohexatriene structure in which the interactions between the p orbitals on each carbon atom are pairwise interactions, the corresponding graph G consists of three disconnected line segments (i.e., 3 x 2)-This graph has three... 

The disconnectivity graph illustrated in Figure 14.2 provides a simplified view of the landscape, where only the stationary points involved in the 250 fastest discrete paths are included. Aside from minor differences in detail, the corresponding pathways are very similar, and all correspond to the mechanism described above, with initial C-terminal hairpin formation. The red and blue branches of this graph correspond to minima that are visited in either the fastest or the slowest of the 250 fastest paths, respectively, and appear mostly in an intermediate energy range, between formation of the two hairpins. Overall, this graph exhibits little frustration, since barriers... 

Figure 5.1 is a graph illustrating the relative importance of the flux correction term G with respect to the free-molecular flux term Gq. It is graphed for ej[ = 2 and = 1 which correspond to 13.9 nm particles with dielectric constants k = < and K = 1.67, respectively. The argument e e is simply a measure of the Coulomb interaction which is independent of k. For a constant Coulomb potential e e, an increase in k corresponds to an increase in the turnover distances. Since collisions with neutrals increase in importance as the capture distance increases, the flux correction G must increase. The fact that, e.g., ( i/%)e =i ( l o e =2 but both have the same functional dependence upon can be interpreted o mean... 

The relevance of W and Wp was illustrated by an accurate correlation between the boiling point bp) of alkanes and the values of these indices for the corresponding graphs ... 

Figure A3.2 Graph of the compressibility factor r for a number of gases versus their reduced pressure at several reduced temperatures. Reprinted with permission, taken from Goug-Jen Su, Ind. Eng. Chem.. 38,803 (1946), the data illustrate the validity of the principle of corresponding states. The line is Goug-Jen Su s estimate of the average value for r.

If we let and t2 represent the times corresponding to reaction progress variables and <5J, respectively, the time ratio t2/tl for fixed values of <5 and <5 will depend only on the ratio of rate constants k. One may readily prepare a table or graph of <5 versus k t for fixed k and then cross-plot or cross-tabulate the data to obtain the relation between k and ktt at a fixed value of <5. Table 5.1 is of this type. At specified values of <5 and S one may compute the difference log(fe1t)2 — log f) which is identical with log t2 — log tj. One then enters the table using experimental values of t2 and tx and reads off the value of k = k2/kv One application of this time-ratio method is given in Illustration 5.5. 

As an alternative to this traditional procedure, which involves, in effect, linear regression of equation 5.3-18 to obtain kf (or a corresponding linear graph), a nonlinear regression procedure can be combined with simultaneous numerical integration of equation 5.3-17a. Results of both these procedures are illustrated in Example 5-4. If the reaction is carried out at other temperatures, the Arrhenius equation can be applied to each rate constant to determine corresponding values of the Arrhenius parameters. 

To illustrate how Steward s algorithm is executed, consider the adjacency matrix of Fig. 8a. The first row contains all zero elements and can be removed from the adjacency matrix the equation represented by row 1 is placed first in the ordering sequence for solving the equtions. The removal of the first row corresponds to a cut shown by the dashed lines in the associated graph in Fig. 8b, and the portion of the graph below the dashed line is the graph of the reduced matrix obtained by removing row 1 and column 1 as in Fig. 9a. 

Figure 21.1—Graphical illustration of the data presented in Table 21.1.To illustrate accuracy and precision, the standard deviations are calculated according to equation (21.8). Variations are indicated on the graph for arithmetic averages by a vertical bar and for the corresponding median values by arrows. For the results from chemist 3, the deviation between the mean and median is large. Chemist 1 has probably committed a systematic error. On the right is the classical target illustration of precision and accuracy. This image appears simpler than it is because there are uncertainties in x and y.

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