Histogram for the distribution

FIG. 14. Histograms for the distribution of the number of pairs of neighbors, in arbitrary units, for different values of mIM for (a) isopentane liquid at 301 K and (b) glass at 30 K, with and without annealing. (From Yashonath and Rao (71).)... 

As far as the existing material is sufficient, mean values for numerous combinations of atoms are given in Ref. 86. When CVIS or DIAMOND are used (see Section 10.2), histograms for the distribution of distances are given between atom pairs of the stmcture in question (see Figure 5). 

By giving X different values throughout the spectrum and taking the difference of the number of negative i( v) s belonging to consecutive values, one can obtain a histogram for the distribution of eigenvalues (density of states) of for any desired accuracy. 

Fig. 1.12 Histogram showing the distribution of particle sizes for the sample of powder referred to in Table 1.5. (After Herdan )...

The data in Table 4.12 are best displayed as a histogram, in which the frequency of occurrence for equal intervals of data is plotted versus the midpoint of each interval. Table 4.13 and figure 4.8 show a frequency table and histogram for the data in Table 4.12. Note that the histogram was constructed such that the mean value for the data set is centered within its interval. In addition, a normal distribution curve using X and to estimate p, and is superimposed on the histogram. 

The distribution function of the vectors normal to the surfaces,/(x), for the direction of the magnetic field B, in accord with the directions of the crystallographic axis (100) for the P, D, G surfaces, is presented in Fig. 6. The histograms for the P, D, G are practically the same, as they should be the differences between the histograms are of the order of a line width. The accuracy of the numerical results can be judged by comparing the histograms obtained in our calculation with the analytically calculated distribution function for the P, D, G surfaces [29]. The sohd line in Fig. 6(a) represents the result of analytical calculations [35]. 

Figure 1.8. Schematic frequency distributions for some independent (reaction input or control) resp. dependent (reaction output) variables to show how non-Gaussian distributions can obtain for a large population of reactions (i.e., all batches of one product in 5 years), while approximate normal distributions are found for repeat measurements on one single batch. For example, the gray areas correspond to the process parameters for a given run, while the histograms give the distribution of repeat determinations on one (several) sample(s) from this run. Because of the huge costs associated with individual production batches, the number of data points measured under closely controlled conditions, i.e., validation runs, is miniscule. Distributions must be estimated from historical data, which typically suffers from ever-changing parameter combinations, such as reagent batches, operators, impurity profiles, etc.

Figure 2. The histogram is the distribution of OH stretch frequencies for the water clusters and surrounding point charges, and the solid line is the distribution of frequencies from the quadratic electric field map.

Considering then the phase composition as a significant parameter, we obtain the histogram shown in Fig. 7.1(a) for the distribution of the intermetallic phases according to the stoichiometry of binary prototypes. For instance, the binary Laves phases, the A1B2, Caln2, etc., type phases are all included in the number reported for the 66-67.99 stoichiometry range, even if the real stoichiometry of the specific phase is different, see Fig. 7.1(b). We may note the overall prevalence of phases and, to a certain extent, of structural types, which may be related to simple (1 2, 1 1, 1 3, 2 3, etc.) stoichiometric ratios. 

Model Predictions. The rate for desorption of americium from the fissure surfaces into solution was assumed to equal the rate for the adsorption of americium from solution by the fissure surfaces. The sorption rate and the equilibrium fractionation of americium that were determined in the static experiments were used to determine input parameters to the ARDISC model. The ARDISC model predictions for the distributions of americium on the fissure surfaces in both sets of experiments are presented in Figures 5 through 10 along with the autoradiographs and the experimental histograms representing the various distributions of americium on the fissure surfaces. 

Fig.26. Histogram showing the distribution of the percent of Fe2+ in the octahedral sheet of the dioctahedral 2 1 clay minerals. No Fe2 + was reported for 103 samples and three samples had more than 20% Fe2+.

Solution The data on numbers of particles in each particle range given in Table El.3 can be converted to relative frequencies per unit of particle size as given in Table El. 4. The histogram for the relative frequency per unit of particle size for the data is plotted in Fig. El.2 the histogram yields a total area of bars equal to unity. Superimposed on the histogram is the density function for the normal distribution based on Eqs. (1.24) and (1.30). For this distribution, the values for do and ad are evaluated as 0.342 and 0.181, respectively. Also included in the figure is the density function for the log-normal distribution based on Eq. (1.32a). For this distribution, the values for In doi and od are evaluated as —1.209 and 0.531, respectively. 

The theory was tested with the aid of an ample data array on low-frequency magnetic spectra of solid Co-Cu nanoparticle systems. In doing so, we combined it with the two most popular volume distribution functions. When the linear and cubic dynamic susceptibilities are taken into account simultaneously, the fitting procedure yields a unique set of magnetic and statistical parameters and enables us to conclude the best appropriate form of the model distribution function (histogram). For the case under study it is the lognormal distribution. 

Figure 9.12. Histograms of the distribution of interaction strengths for ammonia (left) and carbon dioxide (right) adsorption of y-Al203, MgO and mixed MgAl-oxides obtained from LDHs. After Shen el al. [183].

Fig. 2.8. Histograms showing the distribution of protection factors from amide hydrogen exchange for (a) the authentic form and (b) the recombinant form of goat a-lactalbumin in the MG-state at pHobs 1.7 and 25°C (Nakamura et al., unpublished)...

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