Values, common

The mode of a set of numbers is that value which occurs with the greatest frequency (the most common value). The mode may not exist, and even if it does exist it may not be unique. The empirical relation that exists between the mean, the mode, and the median for unimodal frequency curves which are moderately asymmetrical is ... 

All the Carnot cycles making up the simple gas turbine cycle have the same efficiency. Likewise, all of the Carnot cycles into which the cycle a-b-c-2-a might similarly be divided have a common value of efficiency lower than the Carnot cycles which comprise cycle 1-2-3-4-1. Thus, the addition of an intercooler, which adds a-b-c-2-a to the simple cycle, lowers the efficiency of the cycle. 

With a common value of boh /Dj = 1/250, the airflow pattern will be similar to isothermal with a modified Ar number limited to 40. 

Obviously, the classical lamination theory stresses in Pagano s example converge to the exact solution much more rapidly than do the displacements as the span-to-thickness ratio increases. The stress errors are on the order of 10% or less for S as low as 20. The displacements are severely underestimated for S between 4 and 30, which are common values for laboratory characterization specimens. Thus, a practical means of accounting for transverse shearing deformations is required. That objective is attacked in the next section. 

The magnitude of t0 can be measured from the intercept of a f(a)—time plot. The existence of the induction period can introduce uncertainty into a reduced time analysis if the temperature coefficient of t0 differs from that later applicable, and it is necessary to plot (t — t0)/(tb — t0) against a where tb is the time at which the selected common value of a is attained. The occurrence of a slow initial process can be reflected in deviations from linearity in the f(a) time plot, though in favourable systems the contribution may be subtracted before analysis [40]. 

A conditional electrode reaction rate constant ) which is defined as the common value of the anodic and cathodic rate constants at the conditional electrode potential is given according to... 

Frequently occurs that extrapolations do not have a common value at their origin ordinates. These deviations may be caused by inadequate lineal extrapolations. The above mentioned is the routine method used for [q] determination. The procedure is laborious and consumes a considerable amount of time and reactive because of this, several equations were developed which estimate intrinsic viscosity at one single concentration and do not require a graphic. They are known as "single-point" methods. 

The MCSCF and the subsequent perturbation calculations were done using a 6-31+G basis set expanded by a set of spd Rydberg functions. Exponents of this additional gaussians were 0.032 and 0.028 for the s and p shells for the oxygen atom, and 0.023 and 0.021 for the carbon atom. For the d functions, a common value of 0.015 was chosen for both heavy atoms. 

Supporting electrolytes at sufficiently high concentration are present in both O and W phases. For the sake of simplicity, we assume that the diffusion coefficients of relevant species in the a phase (a = O, W) have the common value Z) . The W phase is well-buffered, whereas the O phase contains no buffer component. 

In particle size analysis it is important to define three terms. The three important measures of central tendency or averages, the mean, the median, and the mode are depicted in Figure 2.4. The mode, it may be pointed out, is the most common value of the frequency distribution, i.e., it corresponds to the highest point of the frequency curve. The distribution shown in Figure 2.4 (A) is a normal or Gaussian distribution. In this case, the mean, the median and the mode are found to fie in exactly the same position. The distribution shown in Figure 2.4 (B) is bimodal. In this case, the mean diameter is almost exactly halfway between the two distributions as shown. It may be noted that there are no particles which are of this mean size The median diameter lies 1% into the higher of the two distri-... 

The Pm curve (dashed line) is not shifted to the right of the fraction neutral substance curve/ , (see inset in Fig. 7.34b). It just looks that way when unmatched scaling is used [554]. The two curves are exactly superimposed when the vertical coordinates of the Pm and / are normalized to a common value. The Pe curve, in contrast, is shifted to the right for weak acids and to the left for weak bases. In the log-log plot (log Pe vs. pH), the pH value at the intersection of the slope 0 and slope —1 curve segments indicates an apparent pKa (Fig. 7.34a). 

The ionic radii are often difficult to ascertain. Mostly, crystallographic radii rc corrected by the additive term <5, with a constant common value for cations and a different constant value for all anions, are used ... 

But the main advantage of the SNR concept in modern analytical chemistry is the fact that the signal function is recorded continuously and, therefore, a large number of both background and signal values is available. As shown in Fig. 7.9, the principles of the evaluation of discrete and continuous measurement values are somewhat different. The basic measure for the estimation of the limit of detection is the confidence interval of the blank. It can be calculated from Eq. (7.52). For n = 10 measurements of both blank and signal values and a risk of error of a = 0.05 one obtains a critical signal-to-noise ratio (S/N)c = fo.95,9 = 1.83 and a = 0.01 (S/N)c = t0.99,9 = 2.82. The common value (S/N)c = 3 corresponds to a risk of error a = 0.05... 0.02 in case of a small number of measurements (n = 2... 5). When n > 6, a... 

It should be emphasized that the solubility differences between polymorphs or solvates will be maintained only when a less stable form cannot convert to the most stable form. When such conversion can take place, the equilibrium solubility of all forms will approach a common value, namely that of the most stable form at room temperature. 

We again choose the value of the exponential parameter in Eq. (3.76) to be a = —0.45 so that sigma- and pi-electronegativity scales have the same units. The specification of the scale is then completed by choosing the value of xA(7I) for a single atom. For this purpose it is convenient to assign to the carbon atom a common value of a- and 7t-electronegativity,... 

Let agr be the common value of the reactivity coefficients for both isotopes. Replacing the subscripts liq by SW , in by runoff and evaluating, we get the rate of change of 87Sr/86Sr as... 

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