X versus

A plot of G x versus composition is shown in Fig. IV-22 for condensed films of octadecanol with docosyl sulfate. Gaines [241] and Cadenhead and Demchak [242] have extended the above approach, and the subject has been extended and reviewed by Barnes and co-workers (see Ref. 243). 

The adsorption of the surfactant Aerosol OT onto Vulcan Rubber obeys the Langmuir equation [237] the plot of C/x versus C is linear. For C = 0.5 mmol/1, C/x is 100 mol/g, and the line goes essentially through the origin. Calculate the saturation adsorption in micromoles per gram. 

Figure Bl.5.3 Magnitude of the second-order nonlinear susceptibility x versus frequency co, obtained from the anliannonic oscillator model, in the vicinity of the single- and two-photon resonances at frequencies cOq and coq 2> respectively.

When we draw a scatter plot of all X versus Y data, we see that some sort of shape can be described by the data points. From the scatter plot we can take a basic guess as to which type of curve will best describe the X—Y relationship. To aid in the decision process, it is helpful to obtain scatter plots of transformed variables. For example, if a scatter plot of log Y versus X shows a linear relationship, the equation has the form of number 6 above, while if log Y versus log X shows a linear relationship, the equation has the form of number 7. To facilitate this we frequently employ special graph paper for which one or both scales are calibrated logarithmically. These are referred to as semilog or log-log graph paper, respectively. 

Numerical values of sinh x versus x are tabulated in standard sources (e.g.. The Handbook of Tables for Mathematics, Chemical Rubber Company) and the tables can be used to evaluate either sinh x or sinh" y. 

As an example, PL can be used to precisely measure the alloy composition xof a number of direct-gap III-V semiconductor compounds such as Alj Gai j, Inj Gai jfAs, and GaAsjfPj j(, since the band gap is directly related to x. This is possible in extremely thin layers that would be difficult to measure by other techniques. A calibration curve of composition versus band gap is used for quantification. Cooling the sample to cryogenic temperatures can narrow the peaks and enhance the precision. A precision of 1 meV in bandgap peak position corresponds to a value of 0.001 for xin AljfGai j, which may be usefiil for comparative purposes even if it exceeds the accuracy of the x-versus-bandgap calibration. 

Table 6-5 shows the equilibrium eonstant with the equilibrium partial pressure of NH3 starting with a stoiehiometrie mixture of Hj and Nj at pressures of 1, 10, and 100 atm. Figure 6-12 shows the relationship between equilibrium eonversion X versus temperature and pressure for stoiehiometrie feed. 

Though the accuracy of description of flow curves of real polymer melts, attained by means of Eq. (10), is not always sufficient, but doubtless the equation of such a structure based on the idea of relaxation mechanism of non-Newtonian polymer flow, correctly reflects the main peculiarities of viscous properties. Therefore while discussing the effect a filler has on the viscosity properties of polymer melts, besides the dependences Y(filler modifies the characteristic time of relaxation. According to [19], a possible form of the X versus

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For any experimental point the value of the rate constant k can be calculated directly. The arithmetic mean of these values can be considered to be the best estimate of k. The graph (X) versus t can also be plotted (see Fig. 5.4-27) and the slope, k, evaluated. The values of (X) scatter uniformly around the straight line, which indicates the proper choice of the kinetic expression. 

Halogen versus H-Polar (X versus Y). Consideration of this interaction is limited to that which takes place across single bonds. It is therefore. 

Here is one simple example. We need to plot x versus y repeatedly and want to automate the task of generating the plots with an M-file. The necessary statements with comments... 

Figures 2, 3 and 4 show S(x) versus for the phantom network model and for the fixed junction case. The largest changes with angle are if the junctions are fixed, the smallest changes are with the phantom network of lowest functionality.

A measurement of S(x) requires that the SANS spectrometer be calibrated by some absolute standard, a process which is often difficult to achieve with precision. An easier measurement in the ratio of scattering intensities of an anisotropic sample in two different directions. Figure 5 shows a graph of Sj (x)/S (x) versus x for the phantom model and the fixed junction case. 

Figure 6. A plot of S(x)/SD(x) versus f for a network in which junction fluctuations are partially inhibited (k 0) and where molecular deformations are less than...

The scope of this chapter-formatted mini-series is to provide statistical tools for comparing two columns of data, X and Y. With respect to analytical applications such data may be represented for simple linear regression as the concentration of a sample (X) versus an instrument response when measuring the sample (Y). X and Y may also denote a comparison of the reference analytical results (X) versus predicted results (Y) from a calibrated instrument. At other times one may use X and Y to represent the instrument response (X) to a reference value (Y). Whatever data pairs one is comparing as X and Y, there are several statistical tools that are useful to assess the meaning of a change in... 

In routine comparisons of X and Y data for spectroscopic analysis, when X and Y denote a comparison of the reference analytical results (X) versus instrument response (Y), at least three main categories of modeling problems are found ... 

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