Relationships graphical

We know that both G(jco) and Z(G(jco)) are functions of frequency, co. We certainly would like to see the relationships graphically. There are three common graphical representations of the frequency dependence. We first describe all three methods briefly. Our introduction relies on the use the so-called Bode plots and more details will follow with respective examples. 

Figure 7 shows the relationship graphically (taken from McNutt et al., 1990), where Sr/ Sr is plotted against time. It illustrates some important points. 

When a dependent variable z depends on the values of two independent variables x and y, you can display the relationship graphically using a 3-D chart. 

The versatility of the H-X method is also demonstrated in the analysis of the performance of multiple-feed and multiple-product columns. The basic approach is unchanged relate the passing vapor and liquid streams at the point of interest in the column by performing an energy balance, then implement the relationship graphically on the H-X diagram. 

Figure 6.1 illustrates this relationship graphically for a 1-compartment open model plotted on a semi-log scale for two different subjects. Equation (6.15) has fixed effects (3 and random effects U . Note that if z = 0, then Eq. (6.15) simplifies to a general linear model. If there are no fixed effects in the model and all model parameters are allowed to vary across subjects, then Eq. (6.16) is referred to as a random coefficients model. It is assumed that U is normally distributed with mean 0 and variance G (which assesses between-subject variability), s is normally distributed with mean 0 and variance R (which assesses residual variability), and that the random effects and residuals are independent. Sometimes R is referred to as within-subject or intrasubject variability but this is not technically correct because within-subject variability is but one component of residual variability. There may be other sources of variability in R, sometimes many others, like model misspecification or measurement variability. However, in this book within-subject variability and residual variability will be used interchangeably. Notice that the model assumes that each subject follows a linear regression model where some parameters are population-specific and others are subject-specific. Also note that the residual errors are within-subject errors. 

The most important factor in changing the kinetics of the degradation of color in strawberry products is temperature. The preserver can alter this factor to a limited degree in his choice of manufacturing and storage procedures. The rate of color deterioration increases in proportion to the log of the temperature. Figure 2 shows the relationship graphically. 

The dihedral angle between coupled NMR-active spins separated by three bonds modulates the magnitude of the observed J. Figure 6.3 shows this relationship graphically. There are two maxima observed as the dihedral angle varies from 0° to 180°. One maximum occurs... 

While the ordered list shows the numerical score values of relationships between two dimensions, the interactive scatterplot browser best displays the relationship graphically. In the scatterplot browser, users can quickly take a look at scatterplots by using item sliders attached to the scatterplot view. Simply by dragging the vertical or horizontal item slider bar, users can change the dimension for the horizontal or vertical axis. With the current version implemented in HCE 3.0, users can investigate multiple scatterplots at the same time. They can select several scatterplots in the... 

This relationship graphic interpretation for amorphous glassy polymers -polycarbonate (PC) and polyarylate (PAr) - is adduced in Fig. 1.1. Since at r = r (T ) (where T, T and are testing, glass transition and melting temperatures, accordingly) AG =0[10 11], then from the Eq. (1.1) it follows, that at the indicated temperatures cluster structure full decay (9, = 0) should be occurred or transition to thermodynamically equilibrium structure. 

Equations 1.12 and 1.13 govern the behaviour of m/z values with respect to U and V. Figure 1.36 show this relationship graphically. 

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