Graphical interpretation

The graphical interpretation of Eq. (16-197) is shown in Fig. 16-37 for the conditions of Example 12. An operating hne is drawn from the origin to the point of the pure displacer isotherm at = cf. For displacement to occur, the operating hne must cross the pure component isotherms of the feed solutes. The product concentrations in the iso-tachic train are found where the operating hne crosses the isotherms. When this condition is met, the feed concentrations do not affect the final product concentrations. 

Graphical interpretation of the factors influencing the critical distance from air supply to the linear obstacle with a height for air supply through a slot diffuser with height Ioq and for air supply through a round nozzle with outlet diameter are presented in Fig. 7.43. Nonisothermal flow has an influence on... 

In their graphical interpretations, using isentropic rather than polytropic efficiencies, Hawthorne and Davis plotted the following non-dimensional quantities, all against the parameter. v = ... 

For their graphical interpretation, Hawthorne and Davis wrote... 

Graphical interpretations of the results are facilitated by the tensor formulation. 

Figures 9-42 A, B, C, D, E, F present the graphical interpretation of the total hold-up equation. These are more...

A simplification in the graphical interpretation of acyclic chemical compounds is possible in the case of saturated acyclic hydrocarbons, once known as paraffins but now more usually called "alkanes". These have the general formula indicating the... 

One can also gain an insight into the bifurcation for instance, assume that we introduce a parameter A that permits displacing the curve [Pg.341]

Nicolaysen NO (1961) Graphic interpretation of discordant age measrrrements of metamorphic rocks. Arm NY Acad Sci 91 198-206... 

Fig. 18. Graphical interpretation of the criterion for breakup of pointed drops in an extensional flow (Khakhar and Ottino, 1986c).

A graphical interpretation of the derivative is introduced here, as it is extremely important in practical applications. The quantities Ajc and Ay are identified in Fig. 4a. It should be obvious that the ratio, as given by Eq. (8) represents the tangent of the angle 0 and that in the Unfit (Fig. 4b), the slope of the line segment A B (the secant) becomes equal to the derivative given by... 

The graphic interpretation of the above conditions consists in selecting the branch of the cotangent curve in Eq. (A 1.83) that intersects the straight line y = ml Am at the inflection point (see Fig. A 1.3 where the inflection points are connected by a dotted line). For the Debye spectrum, we have... 

Sketch the graphical interpretation of equation 12.3-21 corresponding to that of equation 12.3-2 in Figure 12.1. What does the area under the curve represent ... 

Figure 14.10 Graphical interpretation of equation 14.4-1 total volume V = F, + V2 + V) (shaded areas)...

A graphical interpretation of equation 15.2-2 or -3 is illustrated in Figure 15.2 (for normal kinetics). The area under the curve of reciprocal rate, 1 /( -rA), versus fA is equal to V7FAo or tIcAo. Equations 15.2-1 to -3 apply whether density varies or is constant. 

Figure 15.4 Graphical interpretation of equation 15.2-17 (constant-density system)...

A graphical interpretation of this result is given in Figure 15.4. 

Figure 15.7 Graphical interpretation of equation 15.3-4 for recycle PFR (constant density)...

EXAMPLE 8.1 GRAPHIC INTERPRETATION OF A CONSTRAINED OPTIMIZATION PROBLEM... 

These two conditions stated for determinability correspond to those for the existence of an output set, given by Steward (1962). The first condition warrants that the number of equations is at least equal to the number of unmeasured variables, while the second condition of accessibility takes into account the existence of a subset of equations containing fewer variables than equations. We have shown that if either of the above two conditions is not satisfied, the structural pair (Aj A2) admits a decomposition analogous to that given in the previous section. Thus the same results are still valid when only the structural aspects are considered. A graphical interpretation of these two conditions is instructive. 

Figure 2. Graphical interpretations of the coupled equations (26) and (27) with coefficients in front of R.H.S. given by Nc.

There are four main strategies concerning the processing of outliers. Figures lb to le give a graphical Interpretation of these strategies. 

In references 82-86, the results were treated statistically. Main effects and standard errors were calculated. In references 83, 85, and 86 also a graphical interpretation by means of bar plots was performed. Both positive and negative effects were seen on these plots, but all effects between levels [—1,0] are negative, while all those between [0,4-1] are positive. Possibly, the length of the bars represents the absolute value of the factor effects, and all effects for the interval [—1,0] seem to be given a negative sign, while all those for [0,4-1] a positive. However, the above are assumptions since no details were provided. In references 83 and 86, critical effects are drawn on the bar plots. 

While particle contractions connect an upper right with a lower left label (and are associated with a factor (1 — np)), hole contractions go from upper left to lower right, with a factor —np. Closed loops introduce another factor —LA graphical interpretation is possible, in agreement with that for the conventional particle-hole picture. We postpone this to the more general case of an arbitrary reference function (Section III.E). 

Figure 5. The author s graphical interpretation of the caloric theory of states.

While the visual judgement of black is influenced by the individual ability of the observer to distinguish small color differences in deep black, it is possible, with the help of photometric measurements, to graphically interpret objective evaluations by means of physical data [3.194]. 

In this section, general mathematical formulations and graphic interpretations are presented for several resilience analysis problems (1) feasibility test, (2) resilience (flexibility) test, (3) flexibility index, and (4) resilience index. 

The elasticity of a rocket propellant was measured as the system response. An analysis of Fig. 3.3 indicates that all three components of the composition have large effects and that the response surface is greatly curved or nonlinear. Besides, the greatest response values were obtained dose to the centroid. Large response values also occurred for lower Xi levels and for X3 values between 0.33 and 0.67. Graphic interpretation of the simplex screening experiment may be compared to the response surface contour plots of the same example, Fig. 3.4. 

It is evident that graphic interpretation of the simplex screening experiment offers a robust idea about the form of the response surface. It is therefore not recommended to replace the response surface contour plot with a graphic interpretation of the simplex screening experiment. 

A check of lack of fit in control points No. 8 and 9 showed that the incomplete cube model is adequate. Graphic interpretation of this model as contour lines is shown Fig. 3.11. 

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