Perfect graph

Have the last laugh with a well-drawn graph. There are some points that require an explanation (i.e. Describe how. . . ) Not all free-response questions require a graph, but a garbled paragraph of explanation can be saved with a perfect graph that tells the reader you know the answer to the question. This does not work in reverse. . . ... 

Fig 13 General hierarchies based on partitions of 6,7 and 8 respectively Top levels correspond to linear acenes, star trees and perfect graphs while bottom levels are those of the zigzag polyacenes and paths ... 

Golu80] M.C. Golumbic", Algorithmic Graph Theory and Perfect Graphs", Academic Press, New York, 1980... 

The more quickly and completely a fiber recovers from an imposed strain, the more nearly perfectly elastic it is. The ratio of the instantaneous elastic deformation to the total deformation may be used as a criterion of elasticity (62). The integrated divergences from a theoretical graph of perfect elasticity versus elongation is also used as a criterion for determination of the elasticity index. 

Graphs of operating potential versus current density are called polarization curves, which reflect the degree of perfection that any particular fuel cell technology has attained. High cell operating potentials are the result of many years of materials optimization. Actual polarization curves will be shown below for several types of fuel cell. 

Quite often isochronous data is presented on log-log scales. One of the reasons for this is that on linear scales any slight, but possibly important, non-linearity between stress and strain may go unnoticed whereas the use of log-log scales will usually give a straight-line graph, the slope of which is an indication of the linearity of the material. If it is perfectly linear the slope will be 45°. If the material is non-linear the slope will be less than this. 

In the case of a perfect crystalline solid, for temperature well below the Debye temperature 0D, a c/T3 versus T graph would give a constant value c/T3 a 1 /dD. However, most crystals show deviations from the Debye s law, in particular c/T3 versus T presents a maximum. This behavior is present also in amorphous solids where the maximum is more evident and appears at temperatures higher than in crystals [40],... 

If the product distribution follows a perfect ASF product distribution, then the graph in Figure 10.3 should fit an exponential function. However, this is not the case and can only be done if the production is separated in two product spectra, one being described by al and consisting mostly of <05, and the other one C1-C100+, with the products >05 being mostly from the spectrum described by a.2. 

Setting k = 0, simulate the response to a pulse of tracer for 3 perfectly-stirred tanks in series. Repeat this for various numbers of tanks and plot E versus dimensionless time for these on an overlay graph. 

Figure 1.2 Regression plot. Graph (a) represents the data obtained by analysing samples by two methods which show perfect correlation.

Draw the line of perfect fit as described above. Each point on the graph is plotted so that it lies away from this line (imprecision) but so that the line of best fit matches the perfect line (accuracy). 

Nemst asserted his postulate although the available data were inconclusive. In fact, Richards extrapolated some of his data to give a graph such as that shown in Figure 11.2, which suggests that Equation (11.1) is valid but that Equation (11.3) is not. Numerous subsequent experiments have conhrmed Nemst s postulate if it is limited to perfect crystalline systems. Apparent exceptions have been accounted for satisfactorily. The term perfect implies a single, pure substance. Other restrictions are implied by this term, but they will be discussed later. 

As pointed out above, the bond flux depends on the connectivity of the compound, that is, on the bond graph. This means that the length of a bond depends not only on its immediate environment, but also on the structure of the whole crystal or molecule of which the bond is part. Thus anions such as PO, which ideally are perfect tetrahedra, will often be distorted when they appear in crystals. However, this distortion can normally be predicted via the network equations provided the graph of the bond network is known. 

At this point it seems of interest to include a graph obtained on a quite different polymer, viz. cellulose tricarbanilate. Results from a series of ten sharp fractions of this polymer will be discussed in Chapter 5 in connection with the limits of validity of the present theory. In Fig. 3.5 a double logarithmic plot of FR vs. is given for a molecular weight of 720000. This figure refers to a 0.1 wt. per cent solution in benzophenone. It appears that the temperature reduction is perfect. Moreover, the JeR-value for fiN smaller than one is very close to the JeR value obtained from Figure 3.1 for anionic polystyrenes in bromo-benzene. As in the case of Fig. 3.1, pN is calculated from zero shear viscosity. The correspondence of Figs. 3.1 and 3.5 shows that also the molecules of cellulose tricarbanilate behave like flexible linear chain molecules. For more details on this subject reference is made to Chapter 5. 

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