HELP Plots

This is a three component system, but as it is not closed, the action occupies all three dimensions. It does not occur in a plane. 

The useful aspect of this follows we can determine the regions in the series of spectra in which there is only one component. The spectral vectors are all parallel and the average over all spectra in the region is a good estimate for the pure component spectrum. The main difficulty with this approach is to decide when exactly the deviation from a straight line starts and thus, which selection of spectra we need to average. 

---

Acknowledgements We thank the former Pamour Porcupine Mines and Placer Dome Canada Ltd. for permission to sample and financial support. Drs. Larry Lemke and Carl Freeman helped plot and interpret the data. Stable Isotope analyses were provided by Mr. Bob Drimmie at the University of Waterloo. Bruce Taylor is thanked for his review of an earlier version of the manuscript. 

We urge the interested reader to look up help linspace, help plot, help subplot, help axis, help xlabel, help ylabel, and help legend... 

In robotics, machines are designed to accomplish a wide variety of tasks. Trigonometry is used to help plot the path that the robot must take. One example of the usefiilness of this technology is in the area of physical rehabilitation. Patients in weakened conditions often need to undergo many weeks of rehabilitation. However, there can be a large number of patients and a relatively small number of therapists. Robots are designed to manipulate the body in ways appropriate for the needs of the patient so that all patients can be served in a timely manner. 

A brief summary of the plotting options can be seen in the command window by using help plot . 

Another way to identify correlations is to plot the values of the parameters in graphical form this can help to identify any correlations and the presence of outliers. A Craig plot is a two-dimerrsional scatterplot of one parameter against another ideally, the molecules should sample from all four quadrants of the plot. 

A somewhat different method of plotting the results will help the reader to appreciate the significance of the eutectic temperature. In Fig. 1,11, 2 melting points are plotted against composition. The curve AC portrays the decreasing melting point of a-naphthol as naphthalene is added up to a mol fraction of 0 605. The curve BG represents the... 

Spin densities help to predict the observed coupling constants in electron spin resonance (ESR) spectroscopy. From spin density plots you can predict a direct relationship between the spin density on a carbon atom and the coupling constant associated with an adjacent hydrogen. 

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. 

Known samples should also be run to verify the accuracy and precision of the routine methods to be used during the unit test. Poor quality will manifest itself as poor precision, measurements inconsistent with plant experience or laboratory history, and disagreement among methods. Plotting of laboratory analysis trends wiU help to determine whether calibrations are drifting with time or changing significantly. Repeated laboratory analyses will establish the confidence that can be placed in the results. 

A compressor surges at certain conditions of low flow, and the compressor map, a plot of head versus flow, has a surge line defining the limits. Surge controls help the machine avoid surge by increasing flow. For an air compressor, a simple spill to the atmosphere is sufficient. For a hydrocarbon compressor, recirculation from discharge to suction is used. 

An additional series of process tests and plots can be helpful. The Delta-P over each section should be monitored and the reflux increased/decreased at constant bottom temperature. The composition of the heavy key in the overhead should be monitored. Plots should then be made of both Delta-P and of composition vs. reflux. Additional information concerning these tests can be found in Norman Lieberman s book entitled Troubleshooting Process Operations. ... 

Since fragment A was clearly assigned with the help of HH coupling constants, all of the C atoms not included in A, which, according to the CH COLOC plot, are two or three bonds apart from the equivalent protons at Sh = 6.72 (Table 43.1), belong to the benzene ring B. 

Two struetural fragments A and B ean be dedueed from the HH COSY plot they inelude the AB systems oigeminal protons identified from the C/7COSY diagram (Table 47.1). Fragments A and B ean be eompleted with the help of the CH data in Table 47.1. 

The assignment of the umbelliferone residue in A likewise follows from interpretation of the Jqh and relationships in the CH COSY and CH COLOC plots following Table 48.1. The C signals at 5c = 112.9 and 113.1 ean be distinguished with the help of the eoupled NMR spee-... 

To assist the engineer in making estimates, the curve in Figure 3-6 gives values of efficiency plotted against pressure ratios. The values on the curve include a 95% mechanical efficiency and a valve velocity of 3,000 feet per minute. Table 3-1 and Table 3-2 are included to permit a correction to be made to the compressor horsepower for specific gravity and low inlet pressure. They are included to help illustrate the influence of these factors to the power required. The application of these factors to... 

Finally, the post-proeessor helps to visualize the huge amount of data produeed by the flow solver. Veetor, eontour and shaded eontour plots of the veloeity field, the energy dissipation distribution or other variable fields ean be plotted for lines, eross seetions or surfaees of the geometry. Some paekages even offer partiele traeing faeilities and animation for transient problems. 

The log A -pH plot can display a large range in values on the vertical axis. The properties of this curve are different from those of the t-pH plot. Figure 6-11 is a plot of log k against pH for the same system graphed in Fig. 6-10. The first derivative is found with the help of Eq. (6-50) and the second derivative is obtained from this and Eq. (6-52). If the special case k = k" is excluded, this leads to... 

It will be obvious that the treatment thus far includes only substituents that are meta or para to the reaction site. When Hammett plots are made with data for ortho-substituted reactants, scatter diagrams usually result. This failure might be attributed to steric effects, but this is not very helpful, and many attempts have been made... 

The use of pictorial isometric or oblique views of plot areas as shovtm in Figure 1-15 is very helpful for equipment location evaluation. With talented personnel, this type of layout study can replace model studies. These layouts are also useful for management presentations. 

The models are even more helpful to the process engineer than simple plot plans. The advantages are multiplied, as with models the process engineer can study as well as solicit the advice of other engineers in visualizing a processing condition. 

---