Some Data

It is time to create some data to play with. By creating the data ourselves, we will know exactly what its properties are. We will subject these data to each of the chemometric techniques so that we may observe and discuss the results. We will be able to translate our detailed a priori knowledge of the data into a detailed understanding of how the different techniques function. In this way, we will learn the strengths and weaknesses of the various methods and how to use them correctly. 

As discussed in the first chapter, it is possible to use almost any kind of data to predict almost any type of property. But to keep things simple, we will continue using the vocabulary of spectroscopy. Accordingly, we will call the data we create absorbance spectra, or simply spectra, and we will call the property we are trying to predict concentration. 

In order to make this exercise as useful and as interesting as possible, we will take steps to insure that our synthetic data are suitably realistic. We will include difficult spectral interferences, and we will add levels of noise and other artifacts that might be encountered in a typical, industrial application. 

As we will soon see, the most difficult part of working with these techniques is keeping track of the large amounts of data that are usually involved. We will be constructing a number of different data sets, and we will find it necessary to constantly review which data set we are working with at any particular time. The data crib sheet at the back of this book (preceding the Index) will help with this task. 

To (hopefully) help keep things simple, we will organize all of our data into column-wise matrices. Later on, when we explore Partial Least-Squares (PLS), we will have to remember that the PLS convention expects data to be organized row-wise. This isn t a great problem since one convention is merely the matrix transpose of the other. Nonetheless, it is one more thing we have to remember. 

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Figure III-9u shows some data for fairly ideal solutions [81] where the solid lines 2, 3, and 6 show the attempt to fit the data with Eq. III-53 line 4 by taking ff as a purely empirical constant and line 5, by the use of the Hildebrand-Scott equation [81]. As a further example of solution behavior, Fig. III-9b shows some data on fused-salt mixtures [83] the dotted lines show the fit to Eq. III-SS.

Some data obtained by Nicholas et al. [150] are given in Table III-3, for the surface tension of mercury at 25°C in contact with various pressures of water vapor. Calculate the adsorption isotherm for water on mercury, and plot it as F versus P. 

The interest attaching to the nitration of pyridine i-oxide and its derivatives has already been mentioned ( 8.2.5). Some data for these reactions are given in tables 8.1, 8.2 and 8.4. The 4-nitration of pyridine I-oxide is shown to occur through the free base by comparison with the case of i-methoxypyridinium cation ( 8.2.2), by the nature of the rate profile ( 8.2.1), and by consideration of the encounter rate ( 8.2.3). - Some of these criteria have been used to show that the same is true for... 

The notion that carbocation formation is rate determining follows from our previous experience and by observing how the reaction rate is affected by the shucture of the aUcene Table 6 2 gives some data showing that alkenes that yield relatively stable carbocations react faster than those that yield less stable carbocations Protonation of ethylene the least reactive aUcene m the table yields a primary carbocation protonation of 2 methylpropene the most reactive m the table yields a tertiary carbocation As we have seen on other occa sions the more stable the carbocation the faster is its rate of formation... 

Some data on copolymers of ethylene and propylene (not shown) is also consistent inasmuch as the values of f decrease as the ethylene (unsubstituted) content increases. 

Figure 6.3 shows some data which constitute a test of Eq. (6.26). In Fig. 6.3a, Rp and [M] are plotted on a log-log scale for a constant level of redox initiator. The slope of this line, which indicates the order of the polymerization with respect to monomer, is unity, showing that the polymerization of methyl methacrylate is first order in monomer. Figure 6.3b is a similar plot of the initial rate of polymerization—which essentially maintains the monomer at constant con-centration—versus initiator concentration for several different monomer-initiator combinations. Each of the lines has a slope of indicating a half-order dependence on [I] as predicted by Eq. (6.26).

Figure 9,16 Comparison of theory with experiment for rg/a versus K. The solid line is drawn according to the theory for flexible chains in a cylindrical pore. Experimental points show some data, with pore dimensions determined by mercury penetration (circles, a = 21 nm) and gas adsorption (squares, a= 41 nm). [From W. W. Yau and C. P. yidXont, Polym. Prepr. 12 797 (1971), used with permission.]...

Some data iEustrating the effect of pressure on the water and salt fluxes and the salt rejection of a good quaUty reverse osmosis membrane are shown ia Figure 34 (76). 

Toxicity. Lethality is the primary ha2ard of phosphine exposure. Phosphine may be fatal if inhaled, swallowed, or absorbed through skin. AH phosphine-related effects seen at sublethal inhalation exposure concentrations are relatively small and completely reversible. The symptoms of sublethal phosphine inhalation exposure include headache, weakness, fatigue, di22iness, and tightness of the chest. Convulsions may be observed prior to death in response to high levels of phosphine inhalation. Some data are given in Table 2. 

Fig. 7. Results of linear and nonlinear methods for analyzing the underlying stmcture of some data sets (a) data points randomly distributed (b) data points on d curved line and (c) data points on a circle correspond to Datasets I, II, and III, respectively. Dimensionality was found by dataset, principal...

Toxicity to fish is included in the data Hsted in Table 4. Marine life, particularly fish, may suffer damage from spills in lakes and streams. The chlorobenzenes, because they are denser than water, tend to sink to the bottom and may persist in the area for a long time. However, some data indicate that dissolved 1,2,4-trichlorobenzene can be biodegraded by microorganisms from wastewater treatment plants and also has a tendency to slowly dissipate from water by volatilization (34). 

Relatively few such heterocyclic systems have been studied by microwave spectroscopy some data are Included in Table 2. In 1,3-dioxolane the bent form is more stable than the... 

The NMR spectra of heterocyclic compounds with seven or more ring members are as diverse as the shape, size and degree of unsaturation of the compounds. NMR is perhaps the most important physical method to ascertain the structure, especially the conformational statics and dynamics, of large heterocycles. Proton-proton coupling constants provide a wealth of data on the shape of the molecules, while chemical shift data, heteroatom-proton coupling constants and heteronuclear spectra give information of the electronic structure. Details are found in Chapters 5.16-5.22. Some data on seven-membered rings are included in Table 10. 

Radicals of most small and many large heterocycles are known, but their chemistry has not always been explored in depth. The ESR spectra of small ring radicals have been measured and generally found to be in good agreement with theoretical predictions. Table 1 gives some data for three-membered heterocyclics. Noteworthy is the close similarity of the ESR spectra of 1-aziridinyl, 1-azetidinyl and dimethylaminyl (71TL2247). The radicals in the table are all tt-radicals. 

It should be noted that the values for 100 percent do not agree with some data avadahle elsewhere, e.g., American Institute of Physics Handbook, McGraw-HiU, New York, 1957. Also, see Atack, Handbook of Chemical Data, Reinhold, New York, 1957. 

Figure 18-21 gives some data on the circulation time of the hehcal impeller. It has oeen observed that it takes about three circulation times to get one blend time being the visual uniformity of a dye added to the material. This is a macro-scale blending definition. 

Villa (in Handbook of Heat Mass Transfer, vol. 4, Gidf, 1990, pp. 289-311). Agreements between their correlations and some data were deemed satisfactory. Rate equations are not necessarily the same on different catalysts. 

The ozonizer may be operated at higher rates of flow of oxygen than shown in Tables I and II, provided that the organic compound reacts with ozone at a reasonably rapid rate. Some data on high rates of flow are given in Table IV. 

Preliminary estimates of costs in foreign countries are difficult due to rapidly changing conditions overseas. For the many companies that do not have construction experience in foreign countries, or in the one being considered, help from a contractor who has built plants in that country is necessary in adjusting U.S. costs. If literature data is needed. References 30 and 31 give some data on foreign construction. 

Comparing compressors by type is a somewhat shaky endeavor, because it involves some opinion, some prejudice, and industry-accepted perceptions. Hopefully, the prejudice has been kept under control and the perceptions of industry are based on knowledge, experience, and, at least, some data. 

Some data on the amount of heat required to reduce the temperature of a polymer from a typical melt temperature to the temperature of the mould (in terms of both per unit mass and per unit volume) are given in Table 8.1. Whilst a moulding will usually by withdrawn at some temperature above the mould temperature, the data do provide some comparison of the different heat requirements of different polymers. It will be noticed that there is a more than 7-fold difference between the top and bottom polymers in the table. 

Some typical properties of a fabricated solid grade (Vespel-Du Pont) are given in Table 18.13 together with some data on a graphite-loaded variety and a commercial polyamide-imide (Torlon 2000—Amoco). 

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