Relationships significant

Carbon System. A diagram has not been given for the carbon system since the major feature is simply a conversion of predominant C02 to predominant CH4 with the half-way point at pE(W) = —4.13. At this pE value, where the other oxidation states exhibit maximum relative occurrence, the equilibrium concentration of HCOO" is just 6 X 10-10M, that of CH20 only 5 X 10 17M and that of CH3OH only 10 14M. Formation of solid carbon is thermodynamically possible close to pE = —4.13, but its inclusion does not change other relationships significantly. 

Change these relationships significantly, and our Universe and life as we know it could not exist. For an in-depth discussion on the meaning of these coincidences, see Michael Shermer, Why People Believe Weird Things (New York MJF Books, 1997), 263. Also see Clifford A. Pickover, The Paradox of God and The Science of Omniscience (New York Palgrave, 2002). 

Figure 1 Relationships among variables affecting 6-month MDI/PDI, as revealed through structural equation analyses. Covariate-adjusted parameter estimates (and standardized regression coefficients) are indicated. All relationships significant at p = 0.05 or less, one-tailed tests. After Dietrich et al (1986)...

In reality, the cyclic hemiacetal forms of sugars and their derivatives may assume a wealth of different ring conformations. For purposes of nomenclature, however, linear Fischer Projections and Haworth Representations with their quasi conformation-averaging planar-cyclic habit are best suited to illustrate the manifold stereochemicd relationships significant for carbohydrates. 

Utility costs vary enormously. This is especially true of fuel costs. Not only do costs vary considerably between different fuels (coal, oil, natural gas), but costs also tend to be sensitive to market fluctuations. Contractual relationships also have a significant effect on fuel costs. The price paid for fuel may depend very much on how much is purchased. 

In Section 5.2.8 we shall look at pressure-depth relationships, and will see that the relationship is a linear function of the density of the fluid. Since water is the one fluid which is always associated with a petroleum reservoir, an understanding of what controls formation water density is required. Additionally, reservoir engineers need to know the fluid properties of the formation water to predict its expansion and movement, which can contribute significantly to the drive mechanism in a reservoir, especially if the volume of water surrounding the hydrocarbon accumulation is large. 

There is a number of very pleasing and instructive relationships between adsorption from a binary solution at the solid-solution interface and that at the solution-vapor and the solid-vapor interfaces. The subject is sufficiently specialized, however, that the reader is referred to the general references and, in particular, to Ref. 153. Finally, some studies on the effect of high pressure (up to several thousand atmospheres) on binary adsorption isotherms have been reported [154]. Quite appreciable effects were found, indicating that significant partial molal volume changes may occur on adsorption. 

To foster a close relationship with the chemical, petroleum, gas, and energy industries and governmental agencies for the exchange of information and knowledge and to ensure that research results and discoveries of significance will be effectively exploited... 

We have seen ( 6.2.3) hat there is a close relationship between the rates of electrophilic substitutions and the stabilities of tr-complexes, and facts already quoted above suggest that no such relationship exists between those rates and the stabilities of the 7r-complexes of the kind discussed here. These two contrasting situations are further illustrated by the data given in table 6.2. As noted earlier, the parallelism of rate data for substitutions with stability data for o"-complexes is not limited to chlorination ( 6.2.4). Clearly, rr-complexes have no general mechanistic or kinetic significance in electrophilic substitutions. 

Relationship between confidence intervals and results of a significance test, (a) The shaded area under the normal distribution curves shows the apparent confidence intervals for the sample based on fexp. The solid bars in (b) and (c) show the actual confidence intervals that can be explained by indeterminate error using the critical value of (a,v). In part (b) the null hypothesis is rejected and the alternative hypothesis is accepted. In part (c) the null hypothesis is retained. 

Potentiometric measurements are made using a potentiometer to determine the difference in potential between a working or, indicator, electrode and a counter electrode (see Figure 11.2). Since no significant current flows in potentiometry, the role of the counter electrode is reduced to that of supplying a reference potential thus, the counter electrode is usually called the reference electrode. In this section we introduce the conventions used in describing potentiometric electrochemical cells and the relationship between the measured potential and concentration. 

The relationship between capacity factor and analysis time can be advantageous when a separation produces an acceptable resolution with a large b. In this case it may be possible to decrease b with little loss in resolution while significantly shortening the analysis time. 

In developing these ideas quantitatively, we shall derive expressions for the light scattered by a volume element in the scattering medium. The symbol i is used to represent this quantity its physical significance is also shown in Fig. 10.1. [Our problem with notation in this chapter is too many i s ] Before actually deriving this, let us examine the relationship between i and 1 or, more exactly, between I /Iq and IJIq. 

Increases in broth viscosity significantly reduce k a and cause bubble size distributions to become bimodal (30). Overall, k a decreases approximately as the square root of the apparent broth viscosity (31). k a can also be related to temperature by the relationship (32)... 

A representative list of conversion factors from non-SI to SI units is presented herewith. Factors are given to four significant figures. Exact relationships are followed by a dagger. A more complete Hst is given in the latest editions of ASTM E380 (4) and ANSI Z210.1 (6). 

Fiber dimensions have been studied for hemodialysis. When blood is circulated through the fiber lumen (m vivo), a significant reduction in apparent blood viscosity may occur if the flow-path diameter is below 100 p.m (11). Therefore, current dialy2ers use fibers with internal diameters of 180—250 p.m to obtain the maximum surface area within a safe range (see Dialysis). The relationship between the fiber cross section and the blood cells is shown in Figure 5. In many industrial appUcations, where the bore fluid is dialy2ed under elevated pressure (>200 kPa or 2 atm), fibers may burst at points of imperfection. Failure of this nature is especially likely for asymmetric fibers that display a large number of macro voids within the walls. 

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