The R Value

If the r-value falls short of the formal significance level, this is not to be interpreted as proving the absence of a systematic error. Perhaps the data were insufficient in precision or in number to establish the presence of a constant error. Especially when the calculated value for t is only slightly short of the tabulated value, some additional data may suffice to build up the evidence for a constant error (or the lack thereof). 

The confidence limits for the slope are given by fc where the r-value is taken at the desired confidence level and (A — 2) degrees of freedom. Similarly, the confidence limits for the intercept are given by a ts. The closeness of x to X is answered in terms of a confidence interval for that extends from an upper confidence (UCL) to a lower confidence (LCL) level. Let us choose 95% for the confidence interval. Then, remembering that this is a two-tailed test (UCL and LCL), we obtain from a table of Student s t distribution the critical value of L (U975) the appropriate number of degrees of freedom. 

Returning to the data of Table 7.1, it is apparent that there is a good deal of variability among the r values displayed by various systems. We have already seen the effect this produces on the overall copolymer composition we shall return to the matter of microstructure in Sec. 7.6. First, however, let us consider the obvious question. What factors in the molecular structure of two monomers govern the kinetics of the different addition steps This question is considered in the few next sections for now we look for a way to systematize the data as the first step toward an answer. 

The ratio of Eq. (8.66) to Eq. (8.67) gives the ratio of the concentrations of n-mers in phases P and Q f p/f g = Re ". Taking this ratio to be unity for n = 200 gives Re (200) = which is readily solved for A using the R values given. Once these A values are obtained, f p/f g can be evaluated for the required n values. For the phase volume ratios under consideration, the corresponding values of A are listed below also tabulated are the ratios f p/f g for the various n s ... 

Plastic Stra.ln Ra.tlo. The plastic strain ratio is the ratio of strains measured in the width over the thickness directions in tensile tests. This ratio characterizes the abhity of materials to resist thinning during forming operations (13). In particular, it is a measure of the abhity of a sheet material to resist the thinning and failure at the base of a deep drawn cup. The plastic strain ratio is measured at 0°, 45°, and 90° relative to the rolling direction. These three plastic strain ratios Rq, R, and R q, are combined to obtain the average strain ratio, cahed the R or the R value, and its variation in strain ratio, cahed... 

Much can be predicted from these parameters. Linear correlations have been estabhshed between the R value and the drawabhity parameter, LDR. Thus higher R values are associated with better deep drawabhity. AR, on the other hand, predicts the height and location of ears. Eor example, larger absolute values of AR predict higher ears during deep drawing cup shapes. 

The r values from Eq. (5-1) for the most important materials for pipe coatings are given in Table 5-1. Table 5-2 contains results of long-term field experiments. For comparison, the values of r°are included in Table 5-1. It can be seen that values are always smaller than r values, which is apparently due to the absorption of water when the coating is immersed in the medium. A marked reduction in the coating resistance has been observed with increasing temperature for resins [9,13,14] (see Fig. 5-2 [14]). 

For the chain (homogenous) consisting of one con-former, osmotic forces are similar to the ones stretching the molecule by the ends. Then, labor of the distance being estimated at constant temperature T , one can estimate 5ch value from the condition = F AR = T ASch)- If a more accurate estimation of the distance change valRe between the ends is required, one may calculate the R value, taking into account the distribution function of the distances between the ends R. The value of the mean-square distances between the ends of the chain, being stretched by forces, applied to the ends equals [14] ... 

A home must be correctly insulated to be energy-efficient. Table 1 shows U.S. Department ofEnergy (DOE) recommended minimum insulation values for different climates throughout the country. The R-value is a measure of insulation effectiveness— the higher the R-value, the more insulation is pro-... 

Many everyday heat flows, such as those through windows and walls, involve all three heat transfer mechanisms—conduction, convection, and radiation. In these situations, engineers often approximate the calculation of these heat flows using the concept of R values, or resistance to heat flow. The R value combines the effects of all three mechanisms into a single coefficient. 

Bcu/h-ft ). While the surfaces, Sheetrock, and siding each impede heat flow, 80 percent of the resistance to heat flow in this wall comes from the insulation. If the insulation is removed, and the cavity is filled with air, the resistance of the gap will be 0.16 (W/m -°C)" (0.9 (Btu/h-ft -T)" ) and the total resistance of the wall will drop to 0.54 (W/m -°C)" (3.08 (Btti/h-ft -°F)" ) resulting in a heat flow of 38.89 W/m (12.99 Btu/h-fr). The actual heat flow would probably be somewhat different, because the R-value approach assumes that the specified conditions have persisted long enough that the heat flow is steady-state, so it is not changing as time goes on. In this example the surface resistance at the outer wall is less than half that at the inner wall, since the resistance value at the outer wall corresponds to a wall exposed to a wind velocity of about 3.6 m/s (8 mph), which substantially lowers the resistance of this surface to heat flow. 

In the case of thermal insulation that primarily reduces thermal radiation across air spaces, the term k, is not used. This type of insnlation is called reflective insulation, and R is not always directly proportional to thickness. The R-value of a reflective system is the temperature difference across the system divided by the heat flux. 

The Rvalues determined for various valves, fittings, etc., are specific to the system, particularly valves. For example, most reliable data have been developed with valves and fittings installed in pipe of specific dimensions, then, if a larger or smaller inside diameter valve or fitting is to be installed in a pipe of different inside diameter, a correction of the R value should be made. 

Of course, by selecting the proper equation, flows for vapors and gases can be determined in the same way, as the R value is for the fitting or valve and not for the fluid. 

The oxidation described here was performed in 80% (v/v) acetonitrile — 20 % water (mole fraction of water = 0.42) at 35.0 °C. Figure 2 shows the selectivity as a function of the number of carbon atoms in R2. In the case of oxidation of la and 2a (R2 = branched alkyl groups), the selectivity reaches a sharp maximum (r = 2.4) at the isopentyl group (j = 2)l8). For R2 = straight-chain alkyl groups, alternation in the selectivity is clearly observed 18). The difference between the r value for la and 2a2 and that for la and 2h2 reaches up to 3.7. 

The same phenomenon was observed for oxidation of la and 2a2 in the presence of 7. When a series of branched alkyl groups are used as R4, the selectivity shows a minimum at the isopentyl group (Fig. 4)21). The r value of 1.4 for R4 = n-C5Hu differs largely from that for R4 = i-C5Hn (r = 0.30)21 . These results demonstrate that the more closely the substituent R4 of 7 resembles the isopentyl group of 2 in geometrical shape, the more remarkably the selectivity is lowered. 

Procedure. Pour the developing solvent into the chromatographic tank to a depth of about 0.5 cm and replace the lid. Take a prepared plate and carefully spot 5 pL of each indicator on the origin line (see Section 8.6, under Sample application) using a micropipette. Allow to dry, slide the plate into the tank and develop the chromatogram by the ascending solvent for about 1 h. Remove the plate, mark the solvent front and dry the plate in an oven at 60 °C for about 15 min. Evaluate the R value for each of the indicators using the equation... 

Speculations on the application of the theory of ergons to chemical processes are also put forward.(13) From a knowledge of the r-values of all the atoms in a molecule, the potential energy of the latter may, in simple cases, be calculated, and this is, at low temperatures, equal to the heat of dissociation. 

Figure A3.4 Comparison of the experimental r (dashed lines) with the r values calculated from the Soave equation of state (solid lines). Values for the acentric factor are (a) oj = -0.218 (the value for EC), (b) a, = 0.011 (the value for CH4), (c) lU = 0,250 (the value for NEC), and (d) = 0.344 (the value for ECO).

No extensive comparison with experiment to test the values in Table IV will be made. The close agreement between the purely theoretical and the experimental results in the case of helium and neon allows one to place confidence in the R values for ions with these structures and the same remark applies with less force in the case of the argon structure, where only a small empirical correction was introduced. It is interesting to note that the theoretical values 3-57 and 6-15 for the rubidium and the caesium ion agree very well with the experimental ones, 3-56 and 6-17 (Table III), which were not used at all in the evaluation of the empirical corrections for these structures. Finally, we may mention that our values agree in general with those of Fajans and WulfE.i obtained by them from the experimental R values for salt solutions by the application of only the simplest theoretical considerations. 

There is a small correction factor which takes into account the quenching efficiency of the antibody and the r value for FLPEP on the antibody.)... 

The radii of gyration (R are larger than Tfh for the first and third samples. The M of the first sample is lower than that of the third, while their viscosities are nearly identical but is much larger for the more-branched third sample. The R values are higher than the corresponding linear PIBs, in agreement with our recent results and Stockmayer s prediction that R >R and should increase with B for dendritic samples with broad MWD. " ... 

Figure 2.19. Intersection of two linear regression lines (schematic). In the intersection zone (gray area), at a given c-value two PD-curves of equal area exist that at a specific y-value yield the densities zi and Z2 depicted by the dashed and the full lines. The product zi Z2 is added over the whole y-range, giving the probability-of-intersection value for that x. The cumulative sum of such probabilities is displayed as a sigmoidal curve the r-values at which 5, respectively 95% of Z2) s reached are indicated by vertical arrows. These can be...

The activity of a-chymotrypsin was found to be insensitive to the R value, i.e., from the size of the reversed micelles. This was taken as an indication that this enzyme is able to create its own micelles in the hydrocarbon rather than occupy empty ones and that the so-called exclusion effect, i.e., protein larger than the empty micelle cannot be solubilized, is incorrect [181,182],... 

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