Correlation upper limit

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

Fig. 14. Energy level and correlation diagram of the C2H5 photodissociation system in C8 and C v symmetry. Upper limits of the adiabatic energies of the A2A (3s) and B2A (Sp) states are based on absorption spectra. The crossing of the 2B2 and 2Ai states in Civ symmetry becomes an avoided intersection in Cs. The Biu state of C2H4 is reduced to B2 in C2v when the 2 axis is chosen to be perpendicular to the C2H4 plane. (From Amaral et al.39)...

In this chapter as a continuation of Chapters 58 and 59 [1, 2], the confidence limits for the correlation coefficient are calculated for a user-selected confidence level. The user selects the test correlation coefficient, the number of samples in the calibration set, and the confidence level. A MathCad Worksheet ( MathSoft Engineering Education, Inc., 101 Main Street, Cambridge, MA 02142-1521) is used to calculate the z-statistic for the lower and upper limits and computes the appropriate correlation for the z-statistic. The upper and lower confidence limits are displayed. The Worksheet also contains the tabular calculations for any set of correlation coefficients (given as p). A graphic showing the general case entered for the table is also displayed. 

Likewise for this example, the Z statistic of 1.5606 corresponding to the upper correlation coefficient confidence limit is shown in the graphic below (Graphic 60) as having a p value of 0.91551 this represents the upper confidence limit for the 0.80 correlation example problem. Finally then, for the example problem the correlation confidence limits are from 0.562575 to 0.91551 (i.e., 0.56 to 0.92). 

Graphic 60-6b The z statistic is denoted as Z(p), and the corresponding correlation confidence (p) upper limit can be graphically displayed for our example. 

The adsorbed layer thickness for the llOOnm-size particles could not be measured by photon correlation spectroscopy because of the lOOOnm upper limit of this instrument. Again, the agreement between the two methods is excellent. It is interesting that the adsorbed layer thickness increases with increasing latex particle size and that these values vary with the 0.5 power of the particle radius, i.e., where R is the particle radius. This re-... 

In 1945, H. H. Comly first estimated the correlation between nitrates in drinking water and the incidence of methemoglobinemia. Research shortly afterwards showed that no cases of methemoglobinemia had been reported in any area of the United States where the water supply contained less than 45 ppm of nitrate ion. This value has become accepted in USA as the upper limit for the nitrate concentration in drinking water. At present the WHO limit is also 45 ppm of nitrate but the value of 22 ppm of nitrate has been set for EC countries. 

D. Axelson Based on correlation time measurements the upper limit Tg s that we report are frequency-independent. The results would only be surprising to those who argue for a much higher Tg for the polyethylenes. 

Although OH reacts at near-diffusion-controlled rates with inorganic anions [59], there seems to bean upper limit of ca. 3 x 10 dm mol sec in the case of simple hydrated metal ions, irrespective of the reduction potential of M"". Also, there is no correlation between the measured values of 43 and the rates of exchange of water molecules in the first hydration shell of, which rules out direct substitution of OH for H2O as a general mechanism. Other mechanisms that have been proposed are (i) abstraction of H from a coordinated H2O [75,76], and (ii) OH entering the first hydration shell to increase the coordination number by one, followed by inner-sphere electron transfer [77,78]. Data reported [78] for M" = Cr, for which the half-life for water exchange is of the order of days, are consistent with mechanism (ii) ... 

The experimental diffusion parameters, D /r., at 30°C. are presented in Table II for all the coals. Clearly, no correlation exists between diffusion parameter and rank. If r<> is taken as the average particle radius for the 200 X 325 mesh samples, an upper limit to the values of diffusion coefficient, D, is obtained. The diffusion coefficient ranges from 1.92 X 10 9 sq. cm./sec. for Kelley coal to 1.41 X 10"8 sk. cm./sec. for the Dorrance anthracite. Our previous studies on the change of D /n with particle size suggested that n is not necessarily the particle radius (7) but is a smaller distance related to the average length of the micropores in the particles. That is, the calculated... 

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