Factor discrepancy

A K-refinement of the 0.12 A y-ray data reproduces the absolute scale poorly when the neutron UtJ thermal parameter values are used (Hansen et al. 1987). The discrepancy can be removed by introduction of a core-tc-parameter, which refines t0 Kcore = 0.988 (2), corresponding to a 1.2% linear expansion. This is supported by a similar result obtained with the LH X-ray data, and related to the scale factor discrepancy noted above. Hansen, Schneider, Yellon, and Pearson (1987), conclude that without independent knowledge of either the scale or the thermal parameters, good agreement with experiment can be achieved, but the resulting scale factor may be in error by as much as 2.5%. 

Though the core expansion leads to the appropriate fit, it may not be the proper explanation for the scale factor discrepancy. Hansen et al. (1987) note that the expansion of the core would lead to a decrease of 7.5 eV in the kinetic energy of the core electrons, at variance with the HF band structure calculations of Dovesi et al. (1982), which show the decrease to be only about 1.5 eV. An alternative interpretation by von Barth and Pedroza (1985) is based on the condition of orthogonality of the core and valence wave functions. The orthogonality requirement introduces a core-like cusp in the s-like valence states, but not in the p-states. Because of the promotion of electrons from s - p in Be metal, the high-order form factor for the crystal must be lower than that for the free atom. It is this effect that can be mimicked by the apparent core expansion. 

These partial rate factors have been recalculated from the experimental data of Dewar and Urch. Their reported values for diphenylmethane are not seriously discrepant with the values now given, but this is not so for the values for fluorene. As given, and copied in the literature, the values were /j = 2040 / = 60 fi = 944. There are consequent errors in table 8 and figs. 16 (reproduced as fig. 9. i of this volume) and 32 of ref. 22. 

The discrepancy between the pore area or the core area on the one hand and the BET area on the other is proportionately larger with silica than with alumina, particularly at the higher degrees of compaction. The fact that silica is a softer material than alumina, and the marked reduction In the BET area of the compact as compared with that of the loose material, indicates a considerable distortion of the particles, with consequent departure of the pore shape from the ideal of interstices between spheres. The factor R for cylinders (p. 171), used in the conversion to pore area in the absence of a better alternative, is therefore at best a crude approximation. 

Many presentations of the second virial coefficient of polymer solutions contain different expressions for the quantities we have discussed. The difference lies in the fact that the factor p( - 0/T) appears in place of 1/2 - x-There are several attitudes we can take toward this difference. For one thing, we can regard the discrepancy as nothing more than different notation ... 

For exposure of reasons of observable discrepancy of results of the analysis simulated experiment with application synthetic reference samples of aerosols [1]. The models have demonstrated absence of significant systematic errors in results XRF. While results AAA and FMA depend on sort of chemical combination of an elements, method of an ashing of a material and mass of silicic acid remaining after an ashing of samples. The investigations performed have shown that silicic acid adsorbs up to 40 % (rel.) ions of metals. The coefficient of a variation V, describing effect of the indicated factors on results of the analysis, varies %) for Mn and Fe from 5 up to 20, for Cu - from 10 up to 40, for Pb - from 10 up to 70, for Co the ambassador of a dry ashing of samples - exceeds 50. At definition Cr by a method AAA the value V reaches 70 %, if element presences an atmosphere in the form of Cr O. At photometric definition Cr (VI) the value V is equal 40%, when the element is present at aerosols in the form of chromates of heavy metals. 

Combination of Eq. 7 or Eq. 8 with the Young-Dupre equation, Eq. 3, suggests that the mechanical work of separation (and perhaps also the mechanical adhesive interface strength) should be proportional to (I -fcos6l) in any series of tests where other factors are kept constant, and in which the contact angle is finite. This has indeed often been found to be the case, as documented in an extensive review by Mittal [31], from which a few results are shown in Fig. 5. Other important studies have also shown a direct relationship between practical and thermodynamic adhesion, but a discussion of these will be deferred until later. It would appear that a useful criterion for maximizing practical adhesion would be the maximization of the thermodynamic work of adhesion, but this turns out to be a serious over-simplification. There are numerous instances in which practical adhesion is found not to correlate with the work of adhesion at ail, and sometimes to correlate inversely with it. There are various explanations for such discrepancies, as discussed below. 

Figure 6.34 indicates that heavier fragments will have higher initial velocities. Whether factor K is correct is doubtful. In Baker et al. (1978b), another figure for the determination of K was presented that gives totally different values. No explanation for the discrepancy has been found. It is, therefore, advisable to use K = only. 

There is a discrepancy in the literature concerning 4-hydroxy-cinnoline. Whereas two measurements of pKa values indicate that the cinnolinone structure predominates by a large factor in aqueous solution (see Table III), comparison of the ultraviolet spectra of 4-hy-... 

It has been concluded from data reported in these studies that the skin temperature is the major controlling factor in corrosion, not the rate of heat flow through the metal . It has also been concluded, however, that corrosion rates at a given mid-specimen temperature do depend on the presence or absence of thermal flux . The difference between temperatures at skin and mid-specimen positions may account for this discrepancy. 

The discrepancy enters because water at 73.4°F (23°C) has a specific gravity slightly less than one. To convert density to specific gravity, the following factor can be used (ASTM D 792) ... 

It has been suggested that the discrepancies between the value of k ikK observed and that predicted on the basis of simple statistics may reflect the greater sensitivity of combination to steric factors. Beckhaus and Rtichardt164 reported a correlation between log(A )/ ,<.,) (after statistical correction) and Taft steric parameters for a scries of alkyl radicals. 

Although, there are reports on differences in reactivity ratios observed for conventional radical eopolymeri/.ation v.y living radical copolymeri/.alion (ATRP"75 276 546 >l8 or RAK D48), most research suggests that reactivity ratios are identical31 8 549 and any discrepancies in composition should be attributed to other factors. 

A summary of a number of correlations proposed for volumetric mass-transfer coefficients and specific interfacial area is presented in Table II, which includes data additional to those of Westerterp et al. (W4). It is apparent that disagreement exists as to the numerical values for the exponents. This is due, in part, to the lack of geometric similarity in the equipment used. In addition, variation in operating factors such as the purity of the system (surfactants), kind of chemical system, temperature, etc., also contribute to the discrepancies. To summarize Table II ... 

The entropy discrepancy resulting from mixing the two different orientations of the dimer is 5 ft In 2 = 2.88 J-K -mol"1. The factor of results from the fact that only j mole of N2O2 is present. The experimental difference of 3.2 J-Kr -mol-1 is within experimental error of the expected value. 

Since the rate was independent of acidity even over the range where H0 and pH differ, and the concentration of free amine is inversely proportional to the acidity function it follows that the rate of substitution is proportional to h0. If the substitution rate was proportional to [H30+] then a decrease in rate by a factor of 17 should be observed on changing [H+] from 0.05 to 6.0. This was not observed and the discrepancy is not a salt effect since chloride ion had no effect. Thus the rate of proton transfer from the medium depends on the acidity function, yet the mechanism of the reaction (confirmed by the isotope effect studies) is A-SE2, so that again correlation of rate with acidity function is not a satisfactory criterion of the A-l mechanism. 

If we assume that the same discrepancy between theory and experiment in M-M enters in M +-M, we can estimate the vibrational relaxation times for the molecular ions. Table II shows the estimated vibrational relaxation times r+ at various temperatures. The values are shorter than those for the neutrals by factors given in Figure 4. 

For arrangements (a) and (b) the structure factor in the first order is 4Ba for planes with hSG even and kSG + lSG even, and 0 for all other planes. These arrangements are definitely eliminated by the experimental data for example, (411)SG is absent, and (521)sg> with smaller interplanar distance, reflects very strongly at the same wave length. Such wide discrepancies cannot be explained as due to the effect of sulfur and oxygen atoms. The barium atoms are, therefore, located as in (c). Because of the presence of other atoms no attempt was made to determine the two parameters involved. 

The few remaining discrepancies are probably due to error in the assumed relative reflecting powers. To test this, we made use of an F-curve for OF obtained by linear extrapolation from Na+ and Cf, and one for Tii+ from CF and K+. These F-curves (which are not reproduced here because of uncertainty in their derivation) lead to structure factors which are, for the same final parameter values, also in good but not complete agreement with the observed intensities. Possibly somewhat different F-curves (corresponding to non-linear extrapolation) would give better agreement, but because of the arbitrariness of this procedure no attempt was made to utilize it. 

Basically, there may be three reasons for the inconsistency between the theoretical and experimental friction factors (1) discrepancy between the actual conditions of a given experiment and the assumptions used in deriving the theoretical value, (2) error in measurements, and (3) effects due to decreasing the characteristic scale of the problem, which leads to changing correlation between the mass and surface forces (Ho and Tai 1998). 

There was a discrepancy between water salinity limits for the three locations, which may be attributed to factors related to difference in soil texture and stmcture. This affects soil infiltration capacity and water retention. These soil hydrologic characteristics influence salt development in the soil profile, which affects plant... 

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