Discrepancy

Two data are called discrepant if they differ significantly, i.e., their uncertainty ranges do not overlap. In this context, two cases of discrepancies are considered. Case 1 Two significantly different source data are available. Case 11 Several, mostly consistent source data are available, one of them being significantly different, i.e., an outlier . 

The uncertainties have been assigned by the reviewer. Both experimental methods are satisfactory, and there is no justification to discard one of the data. The selected value is then  

Case II. Outliers This problem can often be solved by either discarding the outlying data point, or by providing it with a large uncertainty to lower its weight. If, however, the outlying value is considered to be of high quality and there is no reason to discard all the other data, this case is treated in a way similar to Case I. Example C.3 illustrates the procedure. 

The following data points are available. The reviewer has assigned the uncertainties and sees no justification for any change. 

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UNLESS A DISCREPANCY IS DETECTED IN THE INPUT FILE, IN WHICH CASE IT... 

ERROR RETURN FOR DISCREPANCY IN INPUT DATA FILE 900 ERIN>5... 

A comparison of the results achieved with the FEM Analysis and the rosetta strain gauge measurements is shown in fig. 19. Differences can be noted in areas labeled B and C. The former can be explained as an effect of the discrepancy between the actual shape of the vessel and the ideal one used in the F.E.M. model. The latter can be ascribed to the presence of a muff, located in the centre of the head of the actual vessel, which has not been taken into account in the model. 

The surface tension of a pure liquid should and does come out to be the same irrespective of the method used, although difficulties in the mathematical treatment of complex phenomena can lead to apparent discrepancies. In the case of solutions, however, dynamic methods, including detachment ones, often tend... 

The following values for the surface tension of a 10 Af solution of sodium oleate at 25°C are reported by various authors (a) by the capillary rise method, y - 43 mN/m (b) by the drop weight method, 7 = 50 mN/m and (c) by the sessile drop method, 7 = 40 mN/m. Explain how these discrepancies might arise. Which value should be the most reliable and why ... 

While Eq. III-18 has been verified for small droplets, attempts to do so for liquids in capillaries (where Rm is negative and there should be a pressure reduction) have led to startling discrepancies. Potential problems include the presence of impurities leached from the capillary walls and allowance for the film of adsorbed vapor that should be present (see Chapter X). There is room for another real effect arising from structural peiturbations in the liquid induced by the vicinity of the solid capillary wall (see Chapter VI). Fisher and Israelachvili [19] review much of the literature on the verification of the Kelvin equation and report confirmatory measurements for liquid bridges between crossed mica cylinders. The situation is similar to that of the meniscus in a capillary since Rm is negative some of their results are shown in Fig. III-3. Studies in capillaries have been reviewed by Melrose [20] who concludes that the Kelvin equation is obeyed for radii at least down to 1 fim. 

The flow can be radial, that is, in or out through a hole in the center of one of the plates [75] the relationship between E and f (Eq. V-46) is independent of geometry. As an example, a streaming potential of 8 mV was measured for 2-cm-radius mica disks (one with a 3-mm exit hole) under an applied pressure of 20 cm H2 on QT M KCl at 21°C [75]. The i potentials of mica measured from the streaming potential correspond well to those obtained from force balance measurements (see Section V-6 and Chapter VI) for some univalent electrolytes however, important discrepancies arise for some monovalent and all multivalent ions. The streaming potential results generally support a single-site dissociation model for mica with Oo, Uff, and at defined by the surface site equilibrium [76]. 

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

The uncertainties in choice of potential function and in how to approximate the surface distortion contribution combine to make the calculated surface energies of ionic crystals rather uncertain. Some results are given in Table VII-2, but comparison between the various references cited will yield major discrepancies. Experimental verification is difficult (see Section VII-5). Qualitatively, one expects the surface energy of a solid to be distinctly higher than the surface tension of the liquid and, for example, the value of 212 ergs/cm for (100)... 

The osmotic coefficients from the HNC approximation were calculated from the virial and compressibility equations the discrepancy between ([ly and ((ij is a measure of the accuracy of the approximation. The osmotic coefficients calculated via the energy equation in the MS approximation are comparable in accuracy to the HNC approximation for low valence electrolytes. Figure A2.3.15 shows deviations from the Debye-Htickel limiting law for the energy and osmotic coefficient of a 2-2 RPM electrolyte according to several theories. 

Moreover, some uncertainty was expressed about the applicability to fluids of exponents obtained for tlie Ising lattice. Here there seemed to be a serious discrepancy between tlieory and experiment, only cleared up by later and better experiments. By hindsight one should have realized that long-range fluctuations should be independent of the presence or absence of a lattice. 

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

A combination of equation (C2.6.13), equation (C2.6.14), equation (C2.6.15), equation (C2.6.16), equation (C2.6.17), equation (C2.6.18) and equation (C2.6.19) tlien allows us to estimate how low the electrolyte concentration needs to be to provide kinetic stability for a desired lengtli of time. This tlieory successfully accounts for a number of observations on slowly aggregating systems, but two discrepancies are found (see, for instance, [33]). First, tire observed dependence of stability ratio on salt concentration tends to be much weaker tlian predicted. Second, tire variation of tire stability ratio witli particle size is not reproduced experimentally. Recently, however, it was reported that for model particles witli a low surface charge, where tire DL VO tlieory is expected to hold, tire aggregation kinetics do agree witli tire tlieoretical predictions (see [60], and references tlierein). 

Naghibi H, Tamura A and Sturtevant J M 1995 Significant discrepancies between van t Hoff and calorimetric enthalpies Proc. Natl Acad. Sc/. USA 92 5597-9... 

One otlier common source of nonlinear response, singlet-triplet annihilation, is often tire reason for a discrepancy between fluorometric and absorjDtion kinetic measurements [27, 28 and 29]. 

HCR and co-workers carried out a number of studies by employing 3D potential energy surfaces calculated by means of highly sophisticated ab initio approaches [88,91-101]. The results of these computations are in impressive agreement with the corresponding experimental findings. The discrepancies in the order of 100 wavenumbers, as in early ab initio studies [16,17], have been reduced in the HCR studies to only a few wavenumbers. In conclusion of their paper on the ( H ) system of NH2, Gabriel et al. state We believe... 

These values enable many structures to be correctly predicted discrepancies arising mainly from the false assumption that ions behave entirely as rigid spheres. Some examples are given in Table 2.7. 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

The discrepancy is not large and the last term is zero for a system without net charge. Thus we see that the use of a shifted Coulomb force is equivalent to a tin-foil reaction field and almost equivalent to a tin-foil Born condition. 

The ranking of conformational free energies indicated that the closed state of cAPK is favored even in the absence of ligands, which is in contrast to experimental data that showed a preferred population of the open conformation. One reason for this discrepancy could be that the modelled intermediate ... 

Conventional computers initially were not conceived to handle vague data. Human reasoning, however, uses vague information and uncertainty to come to a decision. In the mid-1960 this discrepancy led to the conception of fuzzy theory [14]. In fuzzy logic the strict scheme of Boolean logic, which has only two statements true and false), is extended to handle information about partial truth, i.e., truth values between "absolutely true" and absolutely false". It thus gives a mathematical representation of uncertainty and vagueness and provides a tool to treat them. 

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