Precision correctness

It should be pointed out, however, that the diffusivity of the solute in the mobile phase can be changed in two ways. The solute that is chromatographed can be changed, in which case the above assumptions are clearly valid, as (Ds) is likely to change linearly with (Dm)- However, the solute diffusivity can also be changed by the employing a different mobile phase. In this case, (Dm) will be changed but (Ds) will remain the same. In the second case, the above assumptions are not likely to be precisely correct. Nevertheless, if the resistance to mass transfer in the stationary phase makes only a small contribution to the overall value of (H) (i.e., because df dp (see equation (l)),then the assumption Dm = eDg will still be approximately... 

Thus, when the magnet is sweeping, the field lags the field calculated from the known current. The lag is sweep rate dependent, but may be rather precisely corrected for. 

Consider how a weak electrolyte is distributed across the gastric mucosa between plasma (pH 7.4) and gastric fluid (pH 1.0). In each compartment, the Henderson-Hasselbalch equation gives the ratio of acid-base concentrations. The negative logarithm of the acid dissociation constant is designated here by the symbol pAa rather than the more precisely correct pK1. 

The major analytical complication in Mo isotope analysis is precise correction for isotope fractionation during Mo purification and mass spectrometric analysis. This subject is reviewed in general by Albarede and Beard (2004), and is discussed here in particular reference to Mo. It is important to recognize that this challenge is fundamentally dififerent in mass dependent stable isotope studies as compared to investigations of mass-independent Mo isotope variations produced by nucleosynthesis. The latter have received attention in recent years for high-precision determination of Mo isotope composition (e.g., Dauphas et al. 2002a,b Yin et al. 2002), but are not relevant here. 

The booster-and-attenuator system is selected to provide about the desired shock pressure in the sample wedge. In all but a few of the experiments on which data are presented here, the booster-and-attenuator systems consisted of a plane-wave lens, a booster expl, and an inert metal or plastic shock attenuator. In some instances, the attenuator is composed of several materials, The pressure and particle velocity are assumed to be the same on both sides of the attenuator-and-sample interface. However, because initiation is not a steady state, this boundary condition is not precisely correct. The free-surface velocity of the attenuator is measured, and the particle velocity is assumed to be about half that. The shock Hugoniot of the attenuator can be evaluated using the free-surface velocity measurement. Then, the pressure (P) and particle velocity (Up) in the expl sample are found by determining graphically the intersection of the attenuator rarefaction locus and the explosives-state locus given by the conservation-of-mom-entum relation for the expl, P = p0UpUs where Us = shock velocity and p0 = initial density. The attenuator rarefaction locus is approximated... 

The general form of a lambda sensor is illustrated in Fig. 4.37. The closed end projects into the hot exhaust gas stream heating the sensor to a temperature at which it is sufficiently conductive for the e.m.f. to be measured by a high impedance meter. The input impedance of the meter must be 100 times that of the cell for 1% precision. Corrections for changes in cell temperature (Eq. (4.38)) can be made by monitoring the cell resistance. 

A sixth source of difference, which was unavoidable in preparation of the test cases, is the various ways each program handles the carbonate system. From a practical standpoint, the inorganic carbon system of natural waters is usually determined from the titration alkalinity. Because the titration alkalinity includes both carbonate and non-carbonate alkalinity, the titration alkalinity must -be corrected for noncarbonate alkalinity. Most models correct for the presence of H2BO0 and H SiOT but many other minor species should be considered and there is no general agreement as to the precise correction for non-carbonate alkalinity. In devising the correction used originally in WATEQ, Truesdell and Jones also... 

Finally, although it is not precisely correct to assume that the N electrons in an atom occupy N independent one-electron orbitals, this remains a very useful idea for understanding many atomic properties, including the organization of the periodic table. Recall that for us to account for the arrangement of the atoms on the periodic table, the orbitals that correspond to a given value of n must fill in the order ns, then np, then nd, and, finally, nf. From this observation we would expect the energies of the one-electron SCF orbitals to vary in the order... 

The concepts are imprecise or approximate in the sense tl at their application cannot be expected to produce precisely correct results the concepts themselves are defined precisely. 

Equation (63) is precisely correct for bimolecular reactions by definition, but the unknown steric factor P must be determined before... 

They may also be suitable for following gelation in near-line or laboratory experiments at a constant temperature. For example, a vibrational viscometer was used to determine the coagulation time of reimeted milk at fixed temperatures (Sharma et al., 1989, 1992). However, in non-isothermal physical gelation, the elastic modulus depends on the temperature dependence of the resonant response so that precise correction for the influence of temperature must be known. 

Holzgrefe HH, Cavero I, Gleason CR, et al. Novel probabilistic method for precisely correcting the QT interval for heart rate in telemetered dogs and cynomolgus monkeys. /Pharmacol Toxicol Methods. 2007 55(2) 159-175. 

Electron microscopy data on such catalysts show the average diameters of the metal clusters to be of the order of 10 A or lower. Clusters of this size necessarily consist almost exclusively of surface atoms. The stoichiometry of the strongly chemisorbed fraction thus appears to be close to one hydrogen atom per surface metal atom for platinum-iridium catalysts containing equal amounts of the two metals. If this stoichiometry were precisely correct, a value of H/M from Figure 4.20 would be a direct measure of the metal dispersion, that is, the ratio of surface atoms to total atoms in the metal clusters. 

It was mentioned above that the crystallization of lactose can occur at a critical water content, just above the glass transition. It was further (implicitly) assumed that this would happen at the same mass fraction of water i/fw in skim milk powder. Experiments show that this is not precisely correct but that the critical conditions for crystallization are at the same water activity. Does this imply that the glass transition is determined by aw rather than i//w ... 

The TCNQ one-dimensional conduction band is half-filled. This must be nearly, if not precisely, correct. 

Turning now to the intensity of this absorption band in the [Ti(H20)6]3+ ion, we note that it is extremely weak by comparison with absorption bands found in many other systems. The reason for this is that the electron is jumping from one orbital that is centrosymmetric to another that is also centrosymmetric, and that all transitions of this type are nominally forbidden by the rules of quantum mechanics. One-electron transitions which are allowed have intensities that give molar absorbance values at the absorption peaks of 104. If the postulate of the crystal field theory, that in both the ground and the excited states the electrons of the metal ion occupy completely pure d orbitals that have no other interaction than a purely coulombic one with the environment of the ion, were precisely correct, the intensity of this band would be precisely zero. It gains a little intensity because the postulate is not perfectly valid in ways that will be discussed on page 578. It will also be noted that the band is several thousand cm"1 broad, rather than a sharp line at a frequency precisely equivalent to A0. This too is a general phenomenon that will be discussed in detail below. 

These corrections are large for the terrestrial bodies with the largest masses and internal pressures, Venus and Earth, and smallest for the Moon and Mercury. Note that making precise corrections requires some prior knowledge of the compressibility, and hence the mineralogy and structure, of the interior. These estimates assume that the same basic minerals (Fe-Ni, FeS, and silicates) are present in each body and that all are fully differentiated. 

As Kr and Xe have more isotopes than Ar, an unambiguous determination of the neutron-capture component is easier in principle. Nevertheless, precise corrections for primordial or atmospheric Kr and Xe are often also difficult. 

Now electronic transitions in the polypeptide are associated with the delocalized carbonyl electron. If the carbonyl group alone is considered in C2v symmetry, the n-tt (symmetry forbidden transition) is a2 and tt-tt is b in Cs symmetry one has a" and a allowed transitions. Neither is precisely correct, but for present purposes we can treat the ti-tt transition as polarized perpendicular to the carbonyl bond and in the plane of the peptide group, and tt-tt as in the plane of the peptide group and nearly parallel to... 

In such cases it has been assumed that = w, Y. = B, etc., although in the highest approximations these identities are not precisely correct. Some of the values of in the table have been corrected for breakdown of the Born-Oppenheimer approximation, which can affect the last decimal place. Because of differences in the method of data analysis and limitations in the model, care should be taken in comparing values for different molecules to a precision beyond 0.001 A. 

Later experiments, notably the Joule-Thomson experiment, have shown that Joule s law is not precisely correct for real gases. In Joule s apparatus the large heat capacity of the vat of water and the small heat capacity of the gas reduced the magnitude of the effect below the limits of observation. For real gases, the derivative (dU/dV) is a very small quantity, usually positive. The ideal gas obeys Joule s law exactly. 

Although Eq. (7.42) is precisely correct only for the ideal gas, it is a useful approximation for real gases. 

Finally, although it is not precisely correct to assume that the N electrons in an atom occupy N independent one-electron orbitals, this remains a very useful idea for understanding many atomic properties, including the organization... 

In such cases it has been assumed that fjo = COe, Tq i, etc., although in the highest approximations these identities are not precisely correct. Some... 

The conected intensities for quinine sulfate are shown on Rguie 2.41, and these calculated values are seen to match the initial luiear portum of the curve. For precise corrections, it is preferable to prepare calibration curves using the precise compounds and conditions that will be used for the actual experimentation. Empirical corrections are typically used in most procedures to correct for san ik absev-bance. " ... 

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