Maximum Possible Error

The reflecting powers of Mn and Fe are nearly the same, and may be taken equal without serious error. This reduces the number of distinct structures to three namely, 1 ab, %abc, and 3, of which 1 ab depends on two parameters and the others on one. It is possible to decide among them in the following way. Let us assume that the contribution of oxygen atoms to the intensity of reflection in various orders from (100) is small compared with the maximum possible contribution of the metal atoms that is, with 32M. The metal atom structure factor for structure 1 for (/a 00) is... 

That is, there would be a 10% error, or uncertainty, in the answer. Note that even though terms in the denominator have a negative exponent, the maximum error due to these terms is still cumulative, because a given error may be either positive or negative i.e., errors may either accumulate (giving rise to the maximum possible error) or cancel out (we should be so lucky ). 

Even a small subset of the maximum possible sixteen beat frequencies is sufficient for track update processing based on the frequency-to-track association scheme. Almost all association errors could be avoided in multiple and extended target situations applying this procedure. This... 

The most important aspect of the job of the chemical analyst is to assure that the data and results that are reported are of the maximum possible quality. This means that the analyst must be able to recognize when the test instrument is breaking down and when a human error is suspected. The analyst must be as confident as he or she can be that the readout from an instrument does in fact indicate a true readout as much as is humanly possible. The analyst must be familiar with error analysis schemes that have been developed and be able to use them to the point where confidence and quality is assured. 

In this equation. Act is taken as the maximum possible surface tension lowering. Hence for a solute-free continuous phase, Aa is the difference between the interfacial tension for the solvent-free system and the equilibrium interfacial tension corresponding to the solute concentration in the dispersed phase. Equation (10-6) indicates a strong effect of the viscosity ratio k on the mass transfer coefficient as found experimentally (LI 1). For the few systems in which measurements are reported (Bll, Lll, 04), estimates from Eq. (10-6) have an average error of about 30% for the first 5-10 seconds of transfer when interfacial turbulence is strongest. 

This value, as expected, relates to the maximum possible momentum transferred from the photon to the microparticle, even if some values of the diffusion angle obviously have a very low or even zero probability. As stated before, this formula for the uncertainty in the momentum of the small particle M after the measurement is precisely the same for both microscopes. In either case, it is necessary to keep in mind that, in this step of the measuring process of the error of the two conjugated observables, the interacting photon behaves like a corpuscle. 

The decay portion of the rate curve was fitted to an exponential rate decay expression (6), rate = Mi exp (—t/M2), where Mi is the initial rate and M2 is a time constant for rate decay, and values of Mi and M2 were determined. In most cases exponential decay fit the data well as shown in Figure 3. Figures 4 and 5 show the effect of C6 olefin mole ratio on the decay time constant. The maximum possible error in these points is 10 In the propene system at a Ce C3 ratio of 20 the decay constant is 48,000 sec. With HY at 493°K and C6 olefin = 2, the ratio of the time constant for the ethene system to that for the propene system is about 20. Figure 4 shows that the decay time constant is independent of cation form, and for... 

The worst-case method is useful for estimating the maximum uncertainty expected when the results of several measurements are combined to obtain a result. We assume the maximum uncertainty in each measurement and then calculate the minimum and maximum possible results. These extreme values describe the range and thus the maximum error limit associated with a particular determination. 

The maximum possible error allows us to track the propagation of a set of uncertainties by considering the worse case scenario each time. Consider the following examples, where we are combining two quantities measured as 12.3 0.2 and 3.7 0.4. Thus the first quantity varies between 12.1 and 12.5, and the second between 3.3 and 4.1. 

What is the maximum possible error in A ubH for carbon dioxide ... 

In Chapter 7 we saw that the maximum possible error allows us to estimate the worst case scenario. The maximum probable error, however, takes into account the fact that this rarely is the case, with the error usually being somewhat smaller. It is straightforward to calculate the maximum probable error using the following formulae. In each case we assume that the quantities X and Yare measured, and are used to calculate Z. The estimated absolute errors on each quantity are AX, AY and AZ respectively. 

Using an appropriate number of figures, the difference is then quoted as 8.6 0.5. Note that this is slightfy fess than the maximum possible error calculated previously. 

The overall pressure is given as 4.20 0.10 atm. This is less than the maximum possible error for this calculation. 

Now we can determine the maximum possible errors in the solution of the inverse problem for the given level of the errors in the observed data, equal to 6 = i5d ... 

The smaller the norm of the inverse operator, the bigger the resolution, Rmo aJid the closer to each other are models that can be resolved. If the inverse operator is not bounded, i.e. its norm goes to infinity, the resolution goes to zero, Rmo — 0, and the maximum possible errors in the determination of m are infinitely large. We have exactly this case for the ill-posed problem. 

Among aqueous species, the most important corrections are for stabilities of the complexes U02(0H)2 and U(OH)4, which are apparently less stable than proposed by Grenthe et al. (1992) by about 2.4 and 10.6 kcal/mol, respectively. At near neutral pH s, stabilities of these complexes define the minimal respective solubilities of U(VI) and U(IV) minerals in groundwater. These errors have important implications to nuclear waste disposal, where the solubilities of U(IV) and U(VI) minerals are being used to define maximum possible uranium concentrations that might be released from a geological repository for nuclear waste (cf. McKinley and Savage 1994). 

Most capacitive evaluation circuits do not achieve the maximum possible resolution but are limited by the electromechanical interface, shortcomings in the electronic circuits, or stray signals coupling into the detector and corrupting the output. Section 6.1.2 below illustrates approaches to maximize the sensitivity of capacitive sensor interfaces, potential error sources, and approaches to minimize them. Electronic circuit options are discussed in Section 6.1.3. 

Al3+ The dominant species are A13+-S02 complexes in low pH, high SO4- water (TS-3, MW-86) and Al(OH)3 in low SO4- and near neutral waters (MW-36, MW-15, MW-12, MW-14). It is wise to bear in mind that accurate analyses for dissolved Al are very difficult to perform. Because of its very low dissolved concentrations, particulate and colloidal particles containing Al can dominate an analysis, unless great care is taken. Driscoll and Postek (1996) note that . .. because particulate minerals exhibit a continuous size distribution, no absolute distinction between dissolved and particulate forms can be made, and results show a strong dependence on filter pore size . In the absence of other errors, analyses for Al should be regarded as maximum possible values, from the point of view of geochemical modeling. It should also be noted that if an Al content is not reported (commonly the case), no conclusions at all can be reached about the saturation state of any aluminosilicate mineral. 

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