Errors in estimation

The equation (1) assumes the knowledge of the incident field E (r) which is the electrical field in the anomalous domain considering the flaw absent. This field must be computed before and one can imagine that small errors in estimation of this field may 2586... 

The overall requirement is 1.0—2.0 s for low energy waste compared to typical design standards of 2.0 s for RCRA ha2ardous waste units. The most important, ie, rate limiting steps are droplet evaporation and chemical reaction. The calculated time requirements for these steps are only approximations and subject to error. For example, formation of a skin on the evaporating droplet may inhibit evaporation compared to the theory, whereas secondary atomization may accelerate it. Errors in estimates of the activation energy can significantly alter the chemical reaction rate constant, and the pre-exponential factor from equation 36 is only approximate. Also, interactions with free-radical species may accelerate the rate of chemical reaction over that estimated solely as a result of thermal excitation therefore, measurements of the time requirements are desirable. 

Grimm JW, Lynch JA. 1991. Statistical analysis of errors in estimating wet deposition using five surface estimation algorithms. Atmos Environ 25(2) 317-327. 

Surface runoff (Q) is the second-largest part of the hydrologic water balance for ET landfill covers at many sites in humid regions. Even at dry sites where surface runoff is small, errors in estimates of Q are important, and especially so if the model estimates significant Q on days with no runoff. Estimates of Q are therefore important to the design process at all sites. 

Water leaving the site (Q) reduces the volume that must be stored within the cover. Errors in estimating daily Q will result in erroneous estimates of cover performance as measured by PRK of water below the cover. If the estimated Q is too low, the estimated PRK will be too high and vice versa. 

Gore, J. Ritort, F. Bustamante, C., Bias and error in estimates of equilibrium free-energy differences from nonequilibrium measurements, Proc. Natl Acad. Sci. USA 2003,100, 12564-12569... 

We attempt the calculation in the hope that error in estimating activity coefficients will not be so large as to render the results meaningless. In fact, the situation may be slightly better than might be feared because the activity coefficients appear in the numerator and denominator of the mass action equations, the error tends to cancel itself. 

Both methods are also limited in accuracy of secondary structure determinations because spectral peaks must be deconvolved estimates are made of the overlapping contributions of different structural regions. These estimates may introduce error based on the reference spectra used and because deconvolution methods equate crystallographic secondary structure with the secondary structure of the protein in solution (Pelton and McLean, 2000). As amyloid fibrils are neither crystalline nor soluble, there may be even greater error in estimates of secondary structure. To compound the problem, estimates of /f-sheet content are less reliable than those of a-helix, because of the flexibility and variable twist of / -structure (Pelton and McLean, 2000). In addition, / -sheet and turn bands overlap in FTIR spectroscopy (Jackson and Mantsch, 1995 Pelton and McLean, 2000). Side chains also contribute to spectral peaks in both methods, and they can skew estimates of secondary structure if not properly accounted for. In FTIR spectra, up to 10-15% of the amide I band may arise from side chain contributions (Jackson and Mantsch, 1995). 

These sources of error in estimating secondary structure content from CD and FTIR spectra suggest that the estimates, especially for amyloid fibrils, should be considered qualitative. 

Thus, errors in all the heats, apart from the precisely known water value, are decreased ra-fold in the required heat. The hydrolysis heat A//2 is always much less than At and can be measured less precisely. The reactions involved in reactions 2, 3, and 6 of Table II have been used in the CODATA evaluation of Aif,(F q)), although in theorv reactions 7 and 8 should lead to more accurate values. In practice this may not be true. Thus the fluorination of iodine produces some IF7, together with the bulk of IF5, and errors in estimating the mixture can cause uncertainty in the final value of AZf/IF ). The hydrolysis heat for the reaction... 

Since the constant terms on the right-hand side of the previous equations vary by some 17 orders of magnitude, we may face serious roundoff errors in estimating/(x). One way of scaling the equations is to divide each conservation equation by the total amount of the corresponding component and each mass action relation by the corresponding equilibrium constant. If the choice of the initial estimate x<0) is not too awkward, we should obtain the six equations as differences between numbers of more similar magnitudes (ideally unity for all but the electroneutrality condition)... 

Fig. 1 represents 2> a reaction coordinate plot for a system where a reactant A can undergo conversion to one of two products B or C. The full line represents the real situation the process. <4 > Cis favoured since the corresponding transition state (Y)is lower. The other lines represent calculated paths where we suppose the segment A C to be reproduced correctly, but where errors are made in estimating the properties of B. An error in estimating its... 

The volume fraction of each phase was taken from the fractional area in the transmission electron micrographs. Combined with the values shown in Table 1, the compositions within each phase were calculated and are shown in Table 2. Overall, the results suggest variably 0-20% actual molecular mixing. Noting the probable errors in estimating the experimental Tg s, the and W2 values are probably correct to within +0.05. Thus mixing plays an important role in interpenetration and influences the reinforcement within each phase. 

The dielectric constant of the pure cyanurate network under dry nitrogen atmosphere at 20 °C is 3.0 (at 1 MHz). For the macroporous cyanurate networks, the dielectric constant decreases with the porosity as shown in Fig. 57, where the solid and dotted lines represent experimental dielectric results together with the prediction of the dielectric constant from Maxwell-Garnett theory (MGT) [189]. The small discrepancies between experimental results and MGT might be due to the error in estimated porosities, which are calculated from the density of the matrix material and cyclohexane assuming that the entire amount of cyclohexane is involved in the phase separation. It is supposed that a small level of miscibility after phase separation would result in closer agreement of dielectric constants measured and predicted. Dielectric constant values as low as 2.5 are measured for macroporous cyanurates prepared with 20 wt % cyclohexane. 

The goodness of fit for this simple treatment can only be evaluated by comparison with the more exact but much more complex solutions. From such a comparison we find that the maximum error in estimate of D/wL is given by... 

This is not a very satisfactory fit even when the value of R = 0.9546, as the standard error of boiling point estimation is 32.4 °C. The maximum error in estimation is with methane, where the error is 85.3 °C. The curve of experimental T, versus Nc has a negative second derivative and makes a downward arch, and is not well represented by a straight line, especially at the two ends and at the middle. 

Errors in estimation of the retention volumes from the apexes of skewed peaks (peak skewing depends on the flow rate)... 

In principle, intrinsic viscosities used for estimating branching should be measured under conditions where the expansion factor a is unity, but as indicated in Section 6, it is not easy to identify such conditions. Some authors, e.g. Moore and Millns (40) have measured [tf at the theta-temperature of the corresponding linear polymer, but it is doubtful whether a is unity at that temperature for either linear or branched polymer, if the theories of Casassa or of Candau et al. are valid. If a were the same for both linear and branched polymers under the same conditions g would be unaffected and g could be measured at any convenient temperature some authors have presented data suggesting that g is nearly the same in good and poor solvents, e.g. Hama (42) and Graessley (477), but other authors, e.g. Berry (43) have found g to vary. The best that can be done at present would appear to be to measure g at the theta-temperature on the assumption that this ratio will be less temperature-sensitive than either intrinsic viscosity, and that even if this temperature is not the correct one it will be near it. Errors in estimates of branching due to this effect are likely to be much less serious than those due to the use of an incorrect relation between g and g0. 

An evaluation of the expected errors in estimated hourly deposition was made from radiochemical data for three rainstorms. The results showed that the calculated values agreed with the measured values to within a factor of two, and the estimated and actual depositions rapidly approached the same value as the time period considered was increased. In general, for intervals of 6 hours, the errors do not exceed 30%. 

From the above it follows that the method of estimating the tunneling distance using the dependence of the radiation yield of et on the concentration of acceptor is undoubtedly rougher than the one based on studying the reaction kinetics over a wide time interval. At sufficiently long times of observation, however, the error in estimating Rt from data on the concentration dependence of G seems to be acceptably small. For this reason the use... 

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