Systematic Uncertainties

Due to the high f -quark production cross-section, the uncertainty of the measurement will quickly become systematics dominated. In this chapter we cover the main systematic uncertainties that are expected to influence the measured cross section. Some of the systematic uncertainties are expected to be provided by other groups, others will be measured from data directly. The effects of the uncertainty of the detector description as well as the uncertainty on the dynamics of the process (production. 

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This test code specifies procedures for evaiuation of uncertainties in individuai test measurements, arising from both random errors and systematic errors, and for the propagation of random and systematic uncertainties... 

Our values agree, within the systematic uncertainty of about 40%, with most of the values reported in the literature (see Table V) (Wicke et al.,1982 Bruno,1983 Scott,1983 Toohey et al.,1984 Offermann et al.,1984 PorstendSrfer,1984 Bigu,1985 Israeli,1985 Reineking,1985). However, they are, on the one hand, an order of magnitude lower than those initially reported by Jacobi (1972) and Porstendorfer (1978) and, on the other hand, significantly higher than the recent estimations of Knutson (1983) and Schiller (1984). 

Theory doesn t tell us what initial Li a star has, only what depletion it suffers. An accurate estimate of the initial Li abundance is therefore a pre-requisite before observations and models can be compared. The Sun is a unique exception, where we know the present abundance, A(Li) = 1.1 0.1 (where A(Li)= log[AT(Li)/AT(H)] + 12) and the initial abundance of A(Li)= 3.34 is obtained from meteorites. For recently born stars, the initial Li abundance is estimated from photospheric measurements in young T-Tauri stars, or from the hotter F stars of slightly older clusters, where theory suggests that no Li depletion can yet have taken place. Results vary from 3.0 < A(Li) < 3.4, somewhat dependent on assumed atmospheres, NLTE corrections and TeS scales [23,33]. It is of course quite possible that the initial Li, like Fe abundances in the solar neighbourhood, shows some cosmic scatter. Present observations certainly cannot rule this out, leading to about a 0.2 dex systematic uncertainty when comparing observations with Li depletion predictions. 

The most convincing evidence for the BC model of Mu in III-V materials comes from the nuclear hyperfine structure in GaAs. The hyperfine parameters for the nearest-neighbor Ga and As on the Mu symmetry axis and the corresponding s and p densities are given in Table I. One finds a total spin density on the As(Ga) of 0.45 (0.38) with the ratio of p to 5 density of 23 (4) respectively. The fact that 83% of the spin density is on the two nearest-neighbor nuclei on the Mu symmetry axis agrees with the expectations of the BC model. From the ratios of p to s one can estimate that the As and Ga are displaced 0.65 (17) A and 0.14(6) A, respectively, away from the bond center. The uncertainties of these estimates were calculated from spin polarization effects, which are not known accurately, and they do not reflect any systematic uncertainties in the approximation. These displacements imply an increase in the Ga—As bond of about 32 (7)%, which is similar to calculated lattice distortions for Mu in diamond (Claxton et al., 1986 Estle et al., 1986 Estle et al., 1987) and Si (Estreicher, 1987). 

Radius R, from surface emission, linear surface velocity, or orbital constraints. Estimates of radius have historically been fraught with systematic uncertainties see 6. 

The observation that branches A and B in Fig. 6.25 merge at large Q is consistent with the predictions for and T since 6ti and 18.84 deviate from 16 by less than 15% and statistical errors of the experiment and systematic uncertainties in methods to extract the cumulant exceed this difference. In [325] for both the collective concentration fluctuations and the local Zimm modes the observed rates are too slow by a factor of 2 if compared to the predictions with T (the solvent viscosity) and (the correlation length) as obtained from the SANS data. It is suggested that this discrepancy may be removed by the introduction of an effective viscosity qf that replaces the plain solvent viscosity Finally at very low Q, i.e. 1, branch C should level at the centre of mass... 

What is the uncertainty in the molecular mass of 02 On the inside cover of this book, we find that the atomic mass of oxygen is 15.9994 0.000 3g/mol. The uncertainty is not mainly from random error in measuring the atomic mass. The uncertainty is predominantly from isotopic variation in samples of oxygen from different sources. That is, oxygen from one source could have a mean atomic mass of 15.999 1 and oxygen from another source could have an atomic mass of 15.999 7. The atomic mass of oxygen in a particular lot of reagent has a systematic uncertainty. It could be relatively constant at 15.999 7 or 15.999 1, or any value in between, with only a small random variation around the mean value. 

Propagation of systematic uncertainty Uncertainty in mass of n identical atoms = n x (uncertainty In atomic mass). 

A large potential source of systematic uncertainty is due to the finite image resolution. The measured image can be described as the convolution of the true sharp image with the imaging system point spread function, PSF. The PSF is reasonably approximated by a Gaussian,... 

D.S. Hussey, D.L. Jacobson, M. Rangachary, R. Borup, J. Spendelow, Systematic uncertainties in neutron imaging of proton exchange membrane fuel cells, 214th ECS Meeting, Honolulu, HI October 15, (2008)... 

The primordial abundances of the light elements are not measured easily and simultaneously. The main difficulties come from systematic uncertainties in inferring abundances from observations and in modeling their chemical evolution since the Big Bang. 

With increasing statistics, understanding of systematic uncertainty becomes more and more crucial. The work in progress ( )5) has not only higher statistics than >4 but also eliminates most of systematic uncertainties. 

The quoted error bars arise from statistical and systematical uncertainties and the uncertainty of the ratio u)ec/uj. of the cyclotron frequencies of the electron and the 12C5+-ion (electron mass), respectively. 

It appears likely that the statistical uncertainty will eventually be reduced to around 100 kHz, so we consider sources of systematic error which may be expected to enter at this level. The uncertainty in the second-order Doppler shift (450kHz/eV) will be reduced to 100 kHz by a 5% measurement of the beam energy. The AC Stark shift of the 2S-3S transition will be around 70 kHz for the present laser intensity, and can be extrapolated to zero intensity by varying the UV power. Finally, as mentioned above, the systematic uncertainties will be quite different from those in the microwave and quench anisotropy measurements. 

Table 1. Estimated effects on the formation rate scaling parameter S by the systematic uncertainties in the MC modelling...

To estimate the additional systematic uncertainty which originates from the unknown term of order a(Za)7 we studied a sensitivity of the fit (I) to introduction of some perturbation function h(z)... 

We have done explicit analysis to determine the error associated with the omission of the systematic shift caused by flat detector shape and location off the Rowland circle. This omission revealed a poor determination of the dispersion function and consequent errors of 100 ppm. Including this effect has allowed reduction of the dispersion function uncertainty to 20 ppm through the careful determination of systematic uncertainties. 

Fig. 6 A plot of the final line centers for the 8 configurations in which data were taken. The smaller error bars are the statistical uncertainties. The outer error bars include the systematic uncertainties...

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