Scale factor bias

We note also that, experimentally, the STM contrast is found to change as much as 0.5 A depending on the applied (positive) bias and specific tips. On these grounds, it is reasonable to expect that different tips would result in scaling factors different from the ones reported in [4]. In this respect, simultaneous AFM and STM of the surface acquire additional importance for the identification of experimental tip structures, and consequently, the scaling factor required to gain quantitative agreement between... 

The scale factor can be measured experimentally by a number of techniques, using either single crystal or powder samples (Stevens and Coppens 1975). Measurement for a number of crystals, including orthorhombic sulfur (S8) and x-deutero-glycylglycine, and comparison with least-squares values, indicate that scale factors from spherical-atom refinements are subject to a positive bias of... 

That the positive bias in the scale factors correlates with an increase in thermal parameters is evident from comparison of X-ray and neutron results (Coppens 1968). The apparent increase in thermal parameters of some of the atoms may be interpreted as the response of the spherical-atom model to the existence of overlap density. Because of the positive correlation between the temperature parameters and k, this increase is accompanied by a positive bias in k. 

Xu are the diagonal anharmonicity constants and Go is the polyatomic counterpart of the small Too Dunham constant [82] in diatomics. Consequently [50, 84, 90], the optimal scaling factor for ZPVEs is almost exactly midway between a 2(co) suitable for harmonic frequencies (as an approximate correction for systematic bias in the calculated frequencies) and a 2(v) suitable for fundamental frequencies (which additionally seeks to approximately corrects for anharmonicity). In fact, Alecu et al. [86] found for a large variety of basis sets and ab initio and DFT methods that 2((o)/2(ZPVE) = 1.014 0.002, which is almost exactly the ratio of 1.0143 found by Perdew and coworkers [87] between harmonic frequencies and ZPVEs derived from experimental anharmonic force fields. Note that the small uncertainty of 0.002 on a ZPVE of 140 kcal/mol still would translate to about 0.3 kcaFmol, and even that is probably optimistic for the uncertainty in an individual... 

With the flow of fuel A incorporated as a DV, we can apply the bias algorithm to maintain the total fuel constant. The bias algorithm supports the addition of a scaling factor on its input. In this case we set this factor to — 1. If we think as the output from the temperature controller being the total fuel required, the bias now subtracts the flow of fuel A from this... 

A second factor to consider in a valid sampling plan is the collection of enough individual sample increments to ensure that heterogeneity on a large scale does not bias the results. Estimation of this number can be made straightforwardly if the component of interest is distributed... 

F = 1 versus F = 1/3 for a diffusive conductor), it generally provides higher escape rates. However, the difference in functional form of the rates remains pronounced even upon rescaling with factor 3. The most pronounced feature of the backward bias curves is a plateau at If —> /th with subsequent drop to very small escape rates Tr (beyond the vertical scale of the plot). This is because the current distribution is restricted shot noise current is always of the same sign as the average current. 

Finally, since the intensity of the backscattered electron image used for AIA is highly dependent on the average atomic number of the material in view, pyrite particles with the heavy iron atom cross too often the signal threshold which has been set for a level characterized by clays, thus increasing the possibility of reading more pyrite. A similar bias has been observed previously (9 ), and an empirical factor of 0.75 has been suggested to scale down the inflated pyrite results. 

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