Relative deviation

The time constant is one way of determining the dynamic features of a measurement system. Not all instrument manufacturers use the time constant some use the response time instead. The response time is the time between a step change of the measured quantity and the instant when the instrument s response does not differ from its final value by more than a specified amount.The response time is defined according to a deviation from the final value. Often response times for the relative deviation of 1%, 5%, 10%, or 37% are used. The corresponding response times are denoted by 99%, 95%, 90%, or 63% response time, respectively. The response time for a first-order system can be solved from Eq. (12.15). Note that the 63% response time of a first-order system is the same as the time constant r of the system. 

Table 1. Calculated properties of ratile, anatase, brookite, and columbite phases. Relative deviation from experimental values is shown in brackets. Structural experimental data are from 19,20,21,9 respectively. Bulk modulus of ratile extrapolated to 0 K is from 2.

The resisitivites p corresponding to the DC conductivities results reproduce the measured strong dependence of p on the composition correctly. The CP results agree with the experiments very well. The only exception is the composition with 20% sodium where the relative deviation is about 100% however, the absolute deviation is small. 

For both alloy systems the theoretical results for p obtained in a fully relativistic are found in very satisfying agreement with the corresponding experimental data. In addition to these calculations a second set of calculations has been done making use of the two-current model. This means the partial resistivities p have been calculated by performing scalar relativistic calculations for every spin subsystem separately. As can be seen, the resulting total isotropic resistivity p is reasonably close to the fully relativistic result. Furthermore, one notes that the relative deviation of both sets of theoretical data is more pronounced for Co2,Pdi 2, than for Co2,Pti 2,. This has to be... 

Accuracy The two programs very accurately approximate the tabulated values, the relative deviations (LRR) remaining below 0.01%, except when the equations on lines 10 are used, where they remain below 0.6%. 

The effect of double-closure is shown in Table 31.8. For convenience, we have subtracted a constant value of one from all the elements of Z in order to emphasize the analogy of the results with those obtained by log double-centering in Table 31.7. The marginal means in the table are average values for the relative deviations from expectations and thus must be zero. 

Table 1. Characterisation data and viscosities, ri0, of polystyrene (molar mass distribution Mw/Mn<1.3) in toluene at 25 °C. Theoretical viscosities, ri0(theor), were calculated from Eq. (14). In the last column A represents the relative deviation of ri0(theor) from T 0(exp) ...

Fig. 3a indicates that the bubble-rise velocity measured based on the displacement of the top surface of the bubble ( C/bt) quickly increases and approaches the terminal bubble rise velocity in 0.02 s. The small fluctuation of Ubt is caused by numerical instability. The bubble-rise velocity measured based on the displacement of the bottom surface of the bubble (Ubb) fluctuates significantly with time initially and converges to Ubt after 0.25 s. The overshooting of Ubb can reach 45-50 cm/s in Fig. 3a. The fluctuation of Ubb reflects the unsteady oscillation of the bubble due to the wake flow and shedding at the base of the bubble. Although the relative deviation between the simulation results of the 40 X 40 x 80 mesh and 100 x 100 x 200 mesh is notable, the deviation is insignificant between the results of the 80 x 80 x 160 mesh and those of the 100 X 100 x 200 mesh. The agreement with experiments at all resolutions is generally reasonable, although the simulated terminal bubble rise velocities ( 20 cm/s) are slightly lower than the experimental results (21 25 cm/s). A lower bubble-rise velocity obtained from the simulation is expected due to the no-slip condition imposed at the gas-liquid interface, and the finite thickness for the gas-liquid interface employed in the computational scheme.

Substantial abundance anomalies occur among the heavy oxygen isotopes 170 and 180, which are underabundant by up to about 4 per cent relative to 160 in oxide grains of certain of the CAIs, compared with the bulk composition in which the isotope ratios are closer to a terrestrial standard. The intriguing feature of these anomalous ratios is that, in common with some other meteorites, but in contrast to terrestrial and lunar samples, the relative deviations of the two heavy isotopes are equal most normal fractionation processes would cause 180 to have twice the anomaly of 170, as indeed is observed in terrestrial samples and more differentiated meteorites, where the anomalies are also usually much smaller. While there has been speculation that there might be a substantial admixture of pure 160 from a supernova, there are fractionation mechanisms that may be able to account for the effect, e.g. photo-dissociation of molecules affected by selfshielding (R. Clayton 2002). In this case, it is possible that the terrestrial standard is enriched in the heavy O-isotopes while the inclusions have more nearly the true solar ratio. 

The relative deviation (RD%) is used for monitoring sub-sampling error ... 

The 8180 of a sample is the relative deviation in permit of its 180/160 ratio relative to that ratio in a reference material, usually the standard mean ocean water (SMOW)... 

A natural starting value for z if F. The calculation listed in Table 3.5 was stopped once the relative deviation in z was less than 0.001. The final z value of 0.4306 is converted through equation (3.1.33) into... 

Fig. 12.1 Illustration of the temperature sensitivity of 15N relaxation parameters, Rlf R2t and NOE, as indicated. Shown are the relative deviations in these relaxation parameters from their values at 25 °C as a function of temperature in the range of + 3 °C. The expected variations in / ] and R2 due to temperature deviations of as little as +1 °C are already greater than the typical level of experimental precision ( % ) of these measurements (indicated by the dashed horizontal lines). For simplicity, only temperature variation of the overall tumbling time of the molecule (due to temperature dependence of the viscosity of water) is taken into account the effect of temperature variations on local dynamics is not considered here.

Units which are used in isotopic work depend on the precision of the measurements. Generally 5 units are used for stable isotopes and correspond to permil relative deviation. It is used occasionally also for non linear effects and then they are permil (%o) deviations without reference to mass differences between the isotopes. Since the beginning of the 70s (e.g., Papanastassiou and Wasserburg 1969) thermal ionization data are often given in e units which are fractional deviation from the normal in 0.01%. With the new generation of more precise instruments, results are sometimes given in ppm (parts per million) relative to a terrestrial standard sample. 

Figure 4. Non-linear effects for Sr, Ba, Ndand Sm in the FUN inclusions Cl andEKldl (McCulloch and Wasserburg 1978a,b Papanastassiou and Wasserburg 1978). Relative deviations from terrestrial standard ratios are plotted after normalization with the isotope pair represented with large open squares. Each isotope is labeled with its primary nucleosynthetic source. In using s-process isotopes for normalization, clear excesses in r-process nuclei are seen for Ba and Sm in EK141. Sr is normal in both inclusions except for a deficit in the p-process Sr. AsNdhas only one pure s-process isotope at mass 142, the data in EK141 have been further corrected to yield an excess in Nd identical to that of Sm as these two isotope are pure r-process nuclei expected to be produced in comparable abundances.

The results can be reported in the conventional delta notation of stable isotopes, which is the relative deviation in parts per one thousand of a given isotopic ratio in a sample with respect to the same ratio in a standard sample. Reporting results in the epsilon notation (in parts per 10,000 as in Zhu et al. 2000, 2002) may seem legitimate, but so far stable isotope data have overwhelmingly been reported in per mil and competing notations are a source of confusion. 

C/ tm. With a Si-island underneath, the temperature homogeneity is further improved. For a comparable device with a Si heat spreader a relative deviation of less than 2% equivalent to a temperature gradient of 0.07 °C/pm at 300 °C in the active area was achieved (see Sect 4.4.4 and [81]). 

The relative deviation between measurement results and the temperature-depen-dent MOS transistor model data was less than 10% above 100 °C. In the case of a source-drain bias of 5 V it appeared that the model described the real situation well up to 300 °C, but then started to deviate. 

Run Xai Change with respect to the standard case "a eq. (26) Relative deviation (%) ... 

The best values of the parameter Cj are 1.51, 1.36, and 2.01 for no mass transfer, d and c direetion of transfer respectively. The product af is considered as the agitation variable in the equation, since the fit could not be improved if a and / were treated separately. The average absolute value of the relative deviation in the predicted values of d 2 from the experimental points is 16.3%. Even in packed columns, the separation can be substantially improved by pulsing of the continuous phase resulting from greater shear forces that reduce the drop size and increase the interfacial area [1, Chapter 8]. 

The optimized values of C are 0.63, 0.53, and 0.74 for no mass transfer, c -> <7 and c, respectively. The value of the holdup is ignored due to lack of data. Equation (9.12) predicts the drop size with an average absolute value of the relative deviation of 23%. 

The values of the constant Ci are 9.81 x 10 for no mass transfer and c d transfer, and 0.31 for d -> c transfer. The stage number which varies from 2-17 in the present set of data, shows a rather weak effect on drop size. Equation (9.13) predicts the drop diameter with an average absolute value and relative deviation of 17.6%. 

Gong and Cao described A. annua SEE of artemisinin (1) in SCCO2 determined by static method at three temperatures (313, 323 and 333 K) and pressures varying between 11 and 31 MPa. The solubility data ranged from 0.498 x 10 to 2.915 x 10 mol/mol under these conditions. Two density-based models (Chrastil s and Mendez-Sanfiago-Teja s) were selected to correlate the experimental data and the average absolute relative deviation was 8.32% and 8.33%, respectively. The correlation results were in agreement with experimental data. 

A linear solvation energy relationship (LSER) has been developed to predict the water-supercritical CO2 partition coefficients for a published collection of data. The independent variables in the model are empirically determined descriptors of the solute and solvent molecules. The LSER approach provides an average absolute relative deviation of 22% in the prediction of the water-supercritical CO2 partition coefficients for the six solutes considered. Results suggest that other types of equilibrium processes in supercritical fluids may be modeled using a LSER approach (Lagalante and Bruno, 1998). 

AT),(AT)] ranges from 0.003 to 0.124 eV [31]. The new NDDO-HT parameterization allows one to reproduce these changes rather well. Relative deviations of the semiempirical estimates from the corresponding HF values are about 3% on average. 

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