Relative errors, list

Display Accuracy) presents a list of typical and extreme absolute and relative errors incurred when using the approximation note that the listed errors are in part due to the algebraic approximation as such, and in part to the finite number of digits of the tabulated values. 

Our first chapter in this set [4] was an overview the next six examined the effects of noise when the noise was due to constant detector noise, and the last one on the list is the first of the chapters dealing with the effects of noise when the noise is due to detectors, such as photomultipliers, that are shot-noise-limited, so that the detector noise is Poisson-distributed and therefore the standard deviation of the noise equals the square root of the signal level. We continue along this line in the same manner we did previously by finding the proper expression to describe the relative error of the absorbance, which by virtue of Beer s law also describes the relative error of the concentration as determined by the spectrometric readings, and from that determine the... 

The relative efficiencies have also been obtained by comparing these relative errors to the smallest value of the other estimates for each case studied. The smaller the relative error, the better the model parameter estimation the larger the relative efficiency, the better the estimator. Results are listed in Table 1 for the uniform and t2 distributions. 

Example The [M-Cl]" ion, [CHCl2], represents the base peak in the El spectrum of chloroform. The results of three subsequent determinations for the major peaks of the isotopic pattern are listed below (Fig. 3.15). The typical printout of a mass spectrometer data system provides experimental accurate mass and relative intensity of the signal and an error as compared to the calculated exact mass of possible compositions. For the [ CH Cl2] ion, the experimental accurate mass values yield an average of 82.9442 0.0006 u. The comparatively small absolute error of 0.6 mmu corresponds to a relative error of 7.5 ppm. 

Suppose an intravenous bolus is given at t = 0 and the drug concentration in the plasma is observed beginning at a time point t > 0. In Table 5.3 we list a data set of Cutler (ref. 20) generated by adding 1 /. relative errors of random character to the values of the weighting function... 

The solid lines in Figs. 1 and 2 represent the turnover frequencies predicted by using the previous rate expression and the fitted parameters listed in Table III, which is a list of the values of the fixed and fitted parameters, the 95% confidence limits for the fitted parameters, and the overall relative error of the fitted reaction kinetics data. Figures 1 and 2 show that the kinetic... 

Calculate the % relative error in solubility by using concentrations instead of activities for the following compounds in 0.05000 M KNO3 using the thermodynamic solubility products listed in Appendix 2. (a) CuCl (acu = 0.3 nm). 

Provided the stoichiometry n is secured by supplementary noncalorrmetric evidence and, furthermore, is unperturbed by high concentrations of the interaction partners, an analysis of the statistical error allows some recommendations to be made for parameter adjustment to optimize the precision [24], Hence, under these prerequisites (which admittedly seldom apply in artificial host-guest systems) the enthalpy AH and association constant Kassoc can be determined to less than 1% relative error in a broad range (10 < Kassoc < 10 valid for AH, too, when Kassoc > 30 just following a simple recipe [23] (i) Use no more than 10 injections of the titrant solution (ii) set the final molar ratio in accord with the empirically determined Eq. (3.8), but not smaller than 1.1 where c is as defined in Eq. (3.7) this requires a crude estimate of the binding constant Kassoc- Table 3.1 lists the digest of... 

It is expected that similar to method reported previously based on the use of cyclodextrins and sucrose the present method should have high sensitivity. Its sensitivity can be evaluated from two values the lowest enantiomeric excess (EE% which is defined as EE% = [(R-enantiomer - S-enantiomer)/(R-enantiomer + S-enantiomer)]) that can be determined at the lowest concentration of a sample. It should be noted that these two terms are interdependent to each other, namely, the limit of detection (LOD) on ee% can be improved by increasing sample concentration or vice versa. In an attempt to estimate the sensitivity of the method, we performed measurements on 10 samples of 10.0 mM or 2.66 mg/mL of atenolol with different cc% s in S- CHTA Tf2N. Results obtained are listed in Table 2. It is evident from the table that the method is not only effective but also very sensitive. It can accurately determine samples with concentration as low as micrograms having ee value as high as -90.00% (or +97.00% ) and as low as 0.6%. Furthermore, even at ee as low as 0.6%, the relative error was only 3.33%. 

The quantization of results of the thermal decomposition of pharmaceuticals, using TG and DTG, is rapid and simple in that no calibration is required and time-consuming calculations are not necessary. Moreover, the results are less dependent on the experimental conditions. The relative errors for the determinations are listed in Table 4.6 (95). 

Figure 3. shows the comparison between original and the reconstructed major stress field after 120 days of heating. The reconstructed stress distribution shows very close agreements for all stages of stresses. Table 1. lists relative errors at some selected points inside the pillar. In most cases, errors for the major principal stress show... 

The sample preparation has been carried out at ambient pressure and temperature. The properties of the PEP-polymers used for the cloud-point measurements are listed in Table 8.1, for which the molecular weights have been measured with high temperature gel permeation chromatography (GPC, dynamic viscosity). The estimated relative error in the amounts of the components in the mixtures is <2% for PEP8.7, <0.1% for PEP51 and ethylene, and <0.7% for CO2. 

Analysis of the wastewater samples took place less than 24 h after they were transported to the laboratory. Table 1 lists the results obtained as mean values the relative errors are less than 5%. The pH was tested in situ. The chemical composition of this oil field wastewater is directly influenced by the fact that it comes from Guantao group in North China. The minerals in the wastewater are leached out from the strata under high temperature and pressure conditions when steam injection during heavy oil thermal recovery. There is a lower concentration of organic substances in the oil field wastewater than that of typical municipal wastewater. 

Tables 3.3 and 3.4 show the results of the determination of oligomers contained in 0.5 mg/ml sample solutions of PEG 400 and POE(9)D, respectively. Both analyses were carried out in purely methanolic mobile phases. PEG and POE were selected as standards for corresponding oligomer mixtures. values for the POE( )D series are listed in Table 3.4 together with analytical results. Since fCf values generally included approximately 5% relative errors, the concentrations listed in tables show more ambiguity.

Table III shows the results of titrating 0.5 ml of each limestone solution. The mean relative error of -6 indicates about a -4 error in the dissolution procedure, since the instrumental error amounted to approximately 2% The determinations listed are representative. Variation in instrumental parameters, such as titrant delivery rate (5 1), difference...

Based on the example of PaU rings, the relative error 5 (Ap/ff) for the 873 experimental values listed in Table 4-4a throughout the entire operating range, including the pressure drops at the flooding point, is given as ... 

Table 4-3. List of relative errors <5 (hi) and number of test points for investigating the total liquid hold-up for various random and structured packings...

Based on the constant value of the parameter Cb = 0.4s m, it is possible to verify by calculation 85% of the experimental pressure drop values for irrigated packing elements of any type or size as well as for type Y structured packings (for the latter, the wall factor K = 1 must be substituted into Eq. (4-48) or (4-49), see Chap. 3). The calculation is performed with a relative error of less than 15 %. This was the result of the evaluation of approx. 10000 experimental data items of various systems. The resistance coefficients xf of the tested packing elements for the transition range and the turbulent flow range of the gas phase are listed in Tables 6-la-c. 

For the purpose of comparing the results of the pressure drop calculation, acc. to the models presented above, with those shown in Chap. 4, Eq. (4-48), as well as Eq. (5-2), Tables 5-la-c contain a list of the relative errors for the individual flow ranges and types of packings. They indicate which of the correlations for determining the pressure drop are preferable. 

Although the recoveries are close to one, the balances were individually checked with the y test. The test function h listed in Table 18 was calculated for a relative error on the measurement of 3% and must be compared with a threshold value of 2.71 for 1 degree of freedom and a significance level of 90%. 

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