Trace errors

When calculating the trace error for different values, one finds that this error vanishes for = 1.957 in the ground state and for = 1.215 in the excited state. These values coincide with those corresponding to the minimal RMS deviations of the matrices. Therefore the selection criterion for seems to be adequate. 

Display. Some calculators will display an entire mathematical operation (e.g. 2 + 4 = 6 ), while others simply display the last number/operation. The former type may offer advantages in tracing errors. 

Figure 4.2 A schematic diagram of a tracing error in protein crystaiiography. initiaiiy, on tracingthe density, the residue in biue is missed by the tracing aigorithm. Consequentiy, the residue subsequent to this is erroneousiy...

Diagnostic routine A software program designed to trace errors in software, locate hardware faults, or identify the cause of a breakdown. 

Any systematic error that causes a measurement or result to always be too high or too small can be traced to an identifiable source. 

Sources of Indeterminate Error Indeterminate errors can be traced to several sources, including the collection of samples, the manipulation of samples during the analysis, and the making of measurements. 

Heydorn, K. Detecting Errors in Micro and Trace Analysis by Using Statistics, Anal. Chim. Acta 1993, 283, 494M99. 

A second use of arrays arises in the detection of trace components of material introduced into a mass spectrometer. For such very small quantities, it may well be that, by the time a scan has been carried out by a mass spectrometer with a point ion collector, the tiny amount of substance may have disappeared before the scan has been completed. An array collector overcomes this problem. Often, the problem of detecting trace amounts of a substance using a point ion collector is overcome by measuring not the whole mass spectrum but only one characteristic m/z value (single ion monitoring or single ion detection). However, unlike array detection, this single-ion detection method does not provide the whole spectrum, and an identification based on only one m/z value may well be open to misinterpretation and error. 

Common usage. Steam tracing has been around for many years and many operators are famihar with the system. Because of this familiarity, failures due to operator error are not very common. 

CU-CUSO4 electrodes with saturated CUSO4 solution are recommended for potential measurements in soil. Their potential constancy is about 5 mV. Larger errors can be traced to chemical changes in the CUSO4 solution. These electrodes have been developed for long-life applications in potential-controlled rectifiers and built-... 

The fact that the equilibrium moisture content may be considerable at low humidities is of especial importance in the oven methods. Under ideal conditions no water vapor should be present in the oven, but this is impossible to attain in practice. It is difficult to maintain a dry atmosphere in an air oven, and most commercial vacuum ovens are not air-tight. Thus, the discrepancies in results of different investigators have frequently been traced to different humidities in their ovens. Any attempt to reduce the relative humidity by increasing the oven temperature introduces the danger of error from thermal decomposition. 

It is crucial in quantitative GC to obtain a good separation of the components of interest. Although this is not critical when a mass spectrometer is used as the detector (because ions for identification can be mass selected), it is nevertheless good practice. If the GC effluent is split between the mass spectrometer and FID detector, either detector can be used for quantitation. Because the response for any individual compound will differ, it is necessary to obtain relative response factors for those compounds for which quantitation is needed. Care should be taken to prevent contamination of the sample with the reference standards. This is a major source of error in trace quantitative analysis. To prevent such contamination, a method blank should be run, following all steps in the method of preparation of a sample except the addition of the sample. To ensure that there is no contamination or carryover in the GC column or the ion source, the method blank should be run prior to each sample. 

Such of these errors as are particular important in the determinations of traces or of light elements will be discussed more fully in Chapter 8. 

Manganese, determination by x-ray emission spectrography, 328 in domestic ores, 200, 202, 203 trace analysis by x-ray emission spectrography, 228, 229, 231, 232 Manipulative errors, standard counting error comparable with, 285-287 Mass absorption coefficient, additivity, 15... 

Horton (H9, H10) has obtained additional acoustic-admittance data for a series of composite propellants. At a given frequency, decreasing the mean oxidizer particle size increases the acoustic admittance and thereby the tendency for instability. Horton also investigated the effects on the acoustic admittance of the incorporation of traces of copper chromite, a known catalyst, for the decomposition of ammonium perchlorate, lithium fluoride (a burning-rate depressant), and changes in binder these data are difficult to analyze because of experimental errors. 

A numerical value for the residual error can be obtained by taking the trace of each matrix in Eq. 22. Thus provided the statistics of the noise and turbulence are known, then the error in the reconstruction can be predicted. 

Certain older reports [14] on the existence of extremely sulfur-rich sulfanes in mixtures of high sulfur content obtained from sodium thiosulfate and hydrochloric acid are in error since elemental sulfur was shown to be the main component besides traces of H2S [15]. 

Particular attention has been devoted to the compilation of the cumulative index. Every reference work is only as good as its indexing system. For this reason a presentation has been chosen which allows one to recognize immediately in which volume the key word appears. The same also applies to named reagents which can be traced back to the original publication in almost all cases in order to be able to correct any errors that have crept in. This type of presentation will be continued in future volumes. 

Figure 4.51. Distribution of experimental data. Six experimental formulations (strengths 1, 2, resp. 3 for formulations A, respectively B) were tested for cumulative release at five sampling times (10, 20, 30, 45, respectively 60 min.). Twelve tablets of each formulation were tested, for a total of 347 measurements (13 data points were lost to equipment malfunction and handling errors). The group means were normalized to 100% and the distribution of all points was calculated (bin width 0.5%, her depicted as a trace). The central portion is well represented by a combination of two Gaussian distributions centered on = 100, one that represents the majority of points, see Fig. 4.52, and another that is essentially due to the 10-minute data for formulation B. The data point marked with an arrow and the asymmetry must be ignored if a reasonable model is to be fit. There is room for some variation of the coefficients, as is demonstrated by the two representative curves (gray coefficients in parentheses, h = peak height, s = SD), that all yield very similar GOF-figures. (See Table 3.4.)...

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