Generalization error, sources

A particular attention must be given to the examination of spectra, because they can be an error source. The magnetic spectrum presence is very important, because it conditions the testing sanction. Generally we proceed to an identification of the real defect nature which has lead to the formation of the spectrum... 

There are two sources to the generalization error (Girosi and Anzel-... 

In most situations analysts can achieve a rapid reasonable separation of compounds using an appropriate standard CE method with generic operating conditions [877]. This eliminates or reduces dramatically the need for method development. Major instrumental error sources in CE are detection, integration and injection. General guidelines for validation of CE methods are available and similar to those of HPLC [878]. Validated CE methods often perform the same as, or better than, the corresponding HPLC methods. 

Attention has already been given to the errors associated with peak size measurement and with standardization. There are many other places in the chromatographic process where errors enter into quantitative analytical GC. Detailed analysis of most of these error sources is not possible, especially in the confines of this chapter, but they should and will be mentioned and briefly discussed. Most of the error sources are generally obvious it may indeed seem even ridiculous that some have to be mentioned. However, the mere fact that they are obvious tends to slowly place them in the overlooked category. One has to be constantly reminded of these errors until the consideration of them becomes habitual with each problem. 

Fast-response time-domain measurements suffer from error sources which in general are more commonly associated with spectroscopic techniques (e.g. n.m.r.) than with other dielectric methods. The existence of these sources of error must be recognized, particularly when selecting the most appropriate method for the collection and handling of exp -mental data. It is convenient to separate error sources into foru major categories ... 

Table 5. Compilation of important sources of error in surface exposure dating studies. The quoted uncertainties (2cj level) are only estimates for t5q)ical cases and may in reality be higher or lower depending on the special conditions. Additional error sources which cannot at all be quantified in any general manner include lacking information on erosion rate, uplift or subsidence, complex exposure histories, etc.

CMB Resolution A final issue that may complicate the application of the CMB on ambient data sets is existence of two. sources with similar fingerprints or, more generally, a source whose profile is a linear combination of other source profiles. This is called the collinearity problem. If this is the ca.se then the matrix [A WA] u.sed in (24.15) has two columns that are almost similar, or a linear combination of. several others. This matrix from a mathematical point of view is close to singular and the result of its inversion is extremely. sensitive to small errors. Often, if this is the case, the results of CMB are large positive and negative. source contributions. The simplest solution to this problem is identification of the "offending sources and elimination of one of them. Physically, becau.se the source.s are too... 

There are significant differences between the UV-Vis and IR absorption spectra. IR spectra, even those of samples in condensed states, are generally characterized by a large number of well defined, sharp bands, with easily localizable positions. Therefore, IR spectra are useful for the fast, non-destructive identification of the chemical substances, and it is extremely unlikely that two substances that are chemically different to have, accidentally, identical IR spectra Instead, the quantitative determinations in the IR spectral range are more difficult because diffuse radiation in the IR spectrophotometers is greater than in the UV-Vis spectrophotometer, so the error sources affect the results of quantitative determinations more than in the UV or Vis range. 

The uncertainties on the measured frequencies, either cOi and co+ or co+ and co, translate to an uncertainty on the mass m2 of the unknown ion determined from Equation 10.10. As shown in Figure 10.16, the relative uncertainty depends on the chosen reference measurement as well as the mass ratio p. For a mass ratio larger than 1.25, it appears to be advantageous to determine the mass from co+ and co, however, the difficulties in making a precise determination of cd are sufficiently severe that a mass measurement based on cOi and co+ is generally preferable, provided that error sources, which are more severe for mass measurements based on o), and C0+, for example, drift of the ion-trap frequency and RF-induced secular potentials, are sufficiently small. 

Table 5.12 lists the major sources of random and systematic errors encountered in x-ray spectrometry. Methods for handling these error sources are discussed in subsequent chapters. As Table 5.12 shows, the major sources of random error arise from counting errors and equipment instability. Equipment random error has improved to the point where this source of error is generally of very low order (i.e., approximately 0.05 to 0.1%). Thus, to increase analytical precision, the major systematic errors must be recognized and eliminated or reduced. 

Composite tracking accuracy is generally dominated by antenna performance. Accuracy is determined by instrumentation and propagation error sources as well as the noise-limited precision. Instrumentation errors include antenna illumination errors as well as amplitude and phase imbalance among the monopulse receiver channels. Propagation errors are generally dominated by multipath and tropospheric refraction. Both error sources decrease in severity as elevation angle increases. 

First of all, these 0(6T ) errors refer to a single 6T step, whereas in the simulation in the T-range 0 < T < 1 we take 6T steps. Generally, this reduces the error order by one. Tests show that it is in fact the discretisation of the second derivative which limits the accuracy, hence the 0(H ) error for all methods. We might say that, in view of this, we are lucky that the better methods (CN, RKI) give better results, since they suffer from the same error source. 

As mentioned previously, when a known sample size is required, as in the external standardization technique, the measurement of that sample size will generally be the limiting factor in the analysis. However, improper sample injection can introduce into the analysis errors other than those pertaining to sample size. Thus it will be beneficial to examine the various methods of sample injection and both types of error associated with them. A common error source in split-injection systems comes from the discrimination of components in the mixture on the basis of their boiling point differences. The problem can be attributed to in-needle fractional distillation, nonevaporative transport (mist) that bypasses the column inlet, or poor mixing with the mobile phase when low split ratios are used. Errors associated with the inlet system are covered in detail in Chapter 9, Inlet Systems for Gas Chromatography. ... 

Questions often arise as to which mathematical treatments and instrument types perform optimally for a specific set of data. This is best addressed by saying that reasonable instrument and equation selection composes only a small quantity of the variance or error attributable to the NIR analytical technique for any application. Actually, the greatest error sources in any calibration are generally reference laboratory error (stochastic error source), repack error (nonhomogeneity of sample — stochastic error source), and nonrepresentative sampling in the learning set or calibration set population (undefined error). 

In this section I will discuss a recently proposed error correction scheme designed particularly for the ion trap QC (Cirac et al. 1996). The scheme corrects for an important source of errors during the execution of 2-bit quantum gates. Because the scheme is not intended to correct for the most general error it can be implemented efficiently with regard to time and memory overhead. It is likely that this scheme can be tested as soon as a prototype ion trap QC is available. 

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