Sample domain

X = /(Q) Analytical function in the sample domain, sample composition function ... 

By the operations coding (analytical measurement) and decoding (analytical evaluation) information will be transformed from the sample domain into the signal domain and vice versa as shown in Fig. 2.12. Therefore, quantities which correspond to that of the sample domain (Q and Xq) must also exist in the signal domain. The characteristics in the signal domain are ... 

Fig. 2.12. Relationship between sample domain and signal domain in element analysis (a) and structure analysis (b). The representation in the sample domains is shown in different forms, as a block diagram and a list in case of (a) and as constitution formula and structure matrix, respectively, in case (b)...

The foreground of the representation depicts the relationship between the species Q and their characteristic signals zy while behind that, the relationship between signals zy their intensities yy and the species amounts x is established. Taken together, these relationships establish the composition of the sample (the sample domain) and the signal domain, too. 

Signals used in analytical chemistry have a definite origin from particular species or given structural relationships between constituents of samples. The relation of the sample domain and the signals domain, i.e. the coding and decoding process as represented in Fig. 2.12, must be as unambiguous as possible. 

Chemical dimensions (dimensions in the sample domain) type (Q), number (n) and amount (x) of analytes, i.e. distinct chemical species see Fig. 2.12 (left)... 

In analytical chemistry, calibration represents a set of operations that connects quantities in the sample domain with quantities in the signal domain (see Sect. 2.3, Fig. 2.12). In Table 6.1 the real analytical quantities and properties behind the abstract input and output quantities are listed. 

Limits characterize the detection capability of analytical methods and can be related to both analytical domains, sample domain as well as signal domain. Although there are several limits, namely lower and upper limits3 as well as thresholds, the most important problem in analytical chemistry is the distinction between real measurement values and zero values or blanks, respectively. 

Table 7.5. Analytical limits within the signal and sample domain the most meaningful of which are emphasized... 

Signal domain (measured values) Sample domain (analytical values)... 

The formal transformation of the critical value into the sample domain is necessary to estimate correctly the limit of detection. If the sensitivity is known and without of any uncertainty (e.g. in case of error-free calibration constants fi), then the analytical value at CV is calculated by... 

LD is the limit in the sample domain (analyte domain). It characterizes analytical procedures, in particular with regard to the limit concentration that can be detected. Therefore, the LD stands for the guarantee of absence of an analyte. 

Field of analytical operation that is char- —> Fig. 2.12 acterized by signal properties such as sig- Sample domain nal position, z, and signal intensity, yz. 

The transition to sample domain is done by analytical evaluation (signal decoding). 

Taking these issues into the process sampling domain. Figures 3.12-3.14 show some of the many ways in which sampling valves are designed and implemented in current process technology. A fair estimate... 

When there is a significant IDE present, chances are high that this will produce lEE as well. (In the rare cases this is not so, IDE alone creates a sampling bias.) lEE in the process sampling domain would e.g. be... 

The sample domain was equilibrated in a specific event and compositions are frozen-in . Thus, at the scale of measurement, minerals do not contain growth zonation or retrograde alteration. 

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