Whole spectrum method

It is because of this requirement for at least as many samples as wavelengths that CLS is often called a (or the) whole spectrum method to contrast, it with ILS. In fact the term is frequently employed in a derogatory way with respect to ILS to suggest that ILS is, by contrast to CLS, not a whole spectrum method. 

Variance (cont) of prediction, 167 Variance scaling, 100, 174 Vectors basis, 94 Weighting of data, 100 Whole spectrum method, 71 x-block data, 7 x-data, 7 XE, 94 y-block data, 7 y-data, 7... 

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. 

In favorable cases therefore, H NMR spectroscopy constitutes an absolute method for the determination of the stereoisomeric structure of polymers. This affirmation holds true not ordy in the sense that the spectrum is in agreement with the proposed structure (isotactic for the first polymer, syndiotactic for the second) but also because a detailed examination of the whole spectrum permits the exclusion of other hypotheses that might reasonably be put forward. 

Many chemical substances or mixtures exert a whole spectrum of activities, ranging from beneficial to neutral to lethal. Their effect depends not only on the quantity of the substance to which an organism is exposed, but also on the species and size of the organism, its nutritional status, the method of exposure, and a number of other related factors. 

Mobility measurements by the TOP methods considered in Chapters 3 and 4 are particularly important, but they cannot give information about the whole spectrum of states in the mobility gap of amorphous chalcogenides. Therefore, in addition to TOP, XTOP, IPTOP, TSC, and TSDC, other complimentary techniques that probe the gap states are needed. Xerographic techniques that were initially developed to characterize properties of electrophotographic (xerographic) receptors [1] seemed to be informative, suitable, and widely applicable for the study of amorphous thin films and photoconductive insulator thin films [2],... 

The reliability or stability of a method covers its ability to reach a solution for a wide group of problems in a general range of mixtures, such as wide or narrow boiling, and if it can solve columns across the whole spectrum of boiling point ranges. It also covers the ability of the method to solve the same column with variations in some of the specifications such as number of trays, reflux ratio, or feed conditions. 

Regardless of the spectroscopic method used, the signal level generated by each spectral element, dcr, is dependent on the product of the spectral intensity in do, B(o) (with units of W/cm 1), and the observation time [9]. In FT spectroscopy, the whole spectrum is collected at once, so that each spectral element is sampled for the whole observation time, t. Then the signal from each spectral element is proportional to ... 

For the numerical study of the whole spectrum (for g R fixed), [79] uses a spectral tau-Chebychev discretization in y and the Arnold method (see [88]) to solve the generalized eigenvalue problem (see [89]). This numerical method is based on the orthonormalization of the Krylov space of the iterates of the inverse of the matrix A B. This method has been used more recently in [90]. It has been proven efficient in the stiff problems arising in the study of spectral stability of viscoelastic fluids. 

The popularity of the SOS methods in calculations of non-linear optical properties of molecules is due to the so-called few-states approximations. The sum-over-states formalism defines the response of a system in terms of the spectroscopic parameters, like excitations energies and transition moments between various excited states. Depending on the level of approximation, those states may be electronic or vibronic or electronic-vibrational-rotational ones. Under the assumption that there are few states which contribute more than others, the summation over the whole spectrum of the Hamiltonian can be reduced to those states. In a very special case, one may include only one excited state which is assumed to dominate the molecular response through the given order in perturbation expansion. The first applications of two-level model to calculations of j3 date from late 1970s [93, 94]. The two-states model for first-order hyperpolarizability with only one excited state included can be written as ... 

PLS is a powerful technique that shares the advantages of both the CLS and ILS methods hut does not suffer from the limitations of either these methods. A PLS calibration can, in principle, he based on the whole spectrum, although in practice the analysis is restricted to regions of the spectrum that exhibit variations with changes in the concentrations of the components of interest. As such, the use of PLS can provide significant improvements in precision relative to methods that use only a limited number of frequencies [9]. In addition, like the inverse least squares method, PLS treats concentration rather than spectral intensity as the independent variable. Thus, PLS is able to compensate for unidentified sources of spectral interference, although all such interferences that may be present in the samples to be analysed must also be present in the calibration standards. The utility of PLS will be demonstrated by several examples of food analysis applications presented in Section 4.7. 

A rapid FTIR method for the direct determination of the casein/whey ratio in milk has also been developed [26]. This method is unique because it does not require any physical separation of the casein and whey fractions, but rather makes use of the information contained in the whole spectrum to differentiate between these proteins. Proteins exhibit three characteristic absorption bands in the mid-infrared spectrum, designated as the amide I (1695-1600 cm-i), amide II (1560-1520 cm-i) and amide III (1300-1230 cm >) bands, and the positions of these bands are sensitive to protein secondary structure. From a structural viewpoint, caseins and whey proteins differ substantially, as the whey proteins are globular proteins whereas the caseins have little secondary structure. These structural differences make it possible to differentiate these proteins by FTIR spectroscopy. In addition to their different conformations, other differences between caseins and whey proteins, such as their differences in amino acid compositions and the presence of phosphate ester linkages in caseins but not whey proteins, are also reflected in their FTIR spectra. These spectroscopic differences are illustrated in Figure 15, which shows the so-called fingerprint region in the FTIR spectra of sodium caseinate and whey protein concentrate. Thus, FTIR spectroscopy can provide a means for quantitative determination of casein and whey proteins in the presence of each other. 

A whole spectrum of statistical techniques have been applied to the analysis of DNA microarray data [26-28]. These include clustering analysis (hierarchical, K-means, self-organizing maps), dimension reduction (singular value decomposition, principal component analysis, multidimensional scaling, or correspondence analysis), and supervised classification (support vector machines, artificial neural networks, discriminant methods, or between-group analysis) methods. More recently, a number of Bayesian and other probabilistic approaches have been employed in the analysis of DNA microarray data [11], Generally, the first phase of microarray data analysis is exploratory data analysis. 

Rapidity and detection limits below 1 ppb (10 ) for many elements, make OES one of the best methods of elemental analysis. With instruments containing one array detector it is possible to record in a few seconds the whole spectrum in high resolution (e.g. several thousands emission spectral lines). 

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