Non-linear Sampling

The experiments based on proton detection of rare spin nuclei are usually the most sensitive methods of determining NMR parameters of magnetically diluted spin systems. Unfortunately, recording of 2D correlation maps is usually also a time consuming experiment, especially if wide spectral bands have to be covered in the indirectly detected dimension. The most frequently encountered situation is that only one or a few peaks are expected within a narrow spectral band. However, the position of this band is not known. Several attempts have been made to reduce the experimental time needed to perform such experiments. One approach would be to record a highly truncated data set and use the linear prediction [86,87] to reduce the effect of the data truncation on the appearance of the spectrum. This technique is now available with most 

Selective experiments offer a significant simplification of experiments, and a reduction of dimensionality, instrumentation requirements and data size, and in some cases also of the experimental time. For instance, measurement of spin-spin couplings between rare spin nuclei may require instrumentation for triple resonance experiments, including a special probe. In many cases selective measurements offer simple solutions for these demanding experiments. 

Alternatively, one of the rare spin nuclei (either Si or X) could be selected using selective excitation and/or selective detection techniques. This would reduce not only the instrumental requirements but also the problem of huge dynamic range, and a better signal-to-noise ratio can be obtained. Provided there is little signal overlap, location of rare spin satellites in proton spectra usually does not pose any problems, especially because the magnitude of spin-spin couplings to protons is known, at least approximately, in most cases. 

Apart from the measurements of spin-spin couplings between rare spin nuclei there are, of course, other applications of selective excitation and selective detection in NMR of organosilicon compounds. 

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Since about one decade, the development of fast experiments containing low number of RF pulses and delays to improve sensitivity and reduce the experimental time has been an active research area. It is likely that this area will involve many NMR spectroscopists for the next years. Current "fast methods" such as non-linear sampling, Hadamard and SMART techniques take a few seconds to produce 2D spectra. While these methods are currently rather mysterious for most of the scientists, there is absolutely no doubt that they will be provided by the NMR manufacturers in the next years. It is therefore likely that most of the HMBC spectra will be obtained in only a few minutes in a near future, which opens new perspectives. 

H2170 were reported, using non-linear sampling techniques.568... 

Acquiring spectral projections pertains to measuring linear cross sections in the time domain. This can be considered as a special case of a more general sampling scheme, where data points are sampled at any position of the time domain. The method is known as non-uniform or non-linear sampling (NUS or NLS). A historical perspective of this approach is well presented in Chap. 3. It was introduced almost a quarter of a century ago in a seminal publication by Laue and co-workers... 

The authors note that decrementation in this fashion results in a non-linear sampling across the optimization range used and suggest that linear sampling is preferred using... 

The analyst now has available the complete details of the chemical composition of a gasoline all components are identified and quantified. From these analyses, the sample s physical properties can be calculated by using linear or non-linear models density, vapor pressure, calorific value, octane numbers, carbon and hydrogen content. 

The liquid was applied and dried on cellulose filter (diameter 25 mm). In the present work as an analytical signal we took the relative intensity of analytical lines. This approach reduces non-homogeneity and inequality of a probe. Influence of filter type and sample mass on features of the procedure was studied. The dependence of analytical lines intensity from probe mass was linear for most of above listed elements except Ca presented in most types of filter paper. The relative intensities (reduced to one of the analysis element) was constant or dependent from mass was weak in determined limits. This fact allows to exclude mass control in sample pretreatment. For Ca this dependence was non-linear, therefore, it is necessary to correct analytical signal. Analysis of thin layer is characterized by minimal influence of elements hence, the relative intensity explicitly determines the relative concentration. As reference sample we used solid synthetic samples with unlimited lifetime. 

A second study [33] on samples that contain a mixture of nanotubes, together with several percent buckyonion -type structures, was carried out at temperatures between 4.5 and 300 K, and fields between 0 and 5.5 T. The moment M is plotted as a function of field in Fig. 7, for the low-field range, and in Fig. 8 for the high-field range. The field dependence is clearly non-linear, unlike that of graphite, in which both the basal plane and the c-axis moments are linear in field, except for the pronounced de Flaas-van Alphen oscillations at low temperature. 

A) The use of a calibration graph. This overcomes any problems created due to non-linear absorbance/concentration features and means that any unknown concentration run under the same conditions as the series of standards can be determined directly from the graph. The procedure requires that all standards and samples are measured in the same fixed-path-length cell, although the dimensions of the cell and the molar absorption coefficient for the chosen absorption band are not needed as these are constant throughout all the measurements. 

The accuracy and precision of carotenoid quantification by HPLC depend on the standard purity and measurement of the peak areas thus quantification of overlapping peaks can cause high variation of peak areas. In addition, preparation and dilution of standard and sample solutions are among the main causes of error in quantitative analysis. For example, the absorbance levels at of lutein in concentrations up to 10 mM have a linear relationship between concentration and absorbance in hexane and MeOH on the other hand, the absorbance of P-carotene in hexane increased linearly with increasing concentration, whereas in MeOH, its absorbance increased linearly up to 5 mM but non-linearly at increasingly higher concentrations. In other words, when a stock solution of carotenoids is prepared, care should be taken to ensure that the compounds are fuUy soluble at the desired concentrations in a particular solvent. 

In order to apply RBL or GRAFA successfully some attention has to be paid to the quality of the data. Like any other multivariate technique, the results obtained by RBL and GRAFA are affected by non-linearity of the data and heteroscedast-icity of the noise. By both phenomena the rank of the data matrix is higher than the number of species present in the sample. This has been demonstrated on the PCA results obtained for an anthracene standard solution eluted and detected by three different brands of diode array detectors [37]. In all three cases significant second eigenvalues were obtained and structure is seen in the second principal component. 

Faraday collector, simultaneously with U, U and U during the first sequence. This shortens the analysis routine, consuming less sample. Ion beam intensities are typically larger in MC-ICPMS than in TIMS due to the ease with which signal size can be increased by introducing a more concentrated solution. While this yields more precise data, non-linearity of the low-level detector response and uncertainties in its dead-time correction become more important for larger beam intensities, and must be carefully monitored (Cheng et al. 2000 Richter et al. 2001). 

Reliable chronologies should be based on multiple °Th age determinations at a sampling interval that is appropriate for the spatial resolution of geochemical analysis along the axis of growth and accounts for the possibility of non-linear or discontinuous growth. 

Concentration At high concentrations fluorescence emission l ecomes non-linear due to self-absorption by the sample itself or complete absorption of the excitation energy before it reaches the cell center. High fluorescence Intensity may overload the photomultiplier tube which returns slowly to its normal operating conditions and misrepresents the actual fluorescence signal until restabilized. 

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