The sensitive-point method

The sensitive-point method was introduced in 1974 by Hinshaw [Hinl, Hin2]. The z-component of the magnetic field is modulated in a sinusoidal fashion by application of time-dependent field gradients in x-, y-, and z-directions (Fig. 5.1.2), 

In principle, there is no reason why only the time-independent response should be extracted from the total signal by addition of successive scans with unsynchronized field modulation. Because the time dependence is known for each voxel, the signal can be extracted for any voxel by a lock-in technique, where the reference function is given by the gradient modulation for the particular voxel. This can be executed simultaneously. 

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Biological Aspects.— The application of n.m.r. spectroscopy to biological systems continues to grow. There have been reviews of its use in the study of living tissue and for n.m.r. imaging. In the latter field an alternative sensitive-point method gives improved full spectra but it has limited sensitivity. ... 

See Problem C. Mathematically, Eq. (6.7) says that Qk(T) is the Laplace transform of p(E)k(E). It is natural to want to use an inverse Laplace transform to get k(E) from a measured k(T). Computationally this is not a safe route because taking an inverse Laplace transform is numerically rather unstable and is very sensitive to errors in the measured k(T). What is more satisfactory is to evaluate the Laplace transform by the saddle-point method as introduced in Chapter 3. See Problem P. 

A special case of the basis function method works by choosing a subset of grid blocks - the pilot points, and setting the values in all other blocks using kriging. The pilot points might be chosen subjectively or using sensitivities. It was observed in [116] that the pilot point method is a version of a basis function method. The results in Section 4 are relevant to this observation. 

Historically, the first and most important capacitance method is the vibrating capacitor approach implemented by Lord Kelvin in 1897. In this technique (now called the Kelvin probe), the reference plate moves relative to the sample surface at some constant frequency and tlie capacitance changes as tlie interelectrode separation changes. An AC current thus flows in the external circuit. Upon reduction of the electric field to zero, the AC current is also reduced to zero. Originally, Kelvin detected the zero point manually using his quadrant electrometer. Nowadays, there are many elegant and sensitive versions of this technique. A piezoceramic foil can be used to vibrate the reference plate. To minimize noise and maximize sensitivity, a phase-locked... 

There are two ways in which the sensitivity can be increased. The first, and most obvious, is to decrease the concentration of the titrant, since it is inversely proportional to the sensitivity, k. The second method, which only applies if the analyte is multiprotic, is to titrate to a later equivalence point. When H2SO3 is titrated to the second equivalence point, for instance, equation 9.10 becomes... 

Sensitivity The sensitivity for a one-point fixed-time integral method of analysis is improved by making measurements under conditions in which the concentration of the monitored species is larger rather than smaller. When the analyte s concentration, or the concentration of any other reactant, is monitored, measurements are best made early in the reaction before its concentration has substantially decreased. On the other hand, when a product is used to monitor the reaction, measurements are more appropriately made at longer times. For a two-point fixed-time integral method, sensitivity is improved by increasing the difference between times t and f2. As discussed earlier, the sensitivity of a rate method improves when using the initial rate. 

Analytical and Test Methods. Measurement of the sohdification point using a highly sensitive thermometer and of APHA color by comparison of molten samples to APHA standards is straightforward. Specific impurities are measured by gas chromatography. A nonaqueous titration is used to determine phthahc acid content. 

In acid-base titrations the end point is generally detected by a pH-sensitive indicator. In the EDTA titration a metal ion-sensitive indicator (abbreviated, to metal indicator or metal-ion indicator) is often employed to detect changes of pM. Such indicators (which contain types of chelate groupings and generally possess resonance systems typical of dyestuffs) form complexes with specific metal ions, which differ in colour from the free indicator and produce a sudden colour change at the equivalence point. The end point of the titration can also be evaluated by other methods including potentiometric, amperometric, and spectrophotometric techniques. 

If it is desired to use the biamperometric method for detecting the end point, then the calomel electrode and also the silver rod (if used) must be removed and replaced by two platinum plates 1.25 cm x 1.25 cm. The potentiometer (or pH meter) used to measure the e.m.f. must also be removed, and one of the indicator electrodes is then joined to a sensitive galvanometer fitted with a variable shunt. The indicator circuit is completed through a potential divider... 

The indirect methods discussed thus far have dealt with measurement of color only as it can be correlated with physical characteristics of materials and the effect of these materials on radiant energy. As has been pointed out, the reflectance spectro-photometric curve describes a property of the material. A change in the reflectance spectrophotometric properties may not always result in a change in visual color. The reason is that color of the object is not an unchangeable characteristic of the object itself, dependent only upon these reflectance properties, but is also dependent upon the quality of the illuminating light and the sensitivity of the observer s eye. Thus the measurement and description of visual color are psychophysical problems... 

We have emphasized unequal path interferometry because it is the most familiar method of optical testing these days. However, we have also shown how sensitive this type of interferometry is to environmental disturbances. There are a number of other t)q)es of optical testing including common path methods such as shearing interferometry and Shack-Hartmann testing Malacara, 1992. As we pointed out in the fabrication section, optical testing has no more kept pace with the benefits of increased computing capability than fabrication has. 

It should be pointed out that when using ethidium bromide the sensitivity of the assays varies depending on the physical state of the nucleic acids (see Table I). Ethidium does not discriminate between RNA and DNA, although dyes are available which bind DNA exclusively, so the relative amounts of each may be determined by taking two sets of measurements. Alternatively, nucleases (DNA-ase or RNA-ase) can be used to exclusively remove one or the other in a mixture. Nucleic acids from different sources (see Table II) also show a variation in sensitivity, and the fluorescence assay lacks the selectivity of the hybridization technique. Nevertheless, for rapid screening or quality-control applications the fluorescence assay is still the method of choice. 

The fact that in HPLC only UV-active components are registered, whereas in titration all basic functional groups are detected constitutes a difference in specificity (quality) and sensitivity (quantity) of these two methods relative to a given impurity. See Fig. 4.17 (left). [Solvent A (water) behaves differently from the other four as can be seen from Fig. 4.17 (right). The material was known to exist in a crystal modification that theoretically contains 3.2% water, and moderate drying will most likely drive off only the excess Indeed, the best-dried batches are all close to the theoretical point (circle, arrow in Figs. 4.16-17), and not near zero. This is only partly reflected in Table 4.15, column A for this reason tabular and graphic information has to be combined. Solvent B, which is an alcohol, behaves more like water... 

Two wider ranging, more systematic investigations of conformational dependence have since been performed to establish whether the conformational sensitivity noted in the above PECD smdies may generally provide a means for identifying and distinguishing gas-phase structure of suitable chiral species. The B-spline method has been applied to the model system (l/f,2f )-l,2-dibromo-l,2-dichloro-l,2-difluoroethane [60]. Rotation around the C C bond creates three stable conformational possibilities for this molecule to adopt. The results for both core and valence shell ionizations reaffirm an earlier conclusion a and p are almost unaffected by the rotational conformation adopted, whereas the PECD varies significantly. Eor the C Ij ionization to show any sensitivity at aU to the relative disposition of the halogen atoms further reinforces the point made previously in connection with the core level PECD phenomenon. 

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