Comisarow M B and Marshall A G 1996 Early development of Fourier transform ion cyclotron resonance (FT-ICR) spectroscopy J. Mass Spectrom. 31 581-5 [Pg.1360]

Omitting more details on this point, we refer the readers to the well-developed algorithm of the fast Fourier transform, in the framework of which Q arithmetic operations, Q fa 2N log. N, N = 2 , are necessary in connection with computations of these sums (instead of 0 N ) in the case of the usual summation), thus causing 0(nilog,- 2) arithmetic operations performed in the numerical solution of the Dirichlet problem (2) in a rectangle. [Pg.651]

As in the case of infrared, progress in computing and the development of powerful algorithms for Fourier transforms has made the development of pulse NMR possible. [Pg.65]

Obviously, the theory outhned above can be applied to two- and three-dimensional systems. In the case of a two-dimensional system the Fourier transforms of the two-particle function coefficients are carried out by using an algorithm, developed by Lado [85], that preserves orthogonality. A monolayer of adsorbed colloidal particles, having a continuous distribution of diameters, has been investigated by Lado. Specific calculations have been carried out for the system with the Schulz distribution [86] [Pg.156]

The most notable advance in computational crystallography was the availability of methods for rehning protein structures by least-squares optimization. This developed in a number of laboratories and was made feasible by the implementation of fast Fourier transform techniques [32]. The most widely used system was PROLSQ from the Flendrickson lab [33]. [Pg.287]

Methods and iastmments that are used to monitor phosgene content ia air are well developed and have been reviewed (46—48). One detection iastmment is a porous tape that measures the concentration of phosgene ia air ia quantities as small as 6 ppb (49). Fourier transform ir spectrometry techniques have been developed to permit line and area monitoring ia the area around phosgene plants (50). [Pg.314]

From the time function F t) and the calculation of [IT], the values of G may be found. One way to calculate the G matrix is by a fast Fourier technique called the Cooley-Tukey method. It is based on an expression of the matrix as a product of q square matrices, where q is again related to N by = 2 . For large N, the number of matrix operations is greatly reduced by this procedure. In recent years, more advanced high-speed processors have been developed to carry out the fast Fourier transform. The calculation method is basically the same for both the discrete Fourier transform and the fast Fourier transform. The difference in the two methods lies in the use of certain relationships to minimize calculation time prior to performing a discrete Fourier transform. [Pg.564]

An on-line chromatography/atmospheric pressure chemical ionization tandem mass spectrometry (LC-APCI/MS/MS) methods was developed for rapid screen of pharmacokinetics of different drugs, including 5 (98RCM1216). The electron impact mass spectrum of 5 and ethyl 9,10-difluoro-3-methyl-7-oxo-2,3-dihydro-7Ff-pyrido[l,2,3- fe]-l,4-benzoxazine-6-carboxylate was reported (97MI28). Electron impact/Fourier transform [Pg.268]

When dealing with polymeric materials these early techniques were limited by the fact that only protons could be readily observed in the available fields. The small chemical shifts and the large dipole interactions made work with these systems very difficult. However, the development of the routine Fourier transform method of observation, especially when observing C-13 NMR, significantly changed the situation. [Pg.2]

As mentioned, we also carried out IR studies (a fast vibrational spectroscopy) early in our work on carbocations. In our studies of the norbornyl cation we obtained Raman spectra as well, although at the time it was not possible to theoretically calculate the spectra. Comparison with model compounds (the 2-norbornyl system and nortri-cyclane, respectively) indicated the symmetrical, bridged nature of the ion. In recent years, Sunko and Schleyer were able, using the since-developed Fourier transform-infrared (FT-IR) method, to obtain the spectrum of the norbornyl cation and to compare it with the theoretically calculated one. Again, it was rewarding that their data were in excellent accord with our earlier work. [Pg.143]

Three developments of calorimetry were thus combined in the last decade to dramatically enhance the capabilities of thermal analysis techniques and hence the study of the thermal properties of materials. These were the high precision of conventional adiabatic calorimetry, the speed of operation, and small sample size of DSC and the measurement of frequency dependence of thermal events and thus the MTDSC system evolved. Modulation is perhaps the most significant development with respect to thermal analysis techniques paralleling in significance the Fourier transform development of infrared spectroscopy. [Pg.4757]

The first Raman and infrared studies on orthorhombic sulfur date back to the 1930s. The older literature has been reviewed before [78, 92-94]. Only after the normal coordinate treatment of the Sg molecule by Scott et al. [78] was it possible to improve the earlier assignments, especially of the lattice vibrations and crystal components of the intramolecular vibrations. In addition, two technical achievements stimulated the efforts in vibrational spectroscopy since late 1960s the invention of the laser as an intense monochromatic light source for Raman spectroscopy and the development of Fourier transform interferometry in infrared spectroscopy. Both techniques allowed to record vibrational spectra of higher resolution and to detect bands of lower intensity. [Pg.47]

Thus, identification of all pairwise, interproton relaxation-contribution terms, py (in s ), for a molecule by factorization from the experimentally measured / , values can provide a unique method for calculating interproton distances, which are readily related to molecular structure and conformation. When the concept of pairwise additivity of the relaxation contributions seems to break down, as with a complex molecule having many interconnecting, relaxation pathways, there are reliable separation techniques, such as deuterium substitution in key positions, and a combination of nonselective and selective relaxation-rates, that may be used to distinguish between pairwise, dipolar interactions. Moreover, with the development of the Fourier-transform technique, and the availability of highly sophisticated, n.m.r. spectrometers, it has become possible to measure, routinely, nonselective and selective relaxation-rates of any resonance that can be clearly resolved in a n.m.r. spectrum. [Pg.127]

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