Spectral methods

Feit M D and Fleck J A Jr 1983 Solution of the Schrddinger equation by a spectral method, energy levels of triatomic molecules J. Chem. Phys. 78 301-8... 

One of the reasons for lack offlterature was probably because environmental analysis depends heavily on gas chromatography/mass spectrometry, which is not suitable for most dyes because of their lack of volatility (254). However, significant progress is being made in analyzing nonvolatile dyes by newer mass spectral methods such as fast atom bombardment (EAB), desorption chemical ionization, thermospray ionization, etc. 

Other methods can be used in space, such as the finite element method, the orthogonal collocation method, or the method of orthogonal collocation on finite elements (see Ref. 106). Spectral methods employ Chebyshev polynomials and the Fast Fourier Transform and are quite useful for nyperbohc or parabohc problems on rec tangular domains (Ref. 125). 

The discrete Fourier transform can also be used for differentiating a function, and this is used in the spectral method for solving differential equations. Suppose we have a grid of equidistant points... 

DETERMINATION OF MACRO- AND MICROELEMENTS IN BIOLOGICAL SAMPLES BY ATOMIC SPECTRAL METHODS... 

The molybdenum, tungsten and tantalum concentration influence on LCD nickel-ferrous HRS resistance, used for gas turbine installations parts is investigated. The tests were carried out on modeling compositions. Samples were molded on the basis of an alloy of the ZMI-3C. The concentration of tantalum varied from 0 up to 5% with a step of 0,5%. The contents of elements were determined by a spectral method. 

The three modes of numerical solution techniques are finite difference, finite element, and spectral methods. These methods perform the following steps ... 

Gottlieb, D. and Orszag, S.A., 1977. Numerical Analysis of Spectral Methods Theory and Applications. SIAM, Philadelphia. 

The infrared spectral method has been used to show that certain amino-l,2,4-triazines exist as such (Table VI). Although the separate isolation of 263 and 264 was claimed in 1940, this report is probably erroneous,... 

Evidence for the formation of such a complex was obtained from IR spectroscopy [68] of the solid residue obtained by the treatment of MA with Fe(acac),. Characterization of the complex by the ultraviolet (U V) spectral method also indicated the formation of the complex [68]. Misra et al. have carried out grafting of vinyl mono-... 

Other methods for solving PDE s include Monte Carlo, spectral, and variational. Spectral methods in particular converge more rapidly than finite difference methods, but do not handle problems involving irregular geometries or discontinuities well. 

Molten salt investigation methods can be divided into two classes thermodynamic and kinetic. In some cases, the analysis of melting diagrams and isotherms of physical-chemical properties such as density, surface tension, viscosity and electroconductivity enables the determination of the ionic composition of the melt. Direct investigation of the complex structure is performed using spectral methods [294]. 

IR spectra of the molten system K2TaF7 - KF are more sensitive to the concentration of KF (Fig. 76, b). Molten K2TaF7 is characterized by a strong band at 605 cm"1 and a shoulder at 540 cm 1, as shown before (see Fig. 74, curve 3). The addition of KF to molten K2TaF7 leads to a decrease in the intensity of the above band and to the appearance of a band at 540 cm 1. When the KF concentration equals or exceeds 0.9 mol fraction, a band is observed at 540 cm 1 only. This spectral transformation indicates that the equilibrium in Equation (80) shifts to the left with the increase in KF concentration, and that at KF concentrations above 0.9 mol fraction, only TaF72 complexes are present, while TaF6 ions are not observed by IR emission spectral methods. 

In order to study the mobility of elements of crosslinked structure of CP, it is suitable to use their microdisperse forms [30-35]. On the one hand, in potentiome-tric titration the equilibrium is quickly attained for these forms and on the other hand the effect of light scattering in spectral methods of investigation (e.g., polarized luminescence) can be greatly decreased. 

A major treatise devoted to experimental methods of chemistry is Techniques of Chemistry , edited first by Weissberger, and then by Saunders, Wiley, New York. This publication, which began in 1970, so far consists of 21 volumes, most of them in several parts, covering such topics as electrochemical and spectral methods, kinetic methods, photochronusm, and organic solvents. Techniques of Chemistry is a successor to an earlier series, called Techniques of Organic Chemistry , which appeared in 14 volumes, some of them in more than one edition, from 1945 to 1969. 

Let us investigate the stability of scheme (9) by the spectral method having represented it beforehand in the form... 

Stability theory is the central part of the theory of difference schemes. Recent years have seen a great number of papers dedicated to investigating stability of such schemes. Many works are based on applications of spectral methods and include ineffective results given certain restrictions on the structure of difference operators. For schemes with non-self-adjoint operators the spectral theory guides only the choice of necessary stability conditions, but sufficient conditions and a priori estimates are of no less importance. An energy approach connected with the above definitions of the scheme permits one to carry out an exhaustive stability analysis for operators in a prescribed Hilbert space Hh-... 

Two-dimensional NMR spectroscopy may be defined as a spectral method in which the data are collected in two different time domains acquisition of the FID tz), and a successively incremented delay (tj). The resulting FID (data matrix) is accordingly subjected to two successive sets of Fourier transformations to furnish a two-dimensional NMR spectrum in the two frequency axes. The time sequence of a typical 2D NMR experiment is given in Fig. 3.1. The major difference between one- and two-dimensional NMR methods is therefore the insertion of an evolution time, t, that is systematically incremented within a sequence of pulse cycles. Many experiments are generally performed with variable /], which is incremented by a constant Atj. The resulting signals (FIDs) from this experiment depend... 

Mossoba, M.M., Ed., Spectral Methods in Food Analysis, Marcel Dekker, New York, 1999. 

As is shown in Table 11.1, PLC is mainly used before the identification of isolated compounds with spectral methods such as NMR or IR. Figure 11.6 shows a densi-togram of PLC of Fumaria officinalis herb extract with marked fractions being isolated (Figure 11.6a) and analytical chromatogram of isolated fractions (Figure 11.6b). 

M.E. Elyashberg, Y. Karasev, E.R. Martirosian, H. Thiele and H. Somberg, Expert systems as a tool for the molecular structure elucidation by spectral methods, strategies of solution to the problem. Anal. Chim. Acta, 348 (1997) 443 64. 

DI methods tend to produce even-electron ions such as protonated molecules [M + H]+, or cationised molecules such as [M + Na]+ these stable ions undergo only a minimum amount of fragmentation. Desorption/ionisation mass-spectral methods (in particular FD, EH and LD) may be used for determining molecular... 

T-MS). The main direct mass-spectral methods are thermal desorption and pyrolysis mass spectrometry. Several factors favour the efficiency at which volatiles can be removed from a polymeric matrix ... 

F. X. Schmid, Spectral methods of characterizing protein conformation and conformational changes, in Protein Structure—A Practical Approach (T.E. Creighton, ed.), IRL Press, Oxford, 1989, pp. 251-285. 

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