Iterative analysis

The NMR spectra of cinnoline and its derivatives are complex. The unequivocal assignments are based on the complete iterative analysis of the spectra of a large number... 

For a general Jacobian matiix pertaining to C components and N theoretical trays, as shown by Distefano [Am. Jnst. Chem. Eng. J., 14, 946 (1968)]. Gerschgorin s circle theorem (Varga, Matrix Iterative Analysis, Prentice Hall, Englewood Cliffs, N.J., 1962) may be employed to obtain bounds on the maximum and minimum absolute eigenvalues. Accord-... 

Varga, Richard S., Matrix Iterative Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1962. 

We started this study by developing a computer model to predict the kinetic conditions during the runaway stage of a reaction. The computer model is based on an iterative analysis which permits a step-by-step computation of various variables. 

Figure 1 Is a flow sheet showing some significant aspects of the Iterative analysis. The first step In the program Is to Input data for about 50 physical, chemical and kinetic properties of the reactants. Each loop of this analysis Is conducted at a specified solution temperature T K. Some of the variables computed In each loop are the monomer conversion, polymer concentration, monomer and polymer volume fractions, effective polymer molecular weight, cumulative number average molecular weight, cumulative weight average molecular weight, solution viscosity, polymerization rate, ratio of polymerization rates between the current and previous steps, the total pressure and the partial pressures of the monomer, the solvent, and the nitrogen.

A full iterative analysis of the more-complicated NMR spectra of both dibenzothiophene 5-oxide and 5,5-dioxide has been made. A slight broadening ( 0.05-0.1 Hz) of the lines associated with one of the protons in both compounds was assumed to be due to Jj 9 and this was used to assign peaks in the spectra. ... 

The exchange broadening Awe may be either measured directly from the spectrum or calculated from equation (177) upon substituting for K the value obtained from the iterative analysis. The procedure, after due modifications, can be employed for the estimation of errors for more complicated exchanging systems. 

Iterative analysis of spectra by means of a computer is undoubtedly the most useful and general method available. However, the method depends heavily on the ability of the user to compute, initially, a trial, theoretical spectrum that sufficiently well resembles the experimental spectrum for many line-assignments to be made in the latter spectrum. 

Fig. 5.—Partial, Proton Magnetic Resonance Spectra of 6-Deoxy-l,2 3,5-di-0-isopropylidene-6-phthaIimido-a-D-glucofuranose-6-15N (30). [(a) In solution in benzene-<4 at 220 MHz (h) computed, theoretical spectrum from iterative analysis.]...

For iterative analysis to be worth while, the accuracy of the experimental line-frequencies should preferably be maximized by scanning the spectrum several times in each direction, in order to give mean values for these frequencies. The intensities of the experimental lines are not used as input data to the programs currently available. 

The LAOCOON II program has been used to calculate theoretical spectra for l,3,4,6-tetra-0-acetyl-2,5-0-methylene-D-mannitol-1,1,6,6-d4 (76 p. 73),192 and in the iterative analysis and simulation of spectra of methyl 2,3- and 3,4-anhydroglycopyranosides86 (LAOCN3 was also used), the protons of the sugar portion of many nucleosides,104-105-107 109 for example, 2 -deoxyadenosine251 (84), and adenosine 5 -phosphate126 (55 p. 60). 

The LAOCN3 and TWOSUM programs have been used in the iterative analysis or spectrum simulation of tri-O-acetyl-jS-D-arabinopyranosyl fluoride,252 tri-O-benzoyl-a- and /3-D-ribofuranosyl fluoride,253 and 3,6-anhydro-5-deoxy-5-fluoro-l,2-0-isopropylidene-a-L-idofuranose254 (85). 

The chemical shifts and coupling constants obtained from the p.m.r. spectra of carbohydrates by a valid, computerized, iterative analysis may generally be regarded as particularly accurate examples of these parameters. 

Most double resonance measurements of proton shifts have been homonuclear studies of hidden and unresolved lines (e.g. refs. 107 and 366). However, in NMR, measurements of proton shifts using the correlation of C and spectra by off-resonance decoupling is common. While the aim is usually to assign the signals, it can also be to assign proton signals, as in the case of the N-methylene protons of amides (367) and the methyl signals of valine. (368) H shifts derived from similar experiments can be used as trial parameters for the iterative analysis of complex H spectra this technique was demonstrated for [l,l,3- H3]indene. (369)... 

Varga RS (1962) Matrix iterative analysis, Englewood cliffs, N.J., Prentice Hall... 

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