splitting in both the N02 symmetrical and asymmetrical stretching bands. For example, the dinitrate derivative of -hexadecyl glyceryl ether, unlike the ß isomer, showed these characteristic doublets (Figure 4). The derivative of 1-monostearin, however, showed a single N02 symmetrical and a split asymmetrical stretching band. The absence of the split in the former band of this compound may be due to interference from the 1,3-isomer, which might have formed by isomerization. Some acyl migration would be expected to occur, for example, in the nitration of both mono-and diglycerides as a result of the acidity of the acetyl nitrate solution.The tendency of these compounds to rearrange under various conditions was recently demonstrated by Privett and coworkers (13).CONCLUSIONS Some chromatographic and spectral properties of a variety of fatty nitrates have been presented. These properties are valuable for structural determinations on milligram amounts of the parent hydroxy compounds and for the analysis of complex mixtures containing these substances. The techniques described are only fully exploited, however, when used in conjunction with established methods for the analysis of alcohols and other compounds containing hydroxy groups.
The expectation-maximization (EM) method of parameter estimation is used to calculate adsorption energy distributions of molecular probes from their adsorption isotherms. EM does not require prior knowledge of the distribution function or the isotherm, requires no smoothing of the isotherm data, and converges with high stability towards the maximum-likelihood estimate. The method is therefore robust and accurate at high iteration numbers. The EM "algorithm is tested with simulated energy distributions corresponding to unimodal Gaussian, bimodal Gaussian, Poisson distributions, and the distributions resulting from Misra isotherms. Theoretical isotherms are generated from these distributions using the Langmuir model, and then chromatographic band profiles are computed using the ideal model of chromatography. Noise is then introduced in the theoretical band profiles comparable to those observed experimentally. The isotherm is then calculated using the elution-by-characteristic points method. The energy distribution given by the EM method is compared to the original one. The results are contrasted to those obtained with the House and Jaycock algorithm HILDA, and shown to be superior in terms of both robustness, accuracy, and information theory. The effect of undersampling of the high-pressure/low-energy region of the adsorption is reported and discussed for the EM algorithm, as well as the effect of signal-to-noise ratio on the degree of heterogeneity that may be estimated experimentally.
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