Mass spectrometry of sterols. Electron ionization induced fragmentation of C-4-alkylated cholesterols.
The electron impact ionization of C-4-alkylated cholest-5-en-3beta-hydroxysterols has been investigated. The mass spectra of the C-4-alkylated cholesterols contain a number of ions in the high mass region for which analogous ions are not found in the spectrum of cholesterol. Detailed studies of the composition and origin of these ions have been made by high resolution mass spectrometry and analysis of metastable ions. In addition, a large number of isotopically (deuterium and 18O) substituted C-4-alkylated analogues have been prepared to assist in the interpretation of the spectra. The combined results indicate the occurrence of a number of very complex and unusual electron ionization induced fragmentations. Most notable of the findings reported herein concerns the demonstration of the formation of an ion involving loss of the elements of ring A with an intramolecular shift of the oxygen and hydrogen atoms of the hydroxyl function to the charge-retaining species.
Mass spectra of some steroidal diols
The mass spectral fragmentations of a number of steroidal 3,5- and 4,5-diols and some derivatives have been examined using high resolution mass spectrometry and deuterium labelling. Although the 3,5- and 4,5-diols have very similar mass spectra those of the derived ketols are quite characteristic. A pathway for the formation of the important m/e 332 ion in the mass spectrum of cholestan-4β,5α-diol has been postulated.
On Hilbert's thirteenth problem and related questions
Hilbert's thirteenth problem involves the study of solutions of algebraic equations. The object is to obtain a complexity estimate for an algebraic function. As of now, the problem remains open. There are only a few partial algebraic results in this connection, but at the same time the problem has stimulated a series of studies in the theory of functions with their subsequent applications. The most brilliant result in this cycle is Kolmogorov's theorem on superpositions of continuous functions.