Specific features of photoisomerization of provitamin D 3 in a nematic liquid crystal

Photoisomerization of provitamin D ₃ (7-dehydrocholesterol) in a nematic liquid crystal (ZLI-1695, Merck) is investigated in detail by UV absorption spectroscopy. It is found that dissolution of chiral molecules of provitamin D ₃ induces the cholesteric phase in a nematic. The spectral kinetics of photoisomerization in this phase changes significantly from that in an ethanol solution. A sharp nonmonotonic dependence of the increase in accumulation of trans isomer tachysterol in a liquid crystal matrix with a decrease in the induced cholesteric pitch from 2200 to 25 μm is revealed.     

Negative molecular ions of azafullerenes and their hydrogenated derivatives

The formation and decay of negative molecular ions of azafullerenes and their hydrogenated derivatives are investigated by mass spectrometry. The mechanisms of resonant electron capture and the lifetimes of negative molecular ions with respect to the electron autodetachment in azafullerene molecules are discussed. A comparative analysis of the data obtained for azafullerenes and hydrogenated fullerene derivatives is carried out.     

C- and N-Amidotrichloroethylation of Azoles

1H-Pyrazoles, triazoles, and imidazoles in reaction with ethoxycarbonylimine and arylsulfonylimines of chloral yield addition products, corresponding 1-(1-amidotrichloroethyl)azoles. Derivatives of 1-alkylpyrazoles and pyrazolones react with chloral 4-chlorophenylsulfonylimine to furnish products of C-amidotrichloroethylation into position 4 of the azole ring.     

Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

Coverings of topological loops

In this paper, we show that in some cases, no proper covering of a locally compact group topologically generated by left translations of a topological loop can occur as the group topologically generated by left translations of a topological loop. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 22, Algebra and Geometry, 2004.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

Vibrational spectra and ab initio computations of sarcosinium oxalate monohydrate

Single crystals of sarcosinium oxalate monohydrate (SOM) are grown by the slow-evaporation technique at ambient temperature, and vibrational spectroscopic analysis is carried out using NIR-FT Raman, FT-IR, and SERS spectra. The normal mode frequencies and corresponding vibrational analysis of SOM are examined theoretically using the Gaussian’98 set of quantum chemical codes. The two bands present in the SOM ν C=O region, clearly observed in the Raman spectrum, are assigned to “free” and “bonded” carbonyl groups with the hydrogen atom. Vibrational analysis indicates the presence of C-H—O hydrogen bonding interaction producing a blueshift of the C-H stretching frequency.     

Reductions of interval nonlinear programming problem

A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed.     

Nonlinear Theory of Spectra of Thermally Stimulated Currents in Complex Crystals with Hydrogen Bonds

The nonlinear theory of thermally stimulated depolarization currents is developed. The theory explains the processes of hetero- and homocharge relaxation in complex crystals with hydrogen bonds and allows the relaxation oscillator parameters to be calculated using the quadratic approximation for the external electric field.