Invariant Spaces of Entire Functions

Mathematical Notes - Subspaces of the space of analytic functions on a convex domain in the complex plane that are invariant with respect to the differentiation operator are studied. The problem of...     

A criterion for the fundamental principle to hold for invariant subspaces on bounded convex domains in the complex plane

Let D be a bounded convex domain of the complex plane. We study the problem of whether the fundamental principle holds for analytic function spaces on D invariant with respect to the differentiation operator and admitting spectral synthesis. Earlier this problem was solved under a restriction on the multiplicities of the eigenvalues of the differentiation operator. In the present paper, we lift this restriction. Thus, we present a complete solution of the fundamental principle problem for arbitrary nontrivial closed invariant subspaces admitting spectral synthesis on arbitrary bounded convex domains.     

Distribution coefficients of purine alkaloids in water-ammonium sulfate-alkyl acetate-dialkyl phthalate systems

The distribution of purine alkaloids (caffeine, theobromine, theophylline) was studied in the systems: alkyl acetates-dialkyl phtalate-salting-out agent (ammonium sulfate). The quantitative characteristics of the extraction-distribution coefficients (D) and the degree of extraction (R, %) are calculated. The relationships between the distribution coefficients of alkaloids and the length of the hydrocarbon radical in the molecule of alkyl acetate (dialkyl phtalate) are determined. The possibility of predicting the distribution coefficients is demonstrated.     

Unified Procedure for the Determination of Polycyclic Aromatic Hydrocarbons and Their Nitro Derivatives by Low-Temperature Luminescence

A method was described for determining polycyclic aromatic hydrocarbons (PAHs) and their nitro derivatives (nitro-PAHs) in samples of complex composition using low-temperature luminescence. Fractionation by HPLC was used to separate compounds with similar spectral properties. At the chromatograph inlet, a test sample was purified from weakly retained components additionally preconcentrated on a concentrator cartridge, which was fixed in the injector in place of the sampling loop. Step gradient fractionation was considered, and a table of retention times for PAHs and nitro-PAHs was presented. The the fractional distribution of the analytes was studied. Phosphorescence spectra of some nitro-PAHs were described. The method proposed is comparable in sensitivity to HPLC with the fluorescence detection, but does not require derivatization for determining nitro-PAHs. A table of spectral parameters of analytes suffices for qualitative analysis, as in chromatography–mass spectrometry. However, in distinction to the latter technique, the method described is selective because of the specificity of excitation and emission spectra of each of the analytes.