Spectral properties of the complex airy operator on the half-line

We prove a theorem on the completeness of the system of root functions of the Schrödinger operator L = ?d ²/dx ² + p(x) on the half-line R₊ with a potential p for which L appears to be maximal sectorial. An application of this theorem to the complex Airy operator L _c = ?d ²/dx ² + cx, c = const, implies the completeness of the system of eigenfunctions of L _c for the case in which |arg c| < 2π/3.We use subtler methods to prove a theorem stating that the system of eigenfunctions of this special operator remains complete under the condition that |arg c| < 5π/6.     

Trace of order (−1) for a string with singular weight

Mathematical Notes - The Sturm–Liouville problem on a finite closed interval with potential and weight of first order of singularity is studied. Estimates for the s-numbers and eigenvalues of...     

Correlation of the parameters of screening libraries of the gas-chromatographic retention data

The possibility interchanging retention data between libraries formed under different conditions (the mode of the carrier gas flow, its profile, and geometric characteristics of columns) is investigated. Factors affecting the interchange are considered. The recalculation is illustrated by the example of libraries used in chemical toxicology and forensic chemistry for phases of different polarity.     

Ergodic decomposition of group actions on rooted trees

We prove a general result about the decomposition into ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree associated with the action, and show that the canonical system of ergodic invariant probability measures coincides with the system of uniform measures on the boundaries of minimal invariant subtrees of the tree. Special attention is paid to the case of groups generated by finite automata. Few examples, including the lamplighter group, Sushchansky group, and so-called universal group, are considered in order to demonstrate applications of the theorem.     

Single-crystal X-ray diffraction analysis of arylamine-containing 2,2′-bipyridine derivatives

The structures of six 2,2′-bipyridine derivatives containing aromatic amine moieties, namely N-aryl-4-aryl-1-(pyridin-2-yl)-6,7-dihydro-5H-cyclopenta[c]pyridine-3-amines, were studied by single-crystal X-ray diffraction. The molecular structures and the effect of the substituents of these compounds on the crystal packing are discussed.

     

Efficient Synthesis of 3-(4-Carboxyphenyl)pyridine-2,6-dicarboxylic Acid

Russian Journal of Organic Chemistry - An efficient synthetic approach to 3-(4-carboxyphenyl)pyridine-2,6-dicarboxylic acid has been developed on the basis of “1,2,4-triazine”...     

Best linear methods of approximation and optimal orthonormal systems of the Hardy space

We construct the best linear methods of approximation for functions of the Hardy space H _p on compact subsets of the unit disk. It is shown that the Takenaka-Malmquist systems are optimal systems of functions orthonormal on the unit circle for the construction of the best linear methods of approximation. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 636–646, May, 2008.     

Identification of alkylphosphonic acid derivatives by IR and mass spectrometry

An approach is considered to the problem of identification of alkylphosphonic acid derivatives within Chemical Weapons Convention. The technique is based on correlations between the structural fragments of toxic chemicals and their IR and mass spectra.     

Interaction of Ytterbium Trifluoride with Zirconium in a NaF-ZrF4 Molten Mixture

The interaction of ytterbium trifluoride with zirconium in a molten mixture of sodium and zirconium fluorides have been studied by differential thermal analysis, X-ray diffraction, and electronic and IR spectroscopy. In the temperature range 440–640°C, zirconium reduces YbF₃ to ytterbium. The reaction products also contain low-valence zirconium and ytterbium compounds.