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.     

Valiron deficient vectors of entire curves of finite order

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 52, pp. 122–126, 1989.     

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.     

Approximation of holomorphic functions by Taylor-Abel-Poisson means

We investigate the problem of approximation of functions ƒ holomorphic in the unit disk by means A _{ρ, r} (f) as ρ → 1−. In terms of the error of approximation by these means, a constructive characteristic of classes of holomorphic functions H _p ^r Lipα is given. The problem of the saturation of A _{ρ, r} (f) in the Hardy space H _p is solved. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1253–1260, September, 2007.     

Chromatographic study of the chemical composition and potential toxicity of spirits and alcoholic beverages

The composition of vodkas, rectified food alcohols, cognacs, cognac spirits, and other strong alcoholic beverages was studied by chromatography and compared with the composition of industrial (synthetic and hydrolysis) ethyl alcohols, adulterated cognacs, and homemade spirits (samogon) from the illicit market. It was found that the majority of the test alcohol-containing liquids were close to commercial alcoholic beverages in terms of chemical composition and toxic properties. The samples containing ethylene glycol and enriched components of the head fraction of rectification should be considered most toxic.     

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...     

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.     

Eu(3+)-mediated polymerization of benzenetetracarboxylic acid studied by spectroscopy, temperature-dependent calorimetry, and density functional theory

Thermodynamic parameters for the complexation of Eu(3+) with pyromellitic acid (1,2,4,5-benzenetetracarboxylic acid, BTC) as a model system for polymerizable metal-complexing humic acids were determined using temperature-dependent time-resolved laser-induced fluorescence spectroscopy (TRLFS) and isothermal titration calorimetry (ITC). At low metal and ligand concentrations (<50 μM Eu(3+), <1 mM BTC), a 1:1 monomeric Eu-BTC complex was identified in the range of 25-60 °C. At elevated concentrations (>500 μM Eu(3+) and BTC) a temperature-dependent polymerization was observed, where BTC monomers are linked via coordinating shared Eu(3+) ions. The two methods lead to comparable thermodynamic data (ΔH = 18.5 ± 1.5/16.5 ± 0.1 kJ mol(-1); ΔS = 152 ± 5/130 ± 5 J mol(-1) K(-1); TRLFS/ITC) in the absence of polymerization. With the onset of polymerization, TRLFS reveals the water coordination number of the lanthanide, whereas calorimetry is superior in determining the thermodynamic data in this regime. Evaluating the heat uptake kinetics, the monomer and polymer formation steps could be separated by "time-resolved" ITC, revealing almost identical binding enthalpies for the sequential reactions. Structural features of the complexes were studied by Fourier-transform infrared (FTIR) spectroscopy in combination with density functional theory (DFT) calculations showing predominantly chelating coordination with two carboxylate groups in the monomeric complex and monodentate binding of a single carboxylate group in the polymeric complex of the polycarboxylate with Eu(3+). The data show that pyromellitic acid is a suitable model for the study of metal-mediated polymerization as a crucial factor in determining the effect of humic acids on the mobility of heavy metals in the environment.     

Best linear methods for the approximation of functions of the Bergman class by algebraic polynomials

On concentric circles T _ϱ = {z ∈ ℂ: ∣z∣ = ϱ}, 0 ≤ ϱ < 1, we determine the exact values of the quantities of the best approximation of holomorphic functions of the Bergman class A _p , 2 ≤ p ≤ ∞, in the uniform metric by algebraic polynomials generated by linear methods of summation of Taylor series. For 1 ≤ p < 2, we establish exact order estimates for these quantities. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1674–1685, December, 2006.     

Factors affecting the accuracy of the determination of diethyl phthalate in vodka, ethanol, and samples of illegal alcoholic products

Samples of illegally produced strong alcoholic beverages from the cities of Kyzyl and Stavropol were studied using gas chromatography and gas chromatography-mass spectrometry. It was found that all of the samples were prepared from high-purity food or hydrolysis ethanol (characteristic impurity compounds that are the markers of synthetic alcohol were absent), which met the requirements of GOST (State Standard) R 51698-2000. In the samples of illegal alcohol (from Kyzyl), diethyl phthalate (850–1284 mg/L) and, in one sample, ethylene glycol (380 mg/L, accidental contaminant) were found. The occurrence of diethyl phthalate indicated that vodka (aqueous alcohol mixture) was prepared from commercial denatured alcohol. An analysis of regulatory documents and published data allowed us to draw the following conclusions: (1) diethyl phthalate does not meet the requirements imposed on denaturing additives, and it is used as a denaturing agent only in Russia; (2) the test samples of illegal alcohol do not differ from food ethanol solutions of analogous strength in terms of acute toxicity parameters; and (3) surrogate alcohols in illicit trade are not the main reason for high mortality from alcohol intoxication in the test region (Kyzyl and the Tyva Republic).