Multipliers of Fourier series

New statements are proved regarding multipliers of trigonometric Fourier series in the space C of continuous periodic functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1686–1693, December, 1991.     

Topological analysis of the structure-mesomorphous property ralationship

The use of topological indices to reveal the relationship between molecular structure and mesomorphous properties is discussed. Mathematical models for classification of mesophase types are proposed. The effect of molecular structure and attractive ability on phase transition temperatures is described. Examples of using correlation equations to predict the properties of 2,5-disubstituted 1,3-dioxanes are given. A. V. Bogatskii Physicochemical Institute, Ukrainian Academy of Sciences. Translated fromZhurnal Struktumoi Khimii, Vol. 35, No. 4, pp. 53–60, July–August, 1994. Translated by L. Smolina     

Effect of rigid fragments in the macrocycle on the adaptation of crown ethers to alkali-metal ions

Complexation selectivity curves were obtained by theoretical conformational analysis and penalty functions in terms of the conformational factors in the following crown ethers: 15-crown-5; benzo-15-crown-5: 18-crown-6; benzo-18-crown-6; dibenzo-18-crown-6; cyclohexano-18-crown-6. In the last case the effect of cis—trans isomerism in the bridging bonds on the selectivity of complexation with the ligand was investigated. Analysis of the selectivity curves shows that the introduction of aromatic fragments into the macrocycle reduces its adaptive capabilities. The complexation selectivity of the ligands from the selectivity curves is compared with the experimental stability series of the crown ether complexes with alkali metals.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 3, pp. 355–360, May–June, 1990.     

On the Approximation of Functions by Polynomials and Entire Functions of Exponential Type

Ukrainian Mathematical Journal - We present a brief survey of works in the approximation theory of functions known to the author and connected with V. K. Dzyadyk’s research works.     

Zinc(II) Complexes with Azomethines of 2,4,6-Trimethylaniline and Halogen-Substituted Salicylaldehyde

Russian Journal of General Chemistry - Azomethines were synthesized from 2,4,6-trimethylaniline, salicylaldehyde, and its 3(5)-halogen derivatives, as well as their complexes with zinc(II) (ZnL2)....     

Synthesis,Structure, and Properties of Co2+ and Ni2+ Complexes with the Product of Condensation of 2-(7-Bromo-2-oxo-5-phenyl-3H-1,4-benzodiazepin-1-yl)acetohydrazide and 1H-Indole-2,3-dione

Russian Journal of General Chemistry - [Co(HydrHIz)] and [Ni(HydrHIz)]?2H2O (М = Co, Ni) complexes have been obtained via the reaction of M(CH3COO)2 with...     

Approximation of trigonometric functions by trigonometric polynomials with interpolation

The paper studies the approximation order of periodic functions by trigonometric polynomials with interpolation in arbitrary set of nodes. A method of construction of Hermite interpolation polynomials is pointed out.