Molecular Complexes of Crown Ethers in Crystals and Solutions

A review of the experimental and theoretical studies of the crown ether complexes with polar molecules in their crystals, solutions, and in a gas phase is given. The type of the molecular bonds in the complexes, their stoichiometry, and the change in the macrocycle conformation during complex formation are considered, as well as the effect of the macrocycle structure and the nature of the medium on the efficiency of the molecular bonding. New data are given on the enthalpies of transfer of the crown ethers from tetrachloromethane into solvents capable of forming hydrogen bonds. The enthalpies of specific interactions of macrocycles with the molecules of the solvents in the medium of the same solvents are characterized. The conformations of the crown ethers in the media under study are discussed.     

Studies on Rare-Earth/Iron and Actinide/Iron Multilayers

Hyperfine Interactions - Multilayers of Ce/Fe and U/Fe were fabricated by sputtering and studied by X-ray diffraction and reflectivity, Mössbauer spectroscopy and polarised neutron...     

Four-Dimensional Lie Group Integration of the Klein–Fock Equation

A method of four-dimensional Lie group integration of the Fock–Klein equation is described in the present paper. The method is based on the formalism of co-adjoint representation orbits and on the non-commutative integration method. Right-invariant metrics being solutions of the Einstein equation are also classified for manifolds of four-dimensional Lie groups.     

A rapid and sensitive extractive spectrophotometric determination of copper(II) in pharmaceutical and environmental samples using benzildithiosemicarbazone.

Benzildithiosemicarbazone (BDTSC) is proposed as a sensitive and selective analytical reagent for the extractive spectrophotometric determination of copper(II). BDTSC reacts with copper(II) in the pH range 1.0-7.0 to form a yellowish complex. Beer's law is obeyed in the concentration range 0.5-0.4 microg cm(-3). The yellowish Cu(II)-BDTSC complex in chloroform shows a maximum absorbance at 380 nm, with molar absorptivity and Sandell's sensitivity values of 1.63 x 10(4) dm3 mol(-1) cm(-1) and 0.00389 microg cm(-2), respectively. A repetition of the method is checked by finding the relative standard deviation (RSD) (n = 10), which is 0.6%. The composition of the Cu(II)-BDTSC complex is established as 1:1 by slope analysis, molar ratio and Asmus' methods. An excellent linearity with a correlation coefficient value of 0.98 is obtained for the Cu(II)-BDTSC complex. The instability constant of the complex calculated from Edmond and Birnbaum's method is 7.70 x 10(-4) and that of Asmus' method is 7.66 x 10(-4), at room temperature. The method is successfully employed for the determination copper(II) in pharmaceutical and environmental samples. The reliability of the method is assured by analyzing the standard alloys (BCS 5g, 10g, 19e, 78, 32a, 207 and 179) and by inter-comparison of experimental values, using an atomic absorption spectrometer.     

Remark on minimization of depth of Boolean circuits

It is shown that Lozhkin’s method (1981) for minimization of the depth of formulas with a bounded number of changing types of elements in paths from input to output and Hoover-Klawe-Pippenger’s method (technical report in 1981, journal publication in 1984) for minimization of the depth of circuits with unbounded branching by insertion of trees from buffers with bounded branching of outputs for each buffer are dual to each other and can be proved by one and the same method.     

Monomial ideals

In this paper, we study the numeric characteristics (the Hilbert function and graded Betti numbers) of monomial ideals in the polynomial ring and in the exterior algebra. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 30, Algebra, 2005.