Realization of graphs in a subspace of bounded height

A realization of graphs with vertices of bounded branching in a subspace of bounded depth is considered. A volume order inside of which an arbitrary graph can be realized is determined.     

Microstructural assessment of InN-on-GaN films grown by plasma-assisted MBE

The structural properties of InN thin films, grown by rf plasma-assisted molecular beam epitaxy on Ga-face GaN/Al₂O₃(0001) substrates, were investigated by means of conventional and high resolution electron microscopy. Our observations showed that a uniform InN film of total thickness up to 1 μm could be readily grown on GaN without any indication of columnar growth. A clear epitaxial orientation relationship of , was determined. The quality of the InN film was rather good, having threading dislocations as the dominant structural defect with a density in the range of 10⁹–10¹⁰ cm⁻². The crystal lattice parameters of wurtzite InN were estimated by electron diffraction analysis to be a=0.354 nm and c=0.569 nm, using Al₂O₃ as the reference crystal. Heteroepitaxial growth of InN on GaN was accomplished by the introduction of a network of three regularly spaced misfit dislocation arrays at the atomically flat interface plane. The experimentally measured distance of misfit dislocations was 2.72 nm. This is in good agreement with the theoretical value derived from the in-plane lattice mismatch of InN and GaN, which indicated that nearly full relaxation of the interfacial strain between the two crystal lattices was achieved.     

Analytical scheme calculations of angular momentum coupling and recoupling coefficients

We investigate the Scheme programming language opportunities to analytically calculate the Clebsch-Gordan coefficients, Wigner 6j and 9j symbols, and general recoupling coefficients that are used in the quantum theory of angular momentum. The considered coefficients are calculated by a direct evaluation of the sum formulas. The calculation results for large values of quantum angular momenta were compared with analogous calculations with FORTRAN and Java programming languages. The text was submitted by the authors in English.     

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.     

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.     

Certain constructions of asymptotic analysis related to the Stone-Čcech compactification

The paper considers the representations of attraction sets in topological spaces and their relations with the relaxation of accessibility problems under the conditions of sequentially relaxed constraints. The author studies the structure of approximate (in essence, asymptotic) solutions and generalized elements and establishes the possibility of their real identification for a certain version (related to the Stone-Čech compactification and the Wallman relaxation) of relaxation of the initial problem. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 26, Nonlinear Dynamics, 2005.