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.     

Numerical study of simultaneous natural convection heat transfer from both surfaces of a uniformly heated thin plate with arbitrary inclination

 Numerical studies were conducted to investigate the natural convection heat transfer around a uniformly heated thin plate with arbitrary inclination in an infinite space. The numerical approach was based on the finite volume technique with a nonstaggered grid arrangement. For handling the pressure–velocity coupling the SIMPLE-algorithm was used. QUICK scheme and first order upwind scheme were employed for discretization of the momentum and energy convective terms respectively. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 4.8×10⁶ to 1.87×10⁸. Local and average heat transfer characteristics were compared with regarding to the inclination angle. The empirical expressions for local and average Nusselt number were correlated. It has been found that for inclination angle less than 10^∘, the flow and heat transfer characteristics are complicated and the average Nusselt number can not be correlated by one equation while for inclination angle larger than 10^∘, the average Nusselt number can be correlated into an elegant correlation. Received on 18 April 2001 / Published online: 29 November 2001     

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.     

Foams and surface rheological properties of β-casein, gliadin and glycinin

Interfacial rheological properties and their suitability for foam production and stability of two vegetable proteins were studied and compared to β-casein. Proteins used ranged from flexible to rigid/globular in the order of β-casein, gliadin and soy glycinin. Experiments were performed at pH 6.7. Network forming properties were characterised by the surface dilational modulus (determined with the ring trough) and the critical falling film length (L_still) at which a stagnant protein film will break. Gliadin had the highest dilational modulus, followed by glycinin and β-casein, whereas glycinin formed the strongest film against fracture in the overflowing cylinder. The rate of decrease in the surface tension was studied at the air–water (Wilhelmy plate method) and the oil–water interface (bursting membrane) and the dynamic surface tension during compression and expansion in the caterpillar. Gliadin had the lowest equilibrium interfacial tensions and β-casein the lowest dynamic surface tension during expansion. Hardly any foam could be formed at a concentration of 0.1 g/l by shaking. At a concentration of 1.4 g/l most foam was formed by β-casein, followed by gliadin and glycinin. It seems that in the first place the rate of adsorption is important for foam formation. For the vegetable proteins, adsorption was slow. This resulted in lower foamability, especially for glycinin.     

An Automatic Procedure for Updating the Block Size in the Block Conjugate Gradient Method for Solving Linear Systems

The paper considers the problem of constructing an efficient automatic procedure for reducing the block size in the block conjugate gradient method insuring that the resulting rate of convergence is comparable with that of the block conjugate gradient method with constant block size. The numerical results provided show that, independently of the type of distribution of the smallest eigenvalues of the preconditioned matrix, the procedure suggested always leads to a decrease of the arithmetic costs with respect to those of the block method with constant block size. Bibliography: 8 titles.