New Heat-Resistant Polyimidates Derived from Bisphenols and Mono- and Dicarboxylic Acid Imidoyl Chlorides

New polyimidates were prepared from bisphenols and mono- and dicarboxylic acid imidoyl chlorides. The structures of the polymers were determined, and their physicochemical, chemical, and thermal properties were studied. The possibility of preparing film and compression materials with good mechanical characteristics from these polymers was examined.     

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.     

Inverse Problem with Free Boundary for Heat Equation

We establish conditions for the existence and uniqueness of a solution of the inverse problem for a one-dimensional heat equation with unknown time-dependent leading coefficient in the case where a part of the boundary of the domain is unknown.     

Formation of coherent spatial structures in the reaction-diffusion atmospheric system under the action of a planetary wave

On the example of the effect of an atmospheric wave with given amplitude on the density oscillations of minor gas constituents near the mesopause (at heights 80–90 km, we consider the influence of the quasi-resonant periodic spatial transport on a distributed system responding subharmonically to a periodic external action (diurnal sunlight variations). Numerical modeling revealed the formation of a coherent horizontal distribution of the dynamical variables (i.e., the concentrations of small constituents). Application of this effect to the mesopause conditions is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 47, No. 9, pp. 739–752, September, 2004.     

Finite element method in the solution of the Euler and Navier-Stokes equations for internal flow

Finite element solutions of the Euler and Navier-Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak-Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a Newton method and at each iteration the linear algebraic system is solved by a direct solver with all unknowns fully coupled. Results are presented for two-dimensional transonic inviscid flows and two- and three-dimensional incompressible viscous flows. Convergence of the algorithm is shown to be quadratic, reaching machine accuracy in very few iterations. The inviscid results demonstrate the existence of nonunique numerical solutions to the steady Euler equations.     

Growth and study of single crystals of (Na,K)NbO<Subscript>3</Subscript> solid solutions

(Na, K)NbO₃ crystals with a perovskite structure and a KNbO₃ content up to 40 mol % were grown from flux with the use of the solvent NaBO₂. The dielectric measurements of the crystals grown revealed phase transitions that had never been observed before in ceramic samples.     

Sound propagation in an unstable atmospheric layer

The equation of sound propagation in an unstable medium produced by the presence of supersaturated water vapor in it, which can appear in a hurricane area, is derived. This equation takes into account the effects of sound velocity dispersion, amplification, damping, and nonlinear effects. Some solutions to this equation are presented, illustrating the specific features of sound propagation in an unstable medium. Published in Akusticheskiĭ Zhurnal, 2007, Vol. 53, No. 3, pp. 477–480.     

Vortex ring generation due to the coalescence of a water drop at a free surface

 Results are presented of an experimental investigation of vortex ring formation by a fluid drop contacting a free surface with negligible velocity. The pool fluid is mixed with fluorescein dye, and a laser sheet is used to illuminate a plane of the flow. A series of representative images is recorded by a CCD camera and speculation is made regarding specific sources of vorticity flux through the free surface. Two scaling analyses previously presented by other investigators are demonstrated to be equivalent under the assumptions of this experiment, and they provide the motivation for a series of test runs in which the duration of the coalescence process, τ_*, is related to variations in drop diameter L and fluid surface tension σ. Experimental results are in agreement with the analyses, showing τ_*∼σ^-1/2 and τ_*∼L ^3/2. Received: 22 December 1995 / Accepted: 15 October 1996