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.     

Effective thermal conductivity of water-saturated sintered powder-metal plates

An experimental apparatus and related procedures for the determination of the effective thermal conductivity of sintered powder-metal plates saturated with distilled water at temperatures in the range 20–150°C are discussed. The apparatus and procedures are applied to two samples of sintered powder-metal plates, one made of nickel 200 and the other of stainless steel 316, with porosities of 28.10 and 46.45%, respectively, and each of nominal dimensions 127 mm × 127 mm × 6.35 mm. The experimental results are compared with corresponding predictions yielded by several correlations available in the literature. The correlations based on experimental data for packed beds of spherical particles and also porous plates made of cold-pressed (but not sintered) particles of angular shapes do not apply well to sintered powder-metal plates. A new correlation, which is based on extensions of ideas contained in earlier works and provides improved predictions, is proposed.     

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.     

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     

Investigation of the stability of metal species with respect to liquid chromatographic separations

Summary For accurate speciation analyses it is important to know the stability of the respective species, especially in the case of metal complexes. Factors affecting the chromatographic stability of such metal species are investigated. By using thermodynamic models for complex formation and chromatographic retention equilibria the influence of species concentration, stoichiometry and excess of ligand is calculated and compared with experimental results for iron complexes (lactate, gluconate and citrate species). Iron citrate is the only species, that is chromatographed as 1:2 complex (metal: ligand), while iron lactate and gluconate are transformed to 1:1 species. Problems resulting from the coelution of different species are discussed.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

TLC-screening of important pharmaceutical substances using fluorescence detection

Summary Observation of fluorescence reactions on TLC plates is a valuable additional tool within the scope of screening procedures for many toxicologically relevant substances commonly encountered in clinical- and forensic-toxicological analysis. The reactions are based on native fluorescence without any treatment and on reactions obtained with an approved derivatization procedure. Due to the enormous sensitivity of the fluorescence detection, the method is also applicable to very low concentrations and small amounts of biological materials. The procedures described in this article have proven their high pragmatic usefulness in many practical cases.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Structure of thin block copolymer films studied by X-ray reflectivity

Summary X-ray reflectivity may be used to determine the internal structure of thin polymer films. An electron density difference of 10% for polystyrene and polyisoprene is sufficient to distinguish between a random distribution of lamellae, complete orientation parallel to the substrate surface and a surface induced formation of lamellae. The disappearance of the lamellar Bragg-peaks, with heating of the film, shows the transition into the disordered state.