Asymptotic behavior of solutions of general three term recurrence relations

We consider the solutions of general three term recurrence relations whose coefficients are analytic functions in a prescribed region. We study the ratio asymptotic of such solutions under the assumption that the coefficients are asymptotically periodic, and their strong asymptotic under more restrictive conditions.     

Hadamard Variational Formula for the Green’s Function of the Boundary Value Problem on the Stokes Equations

For every ${\varepsilon > 0}$ , we consider the Green’s matrix ${G_{\varepsilon}(x, y)}$ of the Stokes equations describing the motion of incompressible fluids in a bounded domain ${\Omega_{\varepsilon} \subset \mathbb{R}^d}$ , which is a family of perturbation of domains from ${\Omega\equiv \Omega_0}$ with the smooth boundary ${\partial\Omega}$ . Assuming the volume preserving property, that is, ${\mbox{vol.}\Omega_{\varepsilon} = \mbox{vol.}\Omega}$ for all ${\varepsilon > 0}$ , we give an explicit representation formula for ${\delta G(x, y) \equiv \lim_{\varepsilon\to +0}\varepsilon^{-1}(G_{\varepsilon}(x, y) - G_0(x, y))}$ in terms of the boundary integral on ${\partial \Omega}$ of ${G_0(x, y)}$ . Our result may be regarded as a classical Hadamard variational formula for the Green’s functions of the elliptic boundary value problems.     

Simple multilevel halftoning excelled in gradation reproducibility

A simple multilevel halftoning method, which is based on the conventional error diffusion method and realizes halftoning excelled in the distribution of dots, is proposed. The proposed method consists of three steps, e.g., the image decomposition, the generation of binary halftone images by the error diffusion, and the synthesis of a multilevel halftone image, and each step does not require a complicated algorithm. The effectiveness of the proposed method is indicated by applying it to three- and four-level halftoning of gray-tone and natural images.     

Efficient N-arylation of azole compounds utilizing selective aryl-transfer TMP-iodonium(III) reagents

It was determined that diaryliodonium(III) triflates bearing a trimethoxybenzene (TMP) auxiliary are more reactive than the reported selective aryl-transfer iodonium salts in the N-arylation of benzimidazoles and other types of azole compounds under catalytic conditions. The TMP-iodonium(III) salts can thus effectively facilitate the reaction at 50?°C or below, producing the corresponding N-arylated biaryls without the formation of TMP-derived coupling byproducts. Utilization of this TMP reagent under mild conditions would prevent the underlying problem of participation of the auxiliary group in the coupling reactions, which is observed while using the iodonium(III) salts that require elevated temperatures.     

Comparative Study on Decomposition of CFCl<Subscript>3</Subscript> in Thermal and Cold Plasma

Decomposition of CFCl₃ was investigated in an RF inductively coupled thermal reactor in neutral, oxidative and reductive conditions, and in a silent electric discharge (cold plasma) in neutral and oxidative conditions, respectively. In RF thermal plasma reactor, in neutral conditions, mainly gaseous products and minor amount of solid soot was formed. About 50% the soot could be extracted by toluene. Both the gas phase and the extract contained a wide range of aliphatic and aromatic compounds including chlorine and fluorine containing polyaromatic hydrocarbons (PAHs). In oxidative conditions much less soot was formed as compared to the neutral case. The solid product contained about 45% extractable fraction even in oxidative conditions. However, the extract contained less PAHs than in neutral conditions. In reducing atmosphere the soot yield was similar to the neutral case, but the soot contained 29% extractable fraction only. The extract consisted of polyhalogenated aromatic and polyaromatic hydrocarbons as main components. In neutral conditions different chlorofluorocarbons (CFCs) and chlorine were detected as gaseous products in cold plasma. In oxidative conditions, as final products of decomposition CO₂, CFCs and Cl₃ were formed.     

Indirect high-performance liquid chromatographic separation of stereoisomers of beta-alkyl-substituted amino acids by the application of (S)-N-(4-nitrophenoxycarbonyl)phenylalanine methoxyethyl ester as chiral derivatizing agent

The indirect high-performance liquid chromatographic enantioresolution of beta-alkyl-substituted analogues of tyrosine, phenylalanine, 1,2,3,4-tetrahydroisoquinoline-3-carboxylic acid and tryptophan is reported. (S)-N-(4-Nitrophenoxycarbonyl)phenylalanine methoxyethyl ester, a recently developed chiral derivatizing agent, was used for pre-column derivatization of the investigated analytes. The diastereoisomers formed were analysed under reversed-phase conditions. The effects of parameters such as the amount and type of the organic modifier and the type of the stationary phase on the resolution and retention of the derivatives were investigated. Chromatographic conditions were found for the separation of all four stereoisomers of each analyte.     

Multimode interferometer for guided matter waves

Atoms can be trapped and guided with electromagnetic fields, using nanofabricated structures. We describe the fundamental features of an interferometer for guided matter waves, built of two combined Y-shaped beam splitters. We find that such a device is expected to exhibit high contrast fringes even in a multimode regime, analogous to a white light interferometer.     

Adsorption and direct probing of fibrinogen and sodium myristate at the air/water interface

Fibrinogen (FB), a serum protein, is considered a major inhibitor of lung surfactant function at the lining layer of the alveoli. In this study, the adsorption of aqueous bovine FB at the air/water interface was investigated with tensiometry and directly probed for the first time with ellipsometry and infrared reflection adsorption spectroscopy (IRRAS). The tension results show that FB has moderate surface activity. The surface densities of FB were calculated by using two different ellipsometry models to range from 3±0.2 to 17±2 mg/m², for 7.5 to 750 ppm of FB in water at 25°C. Although FB at concentrations from 75 to 750 ppm reached about the same steady surface tension value, the surface densities at 750 ppm FB were substantially larger. The same techniques were used for studying aqueous mixtures of 7.5 to 750 ppm FB with 2 mM of sodium myristate (SM) to investigate a possible interaction of the SM with the protein. The behavior of the FB/SM mixtures was found to be close to that of SM alone. The surface tension of the FB/SM mixtures reached values less than 10 mN/m under surface area oscillation at 20 or 80 rpm. These results and the ellipsometry and the IRRAS results indicate that at a concentration of 2 mM SM, FB, up to 750 ppm, does not inhibit the surfactant surface-tension-lowering function. In certain cases the results demonstrate that FB and SM may act cooperatively in lowering the surface tension.