Patterns in parabolic problems with nonlinear boundary conditions

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem.     

Interpolation and extrapolation of gamma detection efficiency curve as a function of distance

Summary The paper deals with the common mistake of interpolating calculation of the efficiency of gamma-detectors by the inverse square law of the distance of the source from the detector cap and suggests the use of the distance from the virtual point detector instead.     

Asymptotic Directions for Best Approximations of n-Dimensional Linear Forms

Some results about asymptotic directions for best approximations of linear forms similar to known results on best simultaneous approximations are obtained.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

The ionization constants of alpha-alanine in NaCl at 25 degrees. Effect of the ionic strength based on three models

In the present work we obtained the experimental pKs of the amino acid alpha-alanine in NaCl at 25 degrees and different ionic strengths. The equilibrium constants have been potentiometrically determined with a commercial glass electrode and the results analysed through three models: two directly based on the Pitzer and Scatchard approaches to the ion specific interaction theory and the other based on a simpler modification of the Debye-Hückel equation. The three models fit the data reasonably well and the extrapolated pK values obtained show a good agreement. The goodness of the ridge regression method cannot be probed in this case.     

Radical copolymerization of 2-acryloyl thioxanthone with methyl methacrylate

A novel monomer, 2-acryloyl thioxanthone (TXA), was prepared by reaction of 2-hydroxy thioxanthone with acryloyl chloride. Copolymerization of TXA with methyl methacrylate (MMA) in DMF at 80°C was studied in order to evaluate relative reactivities of these monomers. Values of 1.36 and 0.5 were found for the respective reactivity ratios of MMA and TXA, respectively. The resonance stabilization and polar properties were determined and discussed in terms of spectroscopic data.     

Preparative synthesis of the stable α-fluorosulfatotetrafluoro-ethylbis(perfluoroisopropyl)methyl radical

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2450–2451, October, 1990.