The Value of Bernoulli Polynomials at Rational Numbers

We give a short elementary proof of a result of Almkvist andMeurman [1] on an integrality property of the values taken bythe Bernoulli polynomials at a rational number. We use a lemmaon the divisibility properties of certain binomial coefficientswhich seems to be of independent interest.     

Pattern forming precipitation in gels due to coupling of chemical reactions with diffusion

Precipitate-forming chemical reactions have been studied in chemically cross-linked poly(vinyl alcohol) gel medium. One of the reactive components was incorporated into the gel, the other was allowed to diffuse into it. Depending on the experimental conditions the reaction-diffusion process often results in patterns of different type. Experiments performed in tubes and in thin layers were carried out in order to investigate the effects of various factors (cross-linking density, swelling degree as well as the concentrations of the outer and inner electrolytes) on the morphologies of the precipitate patterns. It was found that precipitation occurs not only in the Liesegang bands, but also between bands. Beside Liesegang-type structures, tree-like patterns have been observed, showing a characteristic periodicity in the density profile obtained by digitalized image analyses.     

Interaction of a point vortex with boundary singularities of higher orders

Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 167–168, May–June, 1993.     

Design and application of double amplified recirculating ring structure for hybrid fibre buses

The design of a double-parallel amplified recirculating optical delay line utilizing an erbium-doped fibre amplifier for a fibre optical bus is described. This structure is used for amplifying, equalizing and filtering multicarrier signals coming from optoelectronic units attached to fibre couplers. The use of this structure for a hybrid multimode-singlemode fibre bus that includes optoelectronic units for sensors is also demonstrated.