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.     

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.     

Solvability in Lebesgue spaces of nonlinear boundary equations of one-sided contact problems of elasticity theory

We investigate the solvability of one-sided contact problems with nonlinear boundary conditions. The results generalize the author's previous results to the case of equations in Lebesgue spaces.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 77–83, 1988.     

Polymorphism in alternating polyketones studied by x-ray diffraction and calorimetry

Differential scanning calorimetry and high temperature x-ray diffraction were used to study the perfectly alternating copolymer of ethene and carbon monoxide (polyketone; POKC2). It was found that oriented POK-C2 fibers show a crystalline phase transition at a temperature between 110–125°C with a 10% change in crystalline density. At this temperature, the crystal structure reported recently (POK-α) is transformed to a crystal structure that was reported in the past for room temperature imperfectly alternating polyketone. The latter structure will be designated as POK-β. The influence of chain defects on the crystal structure was studied by synthesizing terpolymers (POK-C2/C3), in which small amounts of propylene-CO units are incorporated into the polymer backbone. The resulting terpolymers differ from the copolymer by the presence of methyl groups randomly distributed along the polyketone backbone chain. Evidence is presented that indicates that the methyl groups are built into the crystal lattice as defects. With more than 5 mole-% propene the terpolymer fibers crystallize exclusively in the β-modification. Below this level the α/β ratio (at room temperature) increases with decreasing amounts of propene. Both as-synthesized and as-spun POK-C2 were found to consist of both POK-α and POK-β; the α/β ratio depends on the method of preparation. Because the drawn POK-C2 fibers studied here consist exclusively of POK-α, the process of spinning and drawing leads to the transformation of unoriented β-rich material into oriented POK-α. © 1995 John Wiley & Sons, Inc.     

The influence of the electron thermal motion on the surface oscillating potential produced by traversal of a vacuum-plasma interface by a fast charged particle

The passage of a charged particle through a vacuum-plasma interface is considered. Expressions for a surface potential oscillating at the surface-wave frequency are found under conditions of mirror reflection of plasma electrons from the interface. It is shown that allowance for spatial dispersion eliminates a singularity appearing in the model of a cold plasma on the trajectory of particle motion in the near-surface oscillating potential. The possibility of measuring near-surface oscillating fields is discussed.Institute of Radio-Electronics, Armenian Academy of Science, Erevan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1241–1249, December, 1995.