A generalization of the Heine limit for functions which converge on a base

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Бophobcкиe ceчehия пepexoдob meждУ bьicoкoboфбУждehьimи coctoяhияmи atomob пpи ctoлкhobehияx c элeкtpohamи

The total Born cross sections summed over the orbital quantum numbers, as well as the corresponding excitation rates for transitions between highly excited states induced by electron impact, are calculated. The calculations were made for the following principal quantum numbers: 10≤n≤100, Δn/n≤0·3 (Δn=n|n?n′|). The results are presented in a form convenient for interpolations (see Tables 1 and 2).The calculations were performed by using an asymptotic expansion in powers of 1/n and 1/n′, for the exact analytical expression of the total generalized oscillator strength. Comparison of the exact results with the asymptotic ones shows that an accuracy of about 10 percent is achieved for n?2 (see Figs. 1 and 2).For high electron energies, analytical expressions are obtained for the cross sections and the excitation rates. The approximation used is analogous to that of Kramers for the oscillator strenght, the errors do not exceed ～30 percent.     

Cobmecтhaя диффuзия фop;oh;ob и khcy;acтиц b пoлuБecкoheчhom пpocтpahcтbe—I pacпpeдeлehиe boзБuждehhьч aтomob b пoлuБecкoheчhom пpocтpahcтbe

The excited atom distribution produced by the simultaneous action process, namely, excitation transfer by radiation in a spectral line and spce movement of excited atoms, is considered. A kinetic equation describing these process is analysed. For steady-state conditions, an adympototic analytical solutio id obtained. This solution describes the concentration distribution of excited atoms for a plane geometry in a region which is a distance exceeding the effective free path away from the surface limiting the volume.The influence on the general solution of either the excitation transfer process id found as a function of the parameters involved.     

The Torsion Theory Generated by <Emphasis Type="Italic">M</Emphasis>-Small Modules

Let M be a right R-module, the class of all M-small modules, and P a projective cover of M in [M]. We consider the torsion theories = ( ), = ( ), and = ( ) in [M], where is the torsion theory generated by is the torsion theory cogenerated by , and is the dual Lambek torsion theory. We study some conditions for to be cohereditary, stable, or split, and prove that Rej(M, ) = M = (= = ) = Gen_M(P) .2000 Mathematics Subject Classification: 16S90     

Cobmecтhaя диффuзия фoтohob и чacтиц b пoлuбecкoheчhom пpocтpahcтbe—II Кohцehтpaция boзбuждehhыч aтomob пepeд фpohтom uдaphoй boлhы

Steady-state distributions of excited atom concentrations are found ahead of a plane shock wave. The problem is solved for a two-level approximation. An exact analytical solution of the integro-differential equation describing the distribution of the concentration is developed by using the Weiner-Hopf method. The asymptotic behaviour in regions both far away and close to the shock front is investigated as a function of the parameters involved.     

Role of the oxygen partial pressure in the formation of composite Co-CoO nanoparticles by reactive aggregation

The magnetic properties of diluted films composed of nanocomposite Co-CoO nanoparticles (of ~8 nm diameter) dispersed in a Cu matrix have been investigated. The nanoparticles were formed in an aggregation chamber by sputtering at different Ar/O₂ partial pressures (0?C0.015). The exchange-bias properties appear to be insensitive to the amount of O₂ during their formation. However, the temperature dependence of the magnetization, M(T), exhibits two different contributions with relative intensities that correlate with the amount of O₂. The magnetic results imply that two types of particles are formed, nanocomposite Co-CoO (determining the exchange-bias) and pure CoO, as confirmed by transmission electron microscopy observations. Importantly, as the O₂ partial pressure during the sputtering is raised the number of nanocomposite Co-CoO nanoparticles (exhibiting exchange-bias properties) is reduced and, consequently, there is an increase in the relative amount of pure, antiferromagnetic CoO particles.     

ОБ ЁкВИВАлЕНтНых НОР МИРОВкАх пОДпРОстРА НстВL 2

Denote byH(Ω) the subspace of functionsp fromL ₂(Ω) for which \(\mathop \smallint \limits_\Omega p dx = 0\) , and define the norm inH(Ω) as follows It is proved that this norm is equivalent to the norm ofL ₂(Ω) assuming that the boundary ofΩ is piecewise Lipschitzian. As a consequence it is derived that for linear elasticity problems the stresses are uniformly bounded inL ₂ with respect to the Poisson constant.     

О БАжИсАх В пРОстРАНс тВАх ОРлИЧА

The expansion of a given function with respect to a certain basis depends both on the properties of the function and on the metric in which the expansion is considered. Conditions are obtained in the paper that ensure the unconditional convergence of the expansions with respect to the spline systems which were introduced byZ. Ciesielski. In particular, the solution of a problem raised by P. L. Ul'janov is obtained: There exists no functionΩ(u) ↑ ∞ (u ↑ ∞) such that the condition $$\mathop \smallint \limits_0^1 \Phi (f)\omega (f)dt< \infty $$ implies the unconditionalΦ-convergence of the Haar—Fourier series of the functionf.     

Early recognition of oxidative degradation in polymers by chemiluminescence

Most common polymers degrade readily during normal use by reaction with oxygen. Rapid screening tests are requested by industry to characterise the oxidative stability of the materials. The chemiluminescence (CL) method, which is based on the fact that oxidation reactions of most organic materials, including polymers, are accompanied by weak emission of light, has the potential for being such a test. Selected examples of CL measurements, in a commercially available instrumentation, on different kind of materials and material formulations (as used in industrial applications) clearly indicate that the CL technique is capable of determining the relative oxidative stability of polymers at very early stages of degradation.