Inequalities for a unified family of Voigt functions in several variables

The classical Voigt functions occur frequently in a wide variety of problems in astrophysical spectroscopy, emission, absorption and transfer of radiation in heated atmosphere, and plasma dispersion, and indeed also in the theory of neutron reactions. Here, in the present paper, by applying several known upper bounds for the first-kind Bessel function J _ν (x) given recently by (for example) Landau, Olenko and Krasikov, sharp bounding inequalities are obtained for the unified multivariable Voigt function V _μ,ν (x; y) in terms of the confluent Fox-Wright function ₁ψ₀ and its incomplete variant ₁ψ₀. Connections of the unified multivariable Voigt function V _μ,ν (x; y) with other unifications and generalizations of the classical Voigt function are also briefly pointed out.     

Lagrangian Duality in Set-Valued Optimization

In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, pp. 221–228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given. The authors thank the two referees for valuable comments and suggestions on early versions of the paper. The research of the first author was partially supported by Ministerio de Educación y Ciencia (Spain) Project MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06.     

Extraction of strontium using an irradiated extraction agent of crown structure

The partition coefficient of strontium upon its extraction from the aqueous solutions of picric acid into chloroform containing DC-18-crown-6, B-15-crown-5 after their exposition to gamma radiation has been studied. A significant decrease of the partition coefficient in the studied range of doses 10–70 kGy was observed. This effect can be attributed to the radiolytic products of chloroform. The radiation destruction as well as dehydrogenation of crown ethers were not observed.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.     

Thee + e −→¯nn cross section predicted remarkably larger than thee + e −→¯pp one

It is shown that all global analyses of nucleon electromagnetic form factor data predict the electron-positron annihilation into neutron-antineutron cross section (for which there are no data till now) to be in a finite energy region substantially larger than the electron-positron annihilation into the proton-antiproton one.Dedicated to the memory of M. Gmitro.     

RNA self-splicing and energy localization

We establish a mechanism for energy localization in regions of the sugar-phosphate RNA backbone which leads to the formation of transesterification or hydrolysis hot spots. In particular, our results account for the site specificity of the covalent cyclization and cycle reopening in the catalytic intervening sequence (IVS) of a ribosomal RNA.     

Spectral hole burning of photosynthetic antenna of blue-green algae

Photosystem II core antenna of blue-green algae Synechococcus isolated in gel was studied by optical hole burning spectroscopy at 4·2 K. Persistent holes were burned into fluorescence spectra throughout the region 680–696 nm. The hole width extrapolated to zero burning fluence yielded a value 1·0±0·2 cm^–1. A theoretical interpretation of the hole profile in fluorescence is presented. The dependence of saturated hole depth on burning wavelength is related to inhomogeneous site distribution function.Authors would like to thank F. Vácha from the Dept. of Biochemistry, Faculty of Nature Sciences, Charles University, for the preparation of the samples.     

The phase composition of tin-nickel electrodeposited alloys

It was studied the tin phase composition of the electrodeposited alloys produced at different temperatures and current densities from an acid chloride/fluoride electrolyte and an acid chloride bath. Mössbauer spectra were consistent with a Ni₃Sn₄ intermetallic compound, dissolved tin, and a Cu?Sn intermetallic compound formed at the interface of the copper substrate.     

Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.