On the Bavrin Integro-Differential Operators and Their Applications to Solution of Functional Equations

We construct a multiplicative group structure in the class of integro-differential operators specific for a polydisk which was introduced by I. I. Bavrin. We indicate two applications of these operators to solution of functional equations.     

Kinetics of the thermal decomposition of bis(trifluoromethyl) peroxydicarbonate,CF3OC(O)OOC(O)OCF3

Thermal decomposition of bis(trifluoromethyl) peroxydicarbonate has been studied. The mechanism of decomposition is a simple bond fission, homogeneous first‐order process when the reaction is carried out in the presence of inert gases such as N₂ or CO. An activation energy of 28.5 kcal mol^?1 was determined for the temperature range of 50–90°C. Decomposition is accelerated by nitric oxide because of a chemical attack on the peroxide forming substances different from those formed with N₂ or CO. An interpretation on the influence of the substituents in different peroxides on the O? O bond is given. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 35: 15–19, 2003     

Lattice mechanical properties of some fcc f-shell metals

A pseudopotential depending on an effective core radius is proposed to study the binding energy, equation of state, ion-ion interaction, phonon dispersion curves (q-space and r-space analysis), mode Grüneisen parameters and dynamical elastic constants of some fcc f-shell metals La, Yb, Ce and Th. The contribution of the s-like electrons is calculated in the second-order perturbation theory for the potential while d and f-like electron is taken into account by introducing repulsive short-range Born-Mayer term. The parameter of the potential is evaluated by zero pressure condition. An excellent agreement between theoretical investigations and experimental findings is achieved which confirms the present formalism     

Analysis of Two-Dimensional Optical Fields Using an Additional Shift

A solution to the phase problem in optics is considered within the context of registration and analysis of two-dimensional stationary optical fields transformed by the object under study or fields forming an image. To obtain information on amplitude and phase distributions of the light field analyzed, a method of registration of two intensity distributions is used. The first distribution corresponds directly to the amplitude distribution. The other is formed for the sum of the initial field and the field shifted along a certain direction. The intensity distributions obtained allow one to calculate the two-dimensional structure of the field under study. It is noteworthy that the method requires no iteration procedures in solving the problem. This leads to speeding up of the processing and analysis of the information. Two variants of optical schemes for the analysis of light fields are considered. The first one corresponds to registration of the image of the analyzed plane and the second to registration of the spectrum of the spatial frequencies.     

Radiospectroscopic and dielectric spectra of nanomaterials

The shape of lines in the radiospectroscopic (NMR and EPR) and dielectric spectra of materials formed by nanoparticles (hereafter, nanomaterials) is analyzed theoretically. The theory is developed in the framework of the core and shell model according to which a nanoparticle consists of two regions whose properties are affected and unaffected by the surface, respectively. The changes in the resonance frequency, the relaxation time, and the static permittivity due to the surface tension are taken into account, and the Gaussian and Lorentzian shapes of homogeneously broadened lines are considered. The inhomogeneous broadening of the spectral lines is examined for several types of nanoparticle size distributions. It is demonstrated that the splitting of the initial lines in the spectra of bulk systems into pairs of lines with a decrease in the particle size is a specific feature of the spectra of nanoparticles. The intensities and half-widths of the lines are investigated as functions of the parameters of the size distribution of nanoparticles. The results of theoretical calculations are compared with recent experimental data on the ¹⁷O and ²⁵Mg NMR spectra of nanocrystalline MgO. The theoretical dependences of the intensity, the resonance frequency, and the half-width of the spectral lines are in good agreement with the experimental data. The proposed theory offers a satisfactory explanation of the behavior of the static permittivity in BaTiO₃ ceramic materials with nanometer-sized grains.     

Weighted oscillator strengths and lifetimes for the S IX and S X spectra

The weighted oscillator strengths (gf) and the lifetimes presented in this work were carried out in a multi configuration Hartree-Fock relativistic (HFR) approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure, in order to improve the adjustment to experimental energy levels. This method produces gf-values that are in better agreement with intensity observations and lifetime values that are closer to the experimental ones. In this work, we presented all the experimentally known electric dipole S IX and S X spectral lines.     

Noise-impact estimates per FTA and APTA criteria

In a recent paper, light-rail line noise exposures were predicted both in terms of maximum pass-by sound levels for comparison to APTA criteria and day-night average sound levels for comparison to FTA criteria. For the local land uses and ambient noise conditions of the project, the distances for the unmitigated pass-by noise exposures to attenuate to the APTA and FTA criteria limits were estimated and the numbers of included dwellings counted. The results found that the FTA impact-onset (i.e., “some-impact”) criterion curve yielded significantly greater noise exposed areas while the APTA criteria yielded results between those of the FTA “some”- and “severe”-impact curves. However, those results only applied to the specific project under evaluation. This paper attempts to extend and generalize the comparison by parametric computation of exposed areas using both the FTA and APTA procedures. Predicted exposures in this paper are compared as a function of background ambient sound levels, type of land use impacted, numbers of daytime and nighttime operations, and train pass-by maximum sound levels. At very low background ambient sound levels, FTA tended to predict the greatest exposure, while in very noisy environments, APTA predicted more exposure. APTA predicted more exposure with low numbers of daily and/or nighttime operations, and FTA predicted more exposure with high numbers, but the comparative exposures were strongly dependent upon background ambient sound level and land use. For train pass-by maximum sound levels, APTA tended to show more exposure for very quiet pass-bys and to be intermediate to FTA/some and FTA/severe for noisier events—with the comparative exposures strongly dependent upon background ambient and land use.     

Identifying several biased coins encountered by a hidden random walk

Suppose that attached to each site z ∈ ? is a coin with bias θ(z), and only finitely many of these coins have nonzero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its current position. Then we can determine the biases {θ(z)}_z∈?, using only the outcomes of these coin tosses and no information about the path of the random walker, up to a shift and reflection of ?. This generalizes a result of Harris and Keane. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004