Local field effects and stimulated multimode scattering of resonance radiation in a two-level medium

Scattering of resonance radiation in a dense two-level medium is considered with allowance for the local field effects. The system is studied in the framework of the mean-field approximation for a modified hierarchy of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices of an ensemble of atoms and modes of a quantized electromagnetic field. The local field correction is consistently derived from the initial Hamiltonian of the system. The problem of scattering of a short rectangular pulse from a quasi-point sample is considered numerically and theoretically. The possibility of a multimode spectrum of scattered radiation with frequencies multiple of the Rabi frequency and with other intermediate frequencies is demonstrated. The relative intensities of spectral lines are determined.     

Pade form of effective rotational molecular Hamiltonians

Effective rotational molecular Hamiltonians (ERH) are constructed which differ from the traditional representation of the ERH as a power series in the total angular momentum. A Padeform of the ERH is systematically obtained and the nonuniqueness of this form is emphasized.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 8, pp. 86–90, August, 1982.Finally, the authors thank A. V. Burenin for pointing out to us the advantages of the Pade representation of the ERH in the analysis of molecular spectra.     

Study of isobaric analogue resonances in65Cu by proton scattering from64Ni

Zeitschrift für Physik A Hadrons and nuclei - Excitation functions of the elastic proton scattering by64Ni were measured in the energy rangeE p =5.0–6.2 MeV at 90°, 125° and...     

Toxicity of zinc oxide nanoparticles to the annelid <Emphasis Type="Italic">Enchytraeus crypticus</Emphasis> in agar-based exposure media

Toxicity of zinc oxide nanoparticle (ZnO-NPs) powder and water soluble salt of Zn (ZnCl₂) to the annelid Enchytraeus crypticus was tested in agarose gel. Influence of the spiking method on the resulting size of nanoparticles and on E. crypticus mortality was studied. Two methods of ZnO-NPs powder (mean particle size diameter of 10 nm) introduction into the exposure media were used. In the first method, the nano-powder was initially cryogenically ground with dry agar followed by an addition of water. The second procedure began with re-suspension of nanoparticles in demineralized water containing a dispersant (sodium pyrophosphate decahydrate). The obtained colloid was subsequently mixed with hot agar gel. Relative mortality in worms observed after 96 h of their exposure to the ZnO-NPs concentrations (all in mg of ZnO-NPs per kg of agar) of 50, 100, 200, 500 and 1000 in the cryogenically ground medium ranged between 28.9 % and 34.4 % and it did not exhibit any concentration dependence. When the second method of exposure media preparation was applied, the relative mortality ranged from 0 % to 66.6 % in the same concentration region depending on the concentration. Scanning electron microscopy (SEM) revealed the presence of large agglomerates (1–10 µm in diameter) in the media prepared by cryogenic grinding with the highest concentration of ZnO-NPs. Neither the cryogenically ground media with lower ZnO-NPs concentrations nor any media prepared from colloidal solutions contained agglomerates exceeding 100 nm, detectable by SEM. Hydrodynamic diameters of particles in the colloids used in the second method of agar preparation were measured using dynamic light scattering (DLS) and ranged between 164 nm and 240 nm. The observed toxicity was thus clearly dependent on the size of ZnO-NPs agglomerates and the technique of exposure media preparation. Experimentally detected LC₅₀ value for dissolved Zn²⁺ was 37.2 mg kg^?1 in agar. The same concentration of Zn induced an approximately 30 % mortality of E. crypticus when administered in form of cryogenically ground ZnO-NPs with agar. No observable effects were found at this ZnO-NPs concentration when the exposure medium was prepared from the colloid solution.     

New quasi-Newton method for solving systems of nonlinear equations

We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR or LU decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n ²) arithmetic operations per iteration in contrast with the Newton method, which requires O(n ³) operations per iteration. Computational experiments confirm the high efficiency of the new method.     

Nonclassical Solutions of Fully Nonlinear Elliptic Equations

We prove the existence of non-smooth solutions to fully non-linear elliptic equations. Received: June 2006, Accepted: January 2007