Asymptotic approximation of functions and their derivatives by Müller’s Gamma operators

We obtain the complete asymptotic expansion of the image functions of Müller’s Gamma operators and of their derivatives. All expansion coefficients are explicitly calculated. Moreover, we study linear combinations of Gamma operators having a better degree of approximation than the operators themselves. Using divided differences we define general classes of linear combinations of which special cases were recently introduced and investigated by other authors.     

Character formulas for some classes of atypical gl(m+nε)- and p(m)-modules

If p is an arbitrary parabolic subsuperalgebra of g = gl(m + n), p(m), a character formula for the generic finite-dimensional irreducible g-module, such that p is the stabilizer of its lowest weight space, is announced. Furthermore, an estimate for the character of any finite-dimensional irreducible g-module in terms of its highest weight with respect to a distinguished Borel subsuperalgebra is presented (inequality (4)) and a sufficient condition for this to be an equality is found. In this way, two generalizations of the Kac character formula for typical modules are obtained: a formula concerning an arbitrary Borel subsuperalgebra ((1)) and a more effective formula ((3)) for the special case of a distinguished Borel subsuperalgebra. The complete proofs will appear in [14].Partially supported by Contract 911/11.04.88 with the Bulgarian Ministry of Culture, Science, and Education.     

Influence of surroundings on photorefractive effect in lithium niobate crystals

In the paper results of the investigation of the influence of electric properties of the environment surrounding LiNbO₃ crystals on photorefractive effect induced in these crystals by Gaussian Ar⁺ laser beam with various intensities are presented. We show spatial and temporal dependences of changes of the refractive index obtained experimentally in LiNbO₃: Fe and LiNbO₃: Fe:Mn samples surrounded by media with different electric conductivities and different permittivities (water, air, water solution of CaCl₂). The space and time dependences of the refractive index changes induced by the Ar⁺ laser beam are observed by means of the Mach–Zehnder interferometer using light from HeNe laser. The experimentally obtained results are in a good agreement with those following from numerical calculations using the manifold mirroring method. The agreement between calculated and experimental results indicates that the polarization charge at the photorefractive crystal/surrounding medium boundary significantly influences the photorefractive process in the crystal. The experimentally observed slow spontaneous decrease of the refractive index change in a sample placed into a slightly conducting medium (air) after switching off the beam also indicates that the polarization charge in the sample's surroundings affects the photorefraction.     

Mass Spectrometry of Some Benzylidene Imidazolidinediones and Thiazolidinediones. II- chlorobenzyl imidazolidinedione and Fluoro or Chlorobenzyl Thiazolidinedione Compounds

In the present investigation, a study of the electron impact mass spectrometry data is reported for seven compounds of a series of some 3-(4-chlorobenzyl)-5-benzylidene-imidazolidine-2, 4-diones and 3-(4-fluoro or chlorobenzyl)-5-benzylidene-thiazolidine-2, 4-diones previously synthesized.     

Theoretical study of the helio hydrogen cyanide dication HeCNH2+

The structure and stability of the helio hydrogen cyanide molecular ion, HeCNH²⁺, is investigated by standard quantum chemical methods. Single reference calculations are carried out using second-order perturbation theory (MP2), the coupled cluster expansion in the CCSD approximation, and the hybrid approach using a perturbative estimate of the triple excitation energy component designated CCSD(T). Multireference calculations using a complete active space (CASSCF) and a second-order perturbation theory estimate of correlation effects (CASPT2) are reported.     

Center-of-Mass Tomography and Wigner Function for Multimode Photon States

Tomographic probability representation of multimode electromagnetic field states in the scheme of center-of-mass tomography is reviewed. Both connection of the field state Wigner function and observable Weyl symbols with the center-of-mass tomograms as well as connection of the Grönewold kernel with the center-of-mass tomographic kernel determining the noncommutative product of the tomograms are obtained. The dual center-of-mass tomogram of the photon states are constructed and the dual tomographic kernel is obtained. The models of other generalized center-of-mass tomographies are discussed. Example of two-mode even and odd Schrödinger cat states is presented in details.     

Chernoff approximations of Feller semigroups in Riemannian manifolds

Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks.     

μSR Investigation of ethyl radicals adsorbed on silica

SR spectra of the ethyl radical adsorbed on porous silica were observed in transverse and in longitudinal magnetic fields in the temperature range 190–298 K. The line widths reflect the dynamic partial averaging of the hyperfine anisotropy due to reorientation and surface diffusion.     

Optical switching and logic gates with hybrid plasmonic-photonic crystal nanobeam cavities

We propose a hybrid resonance architecture in which a plasmonic element is coupled to a silicon-on-insulator photonic crystal nanobeam cavity operating at telecom wavelengths. It benefits from the combined characteristics of the photonic cavity and the plasmonic element, and exploits the unique properties of Fano resonances resulting from interactions between the continuum and the localized cavity states. As confirmed through 3D time-domain simulations, a strong cavity mode damping by the plasmonic element offers mechanisms of controlling a probe signal propagating in the nanobeam. It makes possible to create optical switching devices and logic gates relying on any optical nonlinear effect.