Characters of irreducibleG-modules and cohomology ofG/P for the lie supergroupG=Q(N)

We prove a character formula for any finite-dimensional irreducible representationV of the “queer” Lie superalgebra g=q(n). It expresses chV in terms of the multiplicities of the irreducible g-subquotients of the cohomology groups of certain dominant g-bundles on the Π-symmetric projective spaces (i.e., on the homogeneous superspacesG/P whose reduced space is a projective space, whereG=Q(n)). We also establish recurrent relations for the above multiplicities, and this enables us to compute explicitly chV for any givenV. This provides a complete solution to the Kac character problem for the Lie superalgebraq(n). Finally, we consider the particular cases ofq(2), q(3), andq(4) in which we compare the new character formula with the generic character formula of [12]. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 41, Algebraic Geometry-7, 1997.     

The signature theorem and some related questions

Some corollaries of the Hirzebruch-Thom signature theorem are discussed. The multiplicativity of the signature and the naturalness of the Pontryagin classes for coverings in the case of ℚ-homology manifolds is proved. A geometric proof of Hirzebruch’s well-known “functional equation” for the virtual signature is outlined. Bibliography: 25 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 197–209. Translated by N. Yu. Netsvetaev.     

Formation of a two-dimensional periodic structure of local melting regions on a silicon surface upon pulsed light irradiation

The first results regarding the formation of a two-dimensional periodic structure of local melting regions on a silicon surface upon pulsed light irradiation are presented. The conditions are established, and the mechanism of the formation of such structures is discussed. Zh. Tekh. Fiz. 67, 97–99 (December 1997)     

High quantum efficiency of intersubband transitions in coherent tunneling of electrons through asymmetric double-barrier structures

A converging perturbation series that can be summed analytically has been obtained for intersubband transitions of electrons coherently tunneling through the middle of a dimensionally quantized level in an asymmetric double-barrier structure in a high-frequency terahertz electric field. The possibility of a substantial increase in tunneling current accompanied by either absorption or emission of a photon has been demonstrated. The quantum efficiency of radiative transitions between dimensionally quantized levels can be up to 66%. Zh. éksp. Teor. Fiz. 112, 237–245 (July 1997)     

Temperature and frequency dependence of the spin-lattice relaxation times of E′1 centers in neutron-irradiated quartz glass

Results are reported for measurements of the spin-lattice relaxation times of E′₁ centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm⁻¹. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation of irradiation centers in crystalline quartz and quartz glass. Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997)     

Integration of the equations of planar and flexural vibrations of anisotropic plates in special functions of generalized complex variables

On the basis of the method of successive approximations in formal series we construct systems of particular solutions of the equations of planar and flexural harmonic vibrations of thin rectilinear anisotropic plates with a plane of symmetry of elastic properties parallel to the faces. The solutions constructed are classified as special sk-functions of generalized complex variables. Translated fromTeoreticheskaya i Prikladnaya Mekhanika No. 24, 1993, pp. 54–61.     

Forecasting call frequency at a financial services call centre

A forecasting model is developed for the number of daily applications for loans at a financial services telephone call centre. The purpose of the forecasts and the associated prediction intervals is to provide effective staffing policies within the call centre. The model building process is constrained by the availability of only 2 years and 7 months of data. The distinctive feature of the data is that demand is driven in the main by advertising. The analysis given focuses on applications stimulated by press advertising. Unlike previous analyses of broadly similar data, where ARIMA models were used, a model with a dynamic level, multiplicative calendar effects and a multiplicative advertising response is developed and shown to be effective.     

Surface grating formation and erasing on a-Se films

Surface relief formation at holographic recording on amorphous selenium films was demonstrated and investigated. The presence of this optical phase modulation component is essential for ensuring significant, stable and erasable optical recording in a-Se films at 290–320 K temperatures, where conventional photodarkening was known as insignificant and unstable. Photocrystallization can only be observed in super-exposed a-Se films at the given experimental conditions of hologram recording. Erasing behavior of surface relief gratings under heat treatment was also investigated in order to reveal further details of the mechanism. Photoinduced structural transformations within the amorphous phase, connected to local ordering under the condition of light-induced fluidity, are proposed as an explanation for the relief formation and erasing. The observed reversible optical recording process may be useful for the various optoelectronic applications of photoconductive a-Se layers. Received: 12 June 2000 / Accepted: 6 June 2001 / Published online: 30 August 2001     

Some remarks on metaplectic cusp forms and the correspondences of Shimura and Waldspurger

The simple relation between representations of the covering groups of SL₂ and GL₂ makes it possible to fuse and extend the recent metaplectic results of Shimura, Waldspurger, Flicker, and ourselves. By giving a new (purely local andL-function theoretic) treatment of the Waldspurger-Shintani correspondence, we also simplify some of Waldspurger’s original results.