On q-Deformed $${{\mathfrak{gl}}_{\ell+1}}$$-Whittaker Function III

In this paper, we identify q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions with a specialization of the Macdonald polynomials. This provides a representation of q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions in terms of the Demazure characters of affine Lie algebra [^(\mathfrakgl)]_l+1{\widehat{\mathfrak{gl}}_{\ell+1}}. We also define a system of dual Hamiltonians for q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Toda chains and give a new integral representation for the q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker functions. Finally, we represent the q-deformed \mathfrakgl_l+1{\mathfrak{gl}_{\ell+1}}-Whittaker function as a matrix element of a quantum torus algebra.     

Signature codes for noisy multiple access adder channel

We prove new lower bounds on the rate of codes for noisy multiple access adder channel and discuss its application to the well-known coin weighing problem in the case when some measurements are incorrect.     

On l p -multipliers of functions analytic in the disk

We consider bounded analytic functions in domains generated by sets with the Littlewood-Paley property. We show that each such function is an l ^p -multiplier.     

Intertwining operators and soliton equations

The fermionic approach to the Kadomtsev-Petviashvili hierarchy, suggested by the Kyoto school (Sato, Date, Jimbo, Kashiwara, and Miwa) in 1981–4, is generalized on the basis of the idea that, in a sense, the components of intertwining operators are a generalization of free fermions forgl _∞. Integrable hierarchies related to symmetries of Kac-Moody algebras are described in terms of intertwining operators. The bosonization of these operators for various choices of the Heisenberg subalgebra is explicity written out. These various realizations result in distinct hierarchies of soliton equations. For example, forsl _N -symmetries this gives the hierarchies obtained by the (n ₁,...,n _s )-reduction from thes-component KP hierarchy introduced by Kac and van de Leur. The research of both authors was supported in part by RFBR grant No. 96-02-18046, grant No. 96-15-96455 for the support of leading scientific schools, and RFBR-CNRS grant No. 98-01-22033. International Center for Nonlinear Science at the Landau Institute of Theoretical Physics. Institute of Theoretical and Experimental Physics. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 33, No. 4, pp. 1–24, October–December, 1999. Translated by M. I. Golenishcheva-Kutuzova     

Tunable continuous-wave operation of a Cr3+,Li+:Mg2SiO4 laser

Room-temperature tunable cw laser oscillation of Cr3+ ions in forsterite crystals (Mg2SiO4) codoped with chromium and lithium has been demonstrated, for the first time to the authors' knowledge, in pumping a crystal with a Ti:sapphire laser into the first excited level of Cr3+ ions (4A2-4T2 transition). The laser is smoothly tunable in the region of 1095-1170 nm. A slope efficiency as great as 4.4% has been achieved.     

Electrohydraulic effect in water-plant heterodisperse systems I. Compositions of the solid residue and the aqueous phase

The electrohydraulic (EH) treatment of water-plant heterodisperse systems leads to the partial degradation of the main components of the plant materials: lignin, cellulose, and carbohydrates. The presence of p-hydroxyphenyl and guaiacyl structures has been established on the basis of the results of the GLC analysis of the ether-extracted phenolic products of plant materials subjected to EH treatment. It has been shown that part of the carbohydrates passes into the aqueous phase in the form of free monosaccharides: pentoses and hexoses.Institute of Chemistry of Plant Substances of Uzbekistan Academy of Sciences, Tashkent. Institute of Organic Chemistry, Siberian Branch, Russian Academy of Sciences, Irkutsk. Siberian Institute of Terrestrial Magnetism, the Ionosphere, and the Propagation of Radio Waves, Siberian Branch, Russian Academy of Sciences, Irkutsk. Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 707–711, November–December, 1992.     

Pyrolysis of 8,8-dimethyl-8-sila-2,3,4,5-tetrathiabicyclo[4.3.0]nonane

Conclusions The main products of the pyrolysis of 8,8-dimethyl-8-sila-2,3,4,5-tetrathiabicycIo-[4.3.0]nonane at 400 are 1,1-dimethylsilacyclopent-3-ene and 1,1-dimethyl-1-sila-2-thiacyclo-hexa-3, 5-diene, and at 600 carbon disulfide and thiophene; silacyclopentene is the sole reaction product, characteristic for the mass-spectrometric decomposition of the initial tetrasulfide.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No, 4, pp. 902–905, April, 1986.     

Additional stringy sources for electric dipole moments

We show that string models with low energy supersymmetry which accommodate the fermion mass hierarchy generally give nonuniversal soft trilinear couplings (A terms). In conjunction with the apparently large Cabibbo-Kobayashi-Maskawa (CKM) phase, this results in large fermion electric dipole moments (EDMs) even in the absence of CP violating phases in the supersymmetry breaking auxiliary fields and the micro term. Nonobservation of the EDMs therefore implies that strings select special flavor and/or supersymmetry breaking patterns.     

Raman scattering spectroscopy of inclusions of carbon in Al<Subscript>2</Subscript>O<Subscript>3</Subscript> films and its solid solutions with HfO<Subscript>2</Subscript>

We apply Raman scattering spectroscopy to study the nature of carbon inclusions in Al₂O₃ and (HfO₂) _x (Al₂O₃)_{1 ? x} films deposited using volatile complex compounds. Raman spectra of the films under investigation contain D and G vibrational modes, which indicate that carbon clusters of the sp ² configuration tend to form in the films. We estimate the size of clusters from the integrated intensity ratio I _D /I _G and find it to be in the range of 14–20 Å. The content of hydrogen in carbon clusters is calculated from the height of the photoluminescence pedestal and is found to vary from 14 to 30 at % depending on the regime of the film’s synthesis.