Classification of graded Hecke algebras for complex reflection groups

The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well as complex reflection groups. Received: July 25, 2001     

Note on André's reflection principle

This note generalizes André's reflection principle to give a new combinatorial proof of a formula for the number of lattice paths lying within certain trapezoids.     

Une méthode de calcul des coefficients de réflexion et de transmission d'une houle bidimensionnelle en milieu confinéA new method for the calculation of transmission and reflection coefficients for water waves in a small basin

This paper presents a method to estimate reflected and transmitted wave amplitude spectra in a bounded domain such as a wave tank, when available data signals must be shortened due to interferences and wall effects. This paper extends the well known Goda and Suzuki two-probe method to three probes. The paper also suggests solutions to compute reliable transmission and reflection coefficients in spite of problems linked to higher harmonics and to the interference between different wave trains propagating in the tank. To cite this article: G. Duclos, A.H. Clément, C. R. Mecanique 331 (2003).     

A method for determining optical constants, dimensions, and concentrations of “soft” absorbing particles in the brightening band region

We investigate the possibilities of creating a method for estimating the optical constants, dimensions, and concentrations of “soft” absorbing particles by applying a theoretical analysis of the angular dependence of the intergrated indicatrix, overall characteristics of light scattering, and absorption on the phase shift and diffraction parameter of particles in the brightening band region. We show that using the investigated optical characteristics, it is possible to determine the unknown parameters of a suspension from experimental data. Institute of Biophysics, Siberian Branch of the Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 807–812, November–December, 1997.     

分布耦合系数对线性啁啾光栅色散的影响

本文从光栅反向耦合波方程出发,经相位共轭变换用Runge-Kuta-Gil方法对其数值求解。针对线性啁啾光栅耦合系数变化服从不同的分布,分析了各种分布对光栅反射谱特性和色散特性的影响。     

Asymptotic behavior of energy band associated with a negative energy level

The mathematical foundation of the tight binding approximation is given. If ₀ is a negative energy level of a real potentialq, then there exists an energy band for a one-dimensional chain with period 2T of the same atoms which lies near ₀. We study this band whenT tends to infinity.On leave of absence from the Department of Physics, Leningrad State University, Leningrad, USSR.     

Conformations, Energy and Spectral Characteristics of 2,3-Trimethylene- and 2,3-Pentamethylene-3,4-dihydro-4-quinazolinones

Quantum-chemical calculations and IR spectroscopy were used to study the conformations as well as the energy and spectral characteristics of 2,3-trimethylene- and 2,3-pentamethylene-3,4-dihydro-4-quinazolinones. The shift of -electron density from the heterocyclic system to the carbonyl group and, thus, the proton affinity of the oxygen atom of this group increase with expansion of the bond angle at the nitrogen atom in going from a five-membered to seven-membered ring.     

Broadband and band-selective IMPRESS-gHMBC: compensation of refocusing inefficiency with synchronized inversion sweep

Compensation of refocusing inefficiency in a gHMBC experiment by replacing the rectangular pi pulse with a pair of adiabatic pulses with synchronized inversion sweep (CRISIS) significantly improves the performance of the gHMBC experiment. The CRISIS-gHMBC experiment retains the pure absorptive shapes in F1 and hence results in better lineshape and higher resolution than the current versions of magnitude mode gHMBC spectra. When used as a broadband experiment, CRISIS-gHMBC, owing to better refocusing efficiency of the adiabatic pulse pairs, gives improved performance across the 13C spectral width. Moreover, it is shown that CRISIS-gHMBC is a robust and improved alternative and when used along with the IMPRESS (Improved Resolution using Symmetrically Shifted pulses) technique further increases the sensitivity and resolution without additional experimental time. The IMPRESS-CRISIS combination is demonstrated for broadband gHMBC and band-selective gHMBC experiments. The ICbs-gHMBC [IMPRESS-CRISIS-band-selective gHMBC] experiment is an attractive and better alternative to individual band-selective gHMBC.     

Synthesis, band structure, and optical properties of Ba2ZnV2O8

A novel compound Ba₂ZnV₂O₈ has been synthesized in high temperature solution reaction and its crystal structure has been characterized by means of single crystal X-ray diffraction analysis. It crystallizes in monoclinic system and belongs to space group P2₁/c with a=7.9050(16), b=16.149(3), , β=90.49(3). It builds up from 1-D branchy chains of [ZnV₂O₈⁴⁻]_∞, and the Ba²⁺ cations are located in the space among these chains. The IR spectrum, ultraviolet-visible diffuse reflection integral spectrum and fluorescent spectra of this compound have been investigated. The calculated results of energy band structure by the density functional theory method show that the solid-state compound of Ba₂ZnV₂O₈ is an insulator with direct band gap of 3.48 eV. The calculated total and partial density of states indicate that the top valence bands are contributions from the mixings of O-2p, V-3d, and Zn-3d states and low conduction bands mostly originate from unoccupied antibonding states between the V-3d and O-2p states. The V-O bonds are mostly covalence characters and Zn-O bonds are mostly ionic interactions, and the ionic interaction strength is stronger between the Ba-O than between the Zn-O. The refractive index of n_x, n_y, and n_z is estimated to be 1.7453, 1.7469, and 1.7126, respectively, at wavelength of 1060 nm for Ba₂ZnV₂O₈ crystal.     

A study of preferential solvation of N-alkyl pyridinium iodides in mixed solvents containing acetonitrile

The charge transfer (CT) band maximum of N-alkyl pyridinium iodide (NAPI) has been studied as a function of the composition of binary mixed dipolar aprotic solvents. The deviation from linearity of the energy maximum (E₁₂) and the mole fraction (of a component solvent) plot is explained as due to a preferential solvation by the more polar cosolvent in the binary mixture. The extent of preferential solvation has been observed to vary with the composition, the maximum being towards the less-polar end. The role of hydrogen bond donating ability of a solvent in preferential solvation is discussed.