A reduction theorem for the Alperin weight conjecture

The Alperin Weight Conjecture was stated by J. Alperin in 1986 and constitutes one of the main problems in the representation theory of finite groups. In this paper, we provide a reduction to simple groups and as an application we prove the conjecture in several cases.     

A note on idempotents in finite AW*-factors

We prove that the value of the quasi-trace on an idempotent element in an AW*-factor of type is the same as the dimension of its left (or right) support.

     

Vertices for characters of -solvable groups

Suppose that is a finite -solvable group. We associate to every irreducible complex character of a canonical pair , where is a -subgroup of and , uniquely determined by up to -conjugacy. This pair behaves as a Green vertex and partitions into ``families" of characters. Using the pair , we give a canonical choice of a certain -radical subgroup of and a character associated to which was predicted by some conjecture of G. R. Robinson.

     

A multiple regression model for urban traffic noise in Hong Kong

This article describes the roadside traffic noise surveys conducted in heavily built-up urban areas in Hong Kong. Noise measurements were carried out along 18 major roads in 1999. The measurement data included L10, L50, L90, Leq, Lmax, the number of light vehicles, the number of heavy vehicles, the total traffic flow, and the average speed of vehicles. Statistical analysis using the analysis of variance (ANOVA) and Tukey test (p<0.05) reveals that the total traffic flow and the number of heavy vehicles are the most significant factors of urban traffic noise. Multiple regression was used to derive a set of empirical formulas for predicting L10 noise level due to road traffic. The accuracy of these empirical formulas is quantified and compared to that of another widely used prediction model in Hong Kong--the Calculation of Road Traffic Noise. The applicability of the selected multiple regression model is validated by the noise measurements performed in the winter of 2000.     

Rotational Analysis of the ΔvSiH=3-6 Stretching Vibrational Overtones of HSiD3

The nν₁ SiH stretching overtone transitions of trideuterosilane, HSiD₃, have been recorded by Fourier transform spectroscopy (n=3 and 4) and by intracavity laser absorption spectroscopy (n=5 and 6). The unusually weak 3ν₁ band is affected by considerable intensity and energy perturbations. The 4ν₁ band is also strongly perturbed but the interaction with the dark states is more limited and part of the rotational structure of the v₁=4 upper state could be satisfactorily modeled. Less pronounced perturbations affect the v₁=5 level, newly detected by ICLAS. Its rotational structure is locally perturbed by anharmonic coupling with an unidentified vibrational dark state. The global modeling of the interacting dyad allowed the determination of the perturber parameters and the assignment of extra lines due to an intensity transfer from the v₁=5 bright state to the dark state. In agreement with a previous ICLAS study, the 6ν₁ band near 12 113 cm⁻¹ was found free of perturbation. About six hundred line positions could be reproduced with an rms of 4.6×10⁻³ cm⁻¹, leading to a significantly improved set of rovibrational parameters. The striking evolution of the rotational structure, which exhibits fewer and fewer perturbations when the SiH excitation increases, is discussed.     

Formation of metal-anion arrays within layered perovskite hosts. Preparation of a series of new metastable transition-metal oxyhalides, (MCl)LaNb(2)O(7) (M = Cr,Mn, Fe,Co)

A new series of transition-metal oxyhalides (MCl)LaNb(2)O(7) (M = Cr, Mn, Fe, Co) have been prepared by a simple topochemical route. Layered perovskite hosts (ALaNb(2)O(7), A = Li, Na, K or Rb) were reacted with the corresponding anhydrous metal halides under mild reaction conditions (<400 degrees C). The compounds were examined by X-ray powder diffraction; the series appears to be isostructural with (CuCl)LaNb(2)O(7), and the layer spacings, with the exception of M = Co, follow the trend expected from transition-metal cationic radii. Thermal analysis with differential scanning calorimetry (DSC) shows the materials to be metastable where all four compounds decompose exothermically above 690 degrees C.     

Synthesis of a mesoporous composite material prepared by the self-assembly of mineral liquid crystals

Here we describe the synthesis of a mesoporous composite material using the self-assembly of well defined tubular building blocks obtained from the exfoliation of [Nb6O17(4-)]n sheets.     

Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating

A novel method for real-time polarization measurement is presented. The method is based on a space-variant wave plate that we realized as a computer-generated space-variant subwavelength dielectric grating. The Stokes parameters of the incident beam are determined by Fourier analysis of the space-variant intensity transmitted through the grating and an analyzer. We discuss the design and realization of such wave plates and demonstrate our technique with polarization measurements of both polarized and partially polarized CO(2)-laser radiation at a wavelength of 10.6 mum.