Projective functors for algebraic groups

We investigate the regular subquotient category introduced by Soergel in [W. Soergel, On the relation between intersection cohomology and representation theory in positive characteristic, J. Pure Appl. Algebra 152 (1–3) (2000) 311–335]. A detailed study of projective functors enables one to relate those categories for semi-simple algebraic group G and its subgroup schemata G_rT. As an application we derive some information about the characters of tilting modules for G.     

A duality property of an uncountable product of $${\mathbb{Z}}$$

We construct a quotient group of an uncountable product of integers which is not Pontryagin reflexive.     

Generalized doubling meets Poincaré

We establish a modified segment inequality on metric spaces that satisfy a generalized volume doubling property. This leads to Sobolev and Poincaré inequalities for such spaces. We also give several examples of spaces that satisfy the generalized doubling condition.     

Baxter-Guttmann-Jensen conjecture for power series in directed percolation problem

A probabilistic model of a flow of fluid through a random medium,percolation model, provides a typical example of statistical mechanical problems which are easy to describe but difficult to solve. While the percolation problem on undirected planar lattices is exactly solved as a limit of the Potts models, there still has been no exact solution for the directed lattices. The most reliable method to provide good approximations is a numerical estimation using finite power-series expansion data of the infinite formal power series for percolation probability. In order to calculate higher-order terms in power series, Baxter and Guttmann [6] and Jensen and Guttmann [33] proposed an extrapolation procedure based on an assumption that thecorrection terms, which show the difference between the exact infinite power series and approximate finite series, are expressed as linear combinations of the Catalan numbers.In this paper, starting from a brief review on the directed percolation problem and the observation by Baxter, Guttmann, and Jensen, we state some theorems in which we explain the reason why the combinatorial numbers appear in the correction terms of power series. In the proof of our theorems, we show several useful combinatorial identities for the ballot numbers, which become the Catalan numbers in a special case. These identities ensure that a summation of products of the ballot numbers with polynomial coefficients can be expanded using the ballot numbers. There is still a gap between our theorems and the Baxter-Guttmann-Jensen observation, and we also give some conjectures.As a generalization of the percolation problem on a directed planar lattice, we present two topics at the end of this paper: The friendly walker problem and the stochastic cellular automata in higher dimensions. We hope that these two topics as well as the directed percolation problem will be of much interest to researchers of combinatorics.     

Weighted Bergman spaces¶associated with causal symmetric spaces

Let H\G be a causal symmetric space sitting inside its complexification H _ℂ\G _ℂ. Then there exist certain G-invariant Stein subdomains Ξ of H _ℂ\G _ℂ. The Haar measure on H _ℂ\G _ℂ gives rise to a G-invariant measure on Ξ. With respect to this measure one can define the Bergman space B ²(Ξ) of square integrable holomorphic functions on Ξ. The group G acts unitarily on the Hilbert space B ²(Ξ) by left translations in the arguments. The main result of this paper is the Plancherel Theorem for B ²(Ξ), i.e., the disintegration formula for the left regular representation into irreducibles. Received: Received: 23 November 1998     

Volterra-like Banach Algebras and their Second Duals

 This paper presents and studies a class of algebras which includes the usual Volterra algebra. Roughly speaking, they relate to the Volterra algebra in the way a general locally compact group relates to ℝ. We show that they can be viewed as quotients of some semigroup algebras introduced by Baker and Baker [1]. Their sets of nilpotent elements are dense. We investigate the second duals of these algebras and find that most of the properties found in [7] for the biduals of the group algebras L ¹(G) for compact G are retained here. Received 8 July 1997; in revised form 17 November 1997     

Structural modifications of diamond like carbon films induced by MeV nitrogen ion irradiation

Diamond-like carbon (DLC) films were deposited on Si(1 0 0) substrates using plasma deposition technique. The deposited films were irradiated using 2 MeV N⁺ ions at fluences of 1×10¹⁴, 1×10¹⁵ and 5×10¹⁵ ions/cm². Samples have been characterized by using Raman spectroscopy, X-ray photoelectron spectroscopy (XPS) and high-resolution transmission electron microscopy (HRTEM). Analysis of Raman spectra shows a gradual shift of both D and G band peaks towards higher frequencies along with an increase of the intensity ratio, I(D)/I(G), with increasing ion fluence in irradiation. These results are consistent with an increase of sp² bonding. XPS results also show a monotonic increase of sp²/sp³ hybridization ratio with increasing ion fluence. Plan view TEM images show the formation of clusters in the irradiated DLC films. HRTEM micrographs from the samples irradiated at a fluence of 5×10¹⁵ ions/cm² show the lattice image with an average interplanar spacing of 0.34 nm, revealing that the clusters are graphite clusters. The crystallographic planes in these clusters are somewhat distorted compared to the perfect graphite structure.     

Transformation mechanism of n-butyl terminated Si nanoparticles embedded into Si1−xCx nanocomposites mixed with Si nanoparticles and C atoms

Bright-field transmission electron microscopy (TEM) images, high-resolution TEM (HRTEM) images, and fast-Fourier transformed electron-diffraction patterns showed that n-butyl terminated Si nanoparticles were aggregated. The formation of Si_1−xC_x nanocomposites was mixed with Si nanoparticles and C atoms embedded in a SiO₂ layer due to the diffusion of C atoms from n-butyl termination shells into aggregated Si nanoparticles. Atomic force microscopy (AFM) images showed that the Si_1−xC_x nanocomposites mixed with Si nanoparticles and C atoms existed in almost all regions of the SiO₂ layer. The formation mechanism of Si nanoparticles and the transformation mechanism of n-butyl terminated Si nanoparticles embedded into Si_1−xC_x nanocomposites mixed with Si nanoparticles and C atoms are described on the basis of the TEM, HRTEM, and AFM results. These results can help to improve the understanding of the formation mechanism of Si nanoparticles.     

A Wide Band Strong Acoustic Absorption in a Locally Network Anechoic Coating

Composite materials with interpenetrating network structures usually exhibit unexpected merit due to the cooperative interaction. Locally resonant phononic crystals （LRPC） exhibit excellent sound attenuation performance based on a periodical arrangement of sound wave scatters. Inspired by the interpenetrating network structure and the LRPC concept, we develop a locally network anechoic coating （LNAC） that can achieve a wide band of underwater strong acoustic absorption. The experimental results show that the LNAC possesses an excellent underwater acoustic absorbing capacity in a wide frequency range. Moreover, in order to investigate the impact of the interpenetrating network structure, we fabricate a faultage structure sample and the network is disconnected by hard polyurethane （PU）. The experimental comparison between the LNAC and the fanltage structure sample shows that the interpenetrating network structure of the LNAC plays an important role in achieving a wide band strong acoustic absorption.     

Experimental measurement of the nonlinearities of electrodynamic microphones

This paper presents an experimental way of characterizing the nonlinearities of electrodynamic microphones used as acoustical sources. This functioning occurs for reciprocal calibration techniques. For this purpose, its electrical impedance is measured with a Wayne Kerr wedge which has an excellent precision. Moreover, it can be noted that the Thiele and Small model is used to characterize its electrical impedance. Furthermore, an experimental method based on Simplex algorithm allows us to construct polynomial laws which describe the dependence of the Thiele and Small parameters with the input voltage. The nonlinear variations obtained allow us to determine the nonlinear differential equation of the electrodynamic microphone. Then, this equation is solved numerically in order to confirm the accuracy of the polynomial laws obtained by the Simplex algorithm. The distortions are measured with a laser Doppler velocimeter and compared with the ones obtained by the numerical solving of the nonlinear differential equation. The experimental displacement spectrum is consistent with the theoretical one.