Function Spaces and Capacity Related to a Sublinear Expectation: Application to <Emphasis Type=Italic>G</Emphasis>-Brownian Motion Paths

In this paper we give some basic and important properties of several typical Banach spaces of functions of G-Brownian motion paths induced by a sublinear expectation—G-expectation. Many results can be also applied to more general situations. A generalized version of Kolmogorov’s criterion for continuous modification of a stochastic process is also obtained. The results can be applied in continuous time dynamic and coherent risk measures in finance, in particular for path-dependence risky positions under situations of volatility model uncertainty.     

Schrödinger Operators with Sparse Potentials: Asymptotics of the Fourier Transform¶of the Spectral Measure

We study the pointwise behavior of the Fourier transform of the spectral measure for discrete one-dimensional Schr?dinger operators with sparse potentials. We find a resonance structure which admits a physical interpretation in terms of a simple quasiclassical model. We also present an improved version of known results on the spectrum of such operators. Received: 17 May 2001 / Accepted: 28 June 2001     

Second-order calculation and beam-foil measurement of atomic lifetimes in Ne-like Al IV

The measured lifetimes of the 4p′(1/2)₀, 4p(5/2)₂ and 4d(5/2)₃ levels in neon-like A1 IV are compared to a second-order calculation of transition probabilities.     

Optical control of arrays of photorefractive screening solitons

We discuss the creation of an array of 9 x 9 photorefractive spatial screening solitons in a strontium barium niobate crystal. We investigate the waveguide properties of each channel with a beam of different wavelength and find that the waveguides guide the probe beam independently. A supplementary beam is used to influence the paths of the array solitons and to effectively combine two channels by use of mutual attraction of solitons. To our knowledge this is the first all-optical control of an array of photorefractive solitons. Furthermore, we show that in principle image procession is possible with parallel propagation of photorefractive solitons.     

Application of wavelet transform to hologram analysis: three-dimensional location of particles

The wavelet analysis provides an efficient tool in numerous signal-processing problems and has been implemented in optical processing techniques, such as in-line holography. When the diffraction pattern recorded on a hologram is analyzed by means of a wavelet transform, the 3-D location of small particles can be determined very accurately. The diffraction process can, in fact, be interpreted as a convolution with a family of wavelet functions, or, merely, as a wavelet transform. The scale parameter of the wavelet family is related to the axial distance z that the wave propagates. The original field is then reconstructed by searching for the optimum value of the scale parameter which produces a maximum of the wavelet transform modulus. The technique proposed is implemented and experimental results are presented.     

Derivation of Hamaker Dispersion Energy of Amorphous Carbon Surfaces in Contact with Liquids Using Photoelectron Energy-Loss Spectra

Hamaker interaction energies and cutoff distances have been calculated for disordered carbon films, in contact with purely dispersive (diiodomethane) or polar (water) liquids, using their experimental dielectric functions ε (q, ω) obtained over a broad energy range. In contrast with previous works, a q-averaged <ε (q, ω) >  _q is derived from photoelectron energy-loss spectroscopy (XPS-PEELS) where the energy loss function (ELF) < Im[?1/ε (q, ω)] >  _q is a weighted average over allowed transferred wave vector values, q, given by the physics of bulk plasmon excitation. For microcrystalline diamond and amorphous carbon films with a wide range of (sp³/sp² + sp³) hybridization, non-retarded Hamaker energies, A ₁₃₂ (L < 1 nm), were calculated in several configurations, and distance and wavenumber cutoff values were then calculated based on A ₁₃₂ and the dispersive work of adhesion obtained from contact angles. A geometric average approximation, H _0?CVL ?=?(H _0?CVC H _0?LVL )^1/2, holds for the cutoff separation distances obtained for carbon-vacuum-liquid (CVL), carbon-vacuum-carbon (CVC) and liquid-vacuum-liquid (LVL) equilibrium configurations. The linear dependence found for A _CVL, A _CLC and A _CLV values as a function of A _CVC, for each liquid, allows predictive relationships for Hamaker energies (in any configuration) using experimental determination of the dispersive component of the surface tension, \( {\gamma}_{CV}^d \), and a guess value of the cutoff distance H _0?CVC of the solid.

Open image in new window

Graphical Abstract

     

Faciliation of Mandarin tone perception by visual speech in clear and degraded audio: implications for cochlear implants

Cochlear implant (CI) users in tone language environments report great difficulty in perceiving lexical tone. This study investigated the augmentation of simulated cochlear implant audio by visual (facial) speech information for tone. Native speakers of Mandarin and Australian English were asked to discriminate between minimal pairs of Mandarin tones in five conditions: Auditory-Only, Auditory-Visual, CI-simulated Auditory-Only, CI-simulated Auditory-Visual, and Visual-Only (silent video). Discrimination in CI-simulated audio conditions was poor compared with normal audio, and varied according to tone pair, with tone pairs with strong non-F0 cues discriminated the most easily. The availability of visual speech information also improved discrimination in the CI-simulated audio conditions, particularly on tone pairs with strong durational cues. In the silent Visual-Only condition, both Mandarin and Australian English speakers discriminated tones above chance levels. Interestingly, tone-nai?ve listeners outperformed native listeners in the Visual-Only condition, suggesting firstly that visual speech information for tone is available, and may in fact be under-used by normal-hearing tone language perceivers, and secondly that the perception of such information may be language-general, rather than the product of language-specific learning. This may find application in the development of methods to improve tone perception in CI users in tone language environments.     

In-situ laser material process monitoring using a cladding power detection technique

Progress in laser material processing may require real-time monitoring and process control for consistent quality and productivity. We report a method of in-situ monitoring of laser metal cutting and drilling using cladding power monitoring of an optical fibre beam delivery system—a technique which detects the light reflected or scattered from the workpiece. The light signal carries information about the quality of the process. Experiments involving drilling and cutting of two samples, a thin aluminum foil and a 2-mm thick stainless steel plate, confirmed the effectiveness of this method.     

Residual Coulomb interaction fluctuations in chaotic systems: the boundary, random plane waves, and semiclassical theory

New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. The dominant features come from the region near the boundary where there is an interplay between Friedel oscillations and fluctuations in the eigenstates. Quite naturally, the fluctuation scale is significantly enhanced for Neumann boundary conditions as compared to Dirichlet. Elements missing from random plane wave modeling of chaotic eigenstates lead surprisingly to significant errors, which can be corrected within a purely semiclassical approach.