On the spectral function of the Poisson–Voronoi cells

Denote by (t)=∑_n1e^−λ_nt, t>0, the spectral function related to the Dirichlet Laplacian for the typical cell of a standard Poisson–Voronoi tessellation in . We show that the expectation E(t), t>0, is a functional of the convex hull of a standard d-dimensional Brownian bridge. This enables us to study the asymptotic behaviour of E(t), when t→0⁺,+∞. In particular, we prove that the law of the first eigenvalue λ₁ of satisfies the asymptotic relation lnP{λ₁t}−2^dω_dj_(d−2)/2^d·t^−d/2 when t→0⁺, where ω_d and j_(d−2)/2 are respectively the Lebesgue measure of the unit ball in and the first zero of the Bessel function J_(d−2)/2.     

Boundary conditions of Sturm-Liouville operators with mixed spectra

We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence constraints are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval [0,N]. These constraints are related to estimates on the measure of sets where the spectral density is positive.     

复杂系统的泛系聚类方法

本文利用半等价算子ε_i和相等化算子δ_i研究了复杂系统的聚类问题;阐述了分析运筹复杂系统的δ(1,3)解耦原理、对偶转化原理和大系统分解原理;详细讨论了复杂系统的连通性与解耦性并提供了有关定理.最后,利用泛系聚类方法讨论了复杂系统的层次分析.     

Objective acoustic voice-quality parameters in the computer phonetogram

A phonetogram is a plot of the dynamic range of the voice as a function of fundamental frequency. Traditionally, the phonetogram only records the sound-pressure level (SPL) of the threshold of phonation and the upper limit in SPL the voice can reach with sustained phonation as a function of the fundamental frequency (F₀). In this study, the phonetogram is extended by including acoustic voice-quality parameters. Three additional parameters are tested: jitter, shimmer, and crest factor. For each individual voice, the variation in the three parameters is evaluated over the entire phonetogram area. By averaging individual phonetograms, standard or norm phonetograms are obtained revealing general patterns in voice-quality variation. These patterns reflect the complex relations between F₀, SPL, and the acoustic voice-quality parameters just mentioned. Jitter and shimmer distributions over the phonetogram show that large variations in perturbation values can be expected when production conditions are altered. Highest perturbation values are found for the low F₀ and low SPL phonations. For all voices, a gradual decrease of the crest factor is found with increasing F₀, reflecting the degrading of spectral complexity with F₀. The crest-factor parameter can also be used to mark those areas in the phonetogram where the fundamental dominates the waveform and where flow control is the main SPL regulating mechanism in voice production. The strong quality variations within the phonetogram stress the need for accurate control of F₀ and SPL in objective voice-quality measurement.     

电感耦合等离子体原子发射光谱分析中光谱干扰校正卡尔曼滤波法研究

本文利用电感耦合等离子体原子发射光谱多色仪的扫描功能,用卡尔曼滤波法对各种光谱干扰进行校正。结果表明,该法能处理各种类型光谱干扰,不需要样品基体匹配,其测定回收率明显优于在峰法和离峰法,具有简便、准确等优点。     

中国股票市场波动特性的实证研究

本文以上证综指和深成分指数的日收益率为研究对象 ,应用 GARCH、TARCH模型理论 ,进一步分析了日收益率波动的条件异方差性、非对称性 ,同时比较了两个股票市场的不同波动特征     

Mbekhta's subspaces and a spectral theory of compact operators

Let be an operator on an infinite-dimensional complex Banach space. By means of Mbekhta's subspaces and , we give a spectral theory of compact operators. The main results are: Let be compact. . The following assertions are all equivalent: (1) 0 is an isolated point in the spectrum of (2) is closed; (3) is of finite dimension; (4) is closed; (5) is of finite dimension; . sufficient conditions for to be an isolated point in ; . sufficient and necessary conditions for to be a pole of the resolvent of .

     

On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.

     

On the spectral sequence constructors of Guichardet and Stefan

The concept of a spectral sequence constructor is generalised to Hopf Galois extensions. The spectral sequence constructions that are given by Guichardet for crossed product algebras are also generalised and shown to provide examples. It is shown that all spectral sequence constructors for Hopf Galois extensions construct the same spectral sequence.