布尔矩阵维数的缺断区间(英)

本文证明了n维布尔矩阵维数的一个新的缺断区间为这一结果扩充了一些已知的结论．     

光致折射效应中空间电荷场建立过程的研究

本文推导了包含自衍射及非线性吸收影响、用以描述空间电荷场建立过程的微分方程组,阐明了周期性的空间电荷场与光强干涉条纹之间的相位差在建立过程中所起的作用,并推导了描述条纹倾斜和弯曲的微分方程。通过数值计算找到了硅酸铋(BSO)晶体中能量转移的规律,讨论了材料特性对过程快慢的影响,提出了用CW激光来探讨瞬态过程快慢的可能性。     

Numerical analysis of a model of cure process for composites

We consider a composite material composed of fibres included in a resin which becomes solid when it is heated up (reaction of reticulation). The mathematical modelling of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. In this paper, we are interested in the computation of approximate solutions. We propose a family of discretized problems depending on two parameters (β₁, β₂) ε [0, 1]² which split the linear and non‐ linear terms in implicit and explicit parts. We prove the stability and convergence of the discretization for any (β₁, β₂) ε [½, 1 ] × [0, 1]. We present also some numerical results. Copyright © 2006 John Wiley & Sons, Ltd.     

Semi-classical limit of the bottom of spectrum of a Schrödinger operator on a path space over a compact Riemannian manifold

We determine the limit of the bottom of spectrum of Schrödinger operators with variable coefficients on Wiener spaces and path spaces over finite-dimensional compact Riemannian manifolds in the semi-classical limit. These are extensions of the results in [S. Aida, Semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space, J. Funct. Anal. 203 (2) (2003) 401-424]. The problem on path spaces over Riemannian manifolds is considered as a problem on Wiener spaces by using Ito's map. However the coefficient operator is not a bounded linear operator and the dependence on the path is not continuous in the uniform convergence topology if the Riemannian curvature tensor on the underling manifold is not equal to 0. The difficulties are solved by using unitary transformations of the Schrödinger operators by approximate ground state functions and estimates in the rough path analysis.     

Volume of Domains in Symmetric Spaces

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.     

Analysis of the characteristics of a two-fiber sensor for monitorship of a turbid medium

Summary Certain characteristics of a two-fiber sensor device, of the type proposed by Papaet al. for sea water turbidity monitorship, are examined. The extension of medium from which most of the received backscattered power originates is investigated, together with possible effects of multiple scattering on the received power. Laboratory measurements testing the results of the analysis are reported.

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Riassunto Sono esaminate alcune caratteristiche di un sensore a due fibre, del tipo di quello proposto da Papaet al. per il monitoraggio della torbidità dell'acqua di mare. è stata studiata l'estensione della zona del mezzo da cui proviene la maggior parte della radiazione retrodiffusa ricevuta. Sono stati considerati effetti di diffusione multipla. I risultati dell'analisi sono stati controllati con misure in laboratorio.

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Резюме Исследуются некоторые характеристики дву-qh-нитевого датчика, предложенного Папа и др. для мониторирования мутности морской воды. Исследуется расширение зоны в среде, из которой формируется основная часть рассеянного назад излучения. Также рассматриваются эффекты многократного рассеяния. На основе лабораторных измерений проводится проверка результатов анализа.

     

De Sitter空间中具有常均曲率的类空超曲面（Ⅱ）

设Ｍ＾ｎ是Ｄｅ Ｓｉｔｔｅｒ空间Ｓ１＾ｎ＋１中具有常数平均曲率且第二基本形式长度的平方为常数的完备类空超曲面，若Ｓ≤２（ｎ－１）＾１／２，则Ｍ＾ｎ是等参超曲面。     

On the Spectral Multiplicity of Some Volterra Operators in Sobolev Spaces

Mathematical Notes -     

AN ENCOMPASSING APPROACH TO MODELING FISHERY DYNAMICS: MODELING DYNAMIC NONLINEAR SYSTEMS

Uncertainty about the nature and significance of nonlinearities and the manner in which dynamics affect future realizations makes model specification the most difficult aspect of modeling dynamic systems. By interpreting several popular fishery models as subcases of a nesting dynamic Taylor series approximation, we isolate the specification differences between these models in a way that accounts for commonalities. On the argument that the differences due to alternative nonlinear forms are likely to be small compared to more mundane considerations such as delay difference and general dynamic lag specification, we propose an alternative model that uses the terms from the first order approximation common to all models combined with a data-based determination of the appropriate lags using the methods of state space time series analysis. Finally, the success of the alternative models is judged in an application to Pacific halibut data.